@article{Abdullaev1995,
author = {Abdullaev, F. Kh. and Darmanyan, S. A. and Djumaev, M. R. and Majid, A. J. and S{\o}rensen, M. P.},
doi = {10.1103/PhysRevE.52.3577},
issn = {1063651X},
journal = {Phys. Rev. E},
number = {4},
pages = {3577--3583},
title = {{Evolution of randomly perturbed Korteweg-de Vries solitons}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.52.3577},
volume = {52},
year = {1995}
}
@article{Abdulloev1976,
author = {Abdulloev, K. O. and Bogolubsky, I. L. and Makhankov, V. G.},
journal = {Phys. Lett.},
pages = {1976},
title = {{One more example of inelastic soliton interaction}},
volume = {56A},
year = {1976}
}
@article{Ablowitz2013,
abstract = {The long-time asymptotic solution of the Korteweg-de Vries equation for general, step-like initial data is analyzed. Each sub-step in well-separated, multi-step data forms its own single dispersive shock wave (DSW); at intermediate times these DSWs interact and develop multiphase dynamics. Using the inverse scattering transform and matched-asymptotic analysis it is shown that the DSWs merge to form a single-phase DSW, which is the ‘largest’ one possible for the boundary data. This is similar to interacting viscous shock waves (VSW) that are modeled with Burgersʼ equation, where only the single, largest-possible VSW remains after a long time.},
author = {Ablowitz, M. J. and Baldwin, D. E.},
doi = {10.1016/j.physleta.2012.12.040},
issn = {03759601},
journal = {Phys. Lett. A},
keywords = {Asymptotic methods,KdV equation,Nonlinear phenomena,Shock wave interactions,Shock waves,Solitons},
month = {feb},
number = {7},
pages = {555--559},
title = {{Interactions and asymptotics of dispersive shock waves - Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S037596011300011X},
volume = {377},
year = {2013}
}
@article{Ablowitz1974,
abstract = {Certain classes of evolution equations are defined which can be solved by the method of inverse scattering. A central point of the method is that given a dispersion relation omega(k) mereomorphic, and real for real k, there is a nonlinear evolution equation whose linearized version has this dispersion relation and for which appropriate initial value problems can be solved exactly. The relationship between scattering theory and Backlund transformations is brought out. The method has many features in common with the method of Fourier transforms and can be considered an extension of Fourier analysis to nonlinear problems.},
author = {Ablowitz, M. J. and Kaup, D. J. and Newell, A. C. and Segur, H.},
journal = {Stud. Appl. Math.},
pages = {249--315},
title = {{The inverse scattering transform-Fourier analysis for nonlinear problems}},
volume = {53},
year = {1974}
}
@book{Ablowitz1981,
author = {Ablowitz, M. J. and Segur, H.},
isbn = {978-0898714777},
pages = {435},
publisher = {Society for Industrial {\&} Applied Mathematics},
title = {{Solitons and the Inverse Scattering Transform}},
year = {1981}
}
@article{Ablowitz1979,
abstract = {We consider the evolution of packets of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions. Two separate models are discussed, depending on whether or not the waves are long in comparison with the fluid depth. These models are two-dimensional generalizations of the Korteweg-de Vries equation (for long waves) and the cubic nonlinear Schr{\"{o}}dinger equation (for short waves). In either case, we find that the two-dimensional evolution of the wave packets depends fundamentally on the dimensionless surface tension and fluid depth. In particular, for the long waves, one-dimensional (KdV) solitons become unstable with respect to even longer transverse perturbations when the surface-tension parameter becomes large enough, i.e. in very thin sheets of water. Two-dimensional long waves (‘lumps’) that decay algebraically in all horizontal directions and interact like solitons exist only when the one-dimensional solitons are found to be unstable. The most dramatic consequence of surface tension and depth, however, occurs for capillary-type waves in sufficiently deep water. Here a packet of waves that are everywhere small (but not infinitesimal) and modulated in both horizontal dimensions can ‘focus’ in a finite time, producing a region in which the wave amplitudes are finite. This nonlinear instability should be stronger and more apparent than the linear instabilities examined to date; it should be readily observable. Another feature of the evolution of short wave packets in two dimensions is that all one-dimensional solitons are unstable with respect to long transverse perturbations. Finally, we identify some exact similarity solutions to the evolution equations.},
author = {Ablowitz, M. J. and Segur, H.},
doi = {10.1017/S0022112079000835},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {691--715},
title = {{On the evolution of packets of water waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112079000835},
volume = {92},
year = {1979}
}
@book{Abraham1988,
abstract = {The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.},
address = {New York},
author = {Abraham, R. and Marsden, J. E. and Ratiu, T.},
doi = {10.1007/978-1-4612-1029-0},
isbn = {978-1-4612-6990-8},
keywords = {Analysis - Applications - Geometry {\&} Topology,Mathematical {\&} Computational Physics},
number = {March 2007},
pages = {656},
publisher = {Springer-Verlag},
title = {{Manifolds, Tensor Analysis, and Applications}},
url = {http://link.springer.com/10.1007/978-1-4612-1029-0},
volume = {75},
year = {1988}
}
@book{Abramowitz1965,
author = {Abramowitz, M. and Stegun, I. A.},
editor = {Abramowitz, M and Stegun, I A},
pages = {1046},
publisher = {Dover Publications},
title = {{Handbook of Mathematical Functions}},
year = {1972}
}
@book{Abrashkin2006,
address = {Moscow},
author = {Abrashkin, A. A. and Yakubovich, E. I.},
isbn = {5-9221-0725-9},
pages = {176},
publisher = {Fizmatlit},
title = {{Vortex dynamics in Lagrangian description}},
year = {2006}
}
@article{Adames2008,
author = {Adames, N. and Leiva, H. and Sanchez, J.},
journal = {Divulgaciones Matematicas},
number = {1},
pages = {29--37},
title = {{Controllability of the Benjamin-Bona-Mahony Equation}},
volume = {16},
year = {2008}
}
@article{Agnon1988,
author = {Agnon, Y. and Mei, C. C.},
doi = {10.1017/S0022112088002381},
journal = {J. Fluid Mech},
pages = {201--221},
title = {{Trapping and resonance of long shelf waves due to groups of short waves}},
volume = {195},
year = {1988}
}
@techreport{Ahrens1981,
address = {FT. Belvoir, VA},
author = {Ahrens, J. P.},
institution = {CETA No. 81-17. U.S. Army Corps of Engineers, Coastal Engineering Research Center},
title = {{Irregular wave runup on smooth slope}},
year = {1981}
}
@article{Airy1845,
author = {Airy, G. B.},
journal = {Philos. Trans. R. Soc. London},
pages = {1--124},
title = {{On the laws of the tides on the coasts of Ireland, as inferred from an extensive series of observations made in connexion with the Ordnance Survey of Ireland}},
year = {1845}
}
@incollection{Aizinger2011,
address = {Berlin},
author = {Aizinger, V.},
booktitle = {Computational Science and High Performance Computing IV},
editor = {Krause, E. and Shokin, Yu. and Resch, M. and Kr{\"{o}}ner, D. and Shokina, N.},
pages = {207--217},
publisher = {Springer},
title = {{A geometry independent slope limiter for the discontinuous Galerkin method}},
year = {2011}
}
@article{Aizinger2013,
author = {Aizinger, V. and Proft, J. and Dawson, C. and Pothina, D. and Negusse, S.},
journal = {Ocean Dynamics},
number = {1},
pages = {89--113},
title = {{A three-dimensional discontinuous Galerkin model applied to the baroclinic simulation of Corpus Christi Bay}},
volume = {63},
year = {2013}
}
@book{Akhmediev1997,
author = {Akhmediev, N. N. and Ankiewicz, A.},
publisher = {Chapman {\&} Hall, London},
title = {{Solitons. Nonlinear Pulses and Beams}},
year = {1997}
}
@book{Aki2002,
abstract = {Updated throughout, the new edition of Aki and Richards's classic text systematically explains key concepts in seismology. The book provides a unified treatment of seismological methods that will be of benefit to advanced students, seismologists, and scientists and engineers working in peripheral areas of seismology.},
author = {Aki, K. and Richards, P. G.},
publisher = {University Science Books},
title = {{Quantitative Seismology}},
year = {2002}
}
@article{Akiyama1999,
author = {Akiyama, J. and Ura, M.},
journal = {Journal of Hydraulic Engineering},
pages = {474--480},
title = {{Motion of 2D buoyant clouds downslope}},
volume = {125},
year = {1999}
}
@article{Akylas1989,
author = {Akylas, T. R.},
journal = {J. Fluid Mech},
pages = {387--397},
title = {{Higher-order modulation effects on solitary wave envelopes in deep water}},
volume = {198},
year = {1989}
}
@article{Al-Salem2006,
author = {Al-Salem, K. and Al-Nassar, W. and Tayfun, M. A.},
journal = {Ocean Engineering},
pages = {788--797},
title = {{Risk analysis for capsizing of small vessels}},
volume = {33},
year = {2006}
}
@book{Alalykin1970,
address = {Moscow},
author = {Alalykin, G. B. and Godunov, S. K. and Kireyeva, L. L. and Pliner, L. A.},
pages = {110},
publisher = {Nauka},
title = {{Solution of One-Dimensional Problems in Gas Dynamics on Moving Grids}},
year = {1970}
}
@article{Alavian1986,
abstract = {Investigation of the behavior of salt solution released down a sloping surface in a tank of freshwater is reported here. Analysis indicates that the dense layer spreads in all directions at a rate proportional to the entrainment coefficient. Observations and measurements revealed a variety of phenomena depending strongly on the buoyancy flux, Richardson number, and the angle of incline. At small slope (approx. less than 1/10) flow was found to be subcritical with negligible entrainment. As the slope increases, flow becomes supercritical and periodic interfacial instabilities appear. Growth and subsequent breakup of these instabilities were found to be the main mechanism for entrainment. Mean layer velocity away from the source can be estimated from the initial conditions and the angle of incline.},
author = {Alavian, V.},
issn = {07339429},
journal = {Journal of Hydraulic Engineering},
keywords = {flow fluids testing,flow water,fluids physical properties},
number = {1},
pages = {27--42},
title = {{Behavior of density currents on an incline}},
volume = {112},
year = {1986}
}
@article{Alcrudo2005,
author = {Alcrudo, F. and Garcia-Navarro, P.},
doi = {10.1002/fld.1650160604},
journal = {Int. J. Numer. Methods Fluids},
pages = {489--505},
title = {{A high-resolution Godunov-type scheme in finite volumes for the 2D shallow-water equations}},
volume = {16(6)},
year = {1993}
}
@book{Aleksandrov1936,
address = {Moscow},
author = {Aleksandrov, P. S. and Efremovich, V. A.},
pages = {97},
publisher = {ONTI - NKTP USSR},
title = {{Outline of the main notions of topology}},
year = {1936}
}
@inbook{aleksgus,
annote = {in Russian},
author = {Alekseev, A. S. and Gusyakov, V. K.},
chapter = {Numerical},
pages = {194--197},
publisher = {Moscow-Erevan},
title = {{Theory of diffraction and wave propagation}},
volume = {2},
year = {1973}
}
@article{Alexander1997,
abstract = {Pulse stability is crucial to the effective propagation of information in a soliton-based optical communication system. It is shown in this paper that pulses in optical fibers, for which attenuation is compensated by phase-sensitive amplifiers, are stable over a large range of parameter values. A fourth-order nonlinear diffusion model due to Kutz and co-workers is used. The stability proof invokes a number of mathematical techniques, including the Evans function and Grillakis' functional analytic approach.},
author = {Alexander, J. C. and Grillakis, M. G. and Jones, C. K. R. T. and Sandstede, B.},
doi = {10.1007/PL00001473},
issn = {0044-2275},
journal = {Zeitschrift f{\"{u}}r angewandte Mathematik und Physik},
keywords = {Key words. Solitons,nonlinear optical pulse propagation,optical fibers,stability},
month = {mar},
number = {2},
pages = {175--192},
title = {{Stability of pulses on optical fibers with phase-sensitive amplifiers}},
url = {http://link.springer.com/10.1007/PL00001473},
volume = {48},
year = {1997}
}
@article{Alfonsi2009,
abstract = {The approach of Reynolds-averaged NavierStokes equations (RANS) for the modeling of turbulent flows is reviewed. The subject is mainly considered in the limit of incompressible flows with constant properties. After the introduction of the concept of Reynolds decomposition and averaging, different classes of RANS turbulence models are presented, and, in particular, zero-equation models, one-equation models (besides a half-equation model), two-equation models (with reference to the tensor representation used for a model, both linear and nonlinear models are considered), stress-equation models (with reference to the pressure-strain correlation, both linear and nonlinear models are considered) and algebraic-stress models. For each of the abovementioned class of models, the most widely-used modeling techniques and closures are reported. The unsteady RANS approach is also discussed and a section is devoted to hybrid RANS/large methods.},
author = {Alfonsi, G.},
doi = {10.1115/1.3124648},
issn = {00036900},
journal = {Applied Mechanics Reviews},
number = {4},
pages = {40802},
publisher = {ASME},
title = {{Reynolds-Averaged Navier-Stokes Equations for Turbulence Modeling}},
url = {http://link.aip.org/link/AMREAD/v62/i4/p040802/s1{\&}Agg=doi},
volume = {62},
year = {2009}
}
@article{Aliev2007,
author = {Aliev, A. V. and Tarnavsky, G. A.},
journal = {Sib. Electr. Math. Rep.},
pages = {376--434},
title = {{The hierarchical SPH-method for mathematical simulation in gravitational gas dynamics}},
volume = {4},
year = {2007}
}
@article{Allaire2002,
author = {Allaire, G. and Clerc, S. and Kokh, S.},
journal = {J. Comput. Phys.},
pages = {577--616},
title = {{A five-equation model for the simulation of interfaces between compressible fluids}},
volume = {181},
year = {2002}
}
@book{Allouche2003,
abstract = {Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.},
author = {Allouche, J.-P. and Shallit, J. O.},
isbn = {9780521823326},
pages = {588},
publisher = {Cambridge University Press},
title = {{Automatic Sequences - Theory, Applications, Generalizations}},
year = {2003}
}
@techreport{Alouges1999,
author = {Alouges, F. and Ghidaglia, J.-M. and Tajchman, M.},
institution = {Centre de Math�matiques et Leurs Applications},
title = {{On the interaction between upwinding and forcing for hyperbolic systems of conservation laws}},
year = {1999}
}
@article{Alvarez2014a,
abstract = {A family of fixed-point iterations is proposed for the numerical computation of traveling waves and localized ground states. The methods are extended versions of Petviashvili type, and they are applicable when the nonlinear term of the system contains homogeneous functions of different degree. The methods are described and applied to several examples of interest, that calibrate their efficiency.},
author = {{\'{A}}lvarez, J. and Dur{\'{a}}n, A.},
doi = {10.1016/j.cnsns.2013.12.004},
issn = {10075704},
journal = {Comm. Nonlin. Sci. Num. Sim.},
keywords = {Ground state generation,Iterative methods for nonlinear systems,Petviashvili type methods,Solitary wave generation},
month = {jul},
number = {7},
pages = {2272--2283},
title = {{An extended Petviashvili method for the numerical generation of traveling and localized waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1007570413005698},
volume = {19},
year = {2014}
}
@article{Alvarez2014,
abstract = {In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems. Conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out.},
author = {{\'{A}}lvarez, J. and Dur{\'{a}}n, A.},
doi = {10.1016/j.cam.2014.01.015},
issn = {03770427},
journal = {Journal of Computational and Applied Mathematics},
keywords = {Iterative methods for nonlinear systems,Orbital convergence,Petviashvili type methods,Traveling wave generation},
month = {aug},
pages = {39--51},
title = {{Petviashvili type methods for traveling wave computations: I. Analysis of convergence}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377042714000363},
volume = {266},
year = {2014}
}
@article{Alvarez2015,
abstract = {An error in Lemma 2 in the paper entitled above is mentioned and corrected here.},
author = {{\'{A}}lvarez, J. and Dur{\'{a}}n, A.},
doi = {10.1016/j.cam.2014.01.015},
issn = {03770427},
journal = {J. Comp. Appl. Math.},
keywords = {Iterative methods for nonlinear systems,Orbital convergence,Petviashvili type methods,Traveling wave generation},
number = {03},
pages = {215--216},
title = {{Corrigendum to "Petviashvili type methods for traveling wave computations: I. Analysis of convergence [J. Comput. Appl. Math. 266 (2014) 39-51]"}},
volume = {277},
year = {2015}
}
@article{Amadori2006,
author = {Amadori, D.},
journal = {Asymptotic Anal.},
number = {1},
pages = {53----79},
title = {{On the homogenization of conservation laws with resonant oscillatory source}},
volume = {46},
year = {2006}
}
@article{Amadori2013,
author = {Amadori, D. and Gosse, L.},
doi = {10.1016/j.jde.2013.04.016},
issn = {00220396},
journal = {J. Diff. Eqns.},
month = {aug},
number = {3},
pages = {469--502},
title = {{Transient L1 error estimates for well-balanced schemes on non-resonant scalar balance laws}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039613001472},
volume = {255},
year = {2013}
}
@article{Amadori2015,
author = {Amadori, D. and Gosse, L.},
doi = {10.1016/j.anihpc.2015.01.001},
issn = {02941449},
journal = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
month = {jan},
title = {{Stringent error estimates for one-dimensional, space-dependent 2x2 relaxation systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0294144915000037},
volume = {In Press},
year = {2015}
}
@article{Amadori2004,
author = {Amadori, D. and Gosse, L. and Guerra, G.},
doi = {10.1016/j.jde.2003.10.004},
issn = {00220396},
journal = {J. Diff. Eqns.},
month = {apr},
number = {2},
pages = {233--274},
title = {{Godunov-type approximation for a general resonant balance law with large data}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039603002912},
volume = {198},
year = {2004}
}
@techreport{Amante2009,
author = {Amante, C. and Eakins, B. W.},
institution = {NOAA Technical Memorandum},
month = {mar},
number = {NESDIS NGDC-24},
title = {{ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis}},
year = {2009}
}
@article{Am,
author = {Amick, C. J.},
journal = {J. Diff. Eqns.},
pages = {231--247},
title = {{Regularity and uniqueness of solutions to the Boussinesq system of equations}},
volume = {54},
year = {1984}
}
@article{Amick1989,
abstract = {We study the large-time behaviour of solutions to the initial-value problem for the Korteweg-de Vries equation and for the regularized long-wave equation, with a dissipative term appended. Using energy estimates, a maximum principle, and a transformation of Cole-Hopf type, sharp rates of temporal decay of certain norms of the solution are obtained.},
author = {Amick, C. J. and Bona, J. L. and Schonbek, M. E.},
doi = {10.1016/0022-0396(89)90176-9},
issn = {00220396},
journal = {J. Diff. Eqns.},
month = {sep},
number = {1},
pages = {1--49},
title = {{Decay of solutions of some nonlinear wave equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0022039689901769},
volume = {81},
year = {1989}
}
@article{Amick1987,
abstract = {The algorithm proposed by Schwartz {\&} Whitney (J. Fluid Mech. 107, 147-171 (1981)) for the numerical calculation of formal power series solutions of the classical standing-wave problem is vindicated by a rigorous proof that resonances do not occur in the calculations. A detailed account of a successful algorithm is given. The analytical question of the convergence of the power series whose coefficients have been calculated remains open. An affirmative answer would be a first demonstration of the existence of standing waves on deep water.},
author = {Amick, C. J. and Toland, J.},
journal = {Proc. Roy. Soc. Lon. A},
pages = {123--137},
title = {{The semianalytic theory of standing waves}},
volume = {411(1840)},
year = {1987}
}
@article{Ammon2005,
author = {Ammon, C. J. and Ji, C. and Thio, H.-K. and Robinson, D. I. and Ni, S. and Hjorleifsdottir, V. and Kanamori, H. and Lay, T. and Das, S. and Helmberger, D. and Ichinose, G. and Polet, J. and Wald, D.},
journal = {Science},
pages = {1133--1139},
title = {{Rupture process of the 2004 Sumatra-Andaman earthquake}},
volume = {308},
year = {2005}
}
@article{Ammon2006,
author = {Ammon, C. J. and Kanamori, H. and Lay, T. and Velasco, A. A.},
journal = {Geophysical Research Letters},
pages = {L24308},
title = {{The 17 July 2006 Java tsunami earthquake}},
volume = {33},
year = {2006}
}
@article{Anastasiou1999,
author = {Anastasiou, K. and Chan, C. T.},
journal = {International Journal for Numerical Methods in Fluids},
pages = {1225--1245},
title = {{Solution of the 2D shallow water equations using the finite volume method on unstructured triangular meshes}},
volume = {24},
year = {1999}
}
@inbook{Ancey2001,
abstract = {Over the last century, mountain ranges in Europe and North America have seen substantial development due to the increase in recreational activities, transportation, construction in high altitude areas, etc. In these mountain ranges, avalanches often threaten man's activities and life. Typical examples include recent disasters, such as the avalanche at Val d'Is{\`{e}}re in 1970 (39 people were killed in a hostel) or the series of catastrophic avalanches throughout the Northern Alps in February 1999 (62 residents killed). The rising demand for higher safety measures has given new impetus to the development of mitigation technology and has given rise to a new scientific area entirely devoted to snow and avalanches. This paper summarises the paramount features of avalanches (formation and motion) and outlines the main approaches used for describing their movement. We do not tackle specific problems related to snow mechanics and avalanche forecasting. For more information on the subject, the reader is referred to the main textbooks published in Alpine countries [1-8].},
author = {Ancey, C.},
chapter = {Snow Avala},
editor = {Balmforth, N J and Provenzale, A},
pages = {319--338},
publisher = {Springer},
title = {{Geomorphological Fluid Mechanics}},
volume = {582},
year = {2001}
}
@techreport{Ancey2003,
author = {Ancey, C.},
institution = {Ecole Polytechnique F�d�rale de Lausanne, Environmental Hydraulics Laboratory},
title = {{Influence of particle entrainment from bed on the powder-snow avalanche dynamics}},
year = {2003}
}
@article{Ancey2004,
author = {Ancey, C.},
doi = {10.1029/2003JF000052},
journal = {J. Geophys. Res.},
pages = {F01005},
title = {{Powder snow avalanches: Approximation as non-Boussinesq clouds with a Richardson number-dependent entrainment function}},
volume = {109},
year = {2004}
}
@book{Ancey2006,
author = {Ancey, C. and Bain, V. and Bardou, E. and Borrel, G. and Burnet, R. and Jarry, F. and Kolbl, O. and Meunier, M.},
publisher = {Presses polytechniques et universitaires romandes (Lausanne, Suisse)},
title = {{Dynamique des avalanches}},
year = {2006}
}
@article{Ancey2007,
author = {Ancey, C. and Cochard, S. and Rentschler, M. and Wiederseiner, S.},
journal = {Physica D},
pages = {32--54},
title = {{Existence and features of similarity solutions for non-Boussinesq gravity currents}},
volume = {226},
year = {2007}
}
@article{Ancey2006a,
author = {Ancey, C. and Cochard, S. and Rentschler, M. and Wiederseiner, S.},
journal = {Water Resources Research},
pages = {W08424},
title = {{Front dynamics of supercritical non-Boussinesq gravity currents}},
volume = {42},
year = {2006}
}
@article{Ancey2004a,
author = {Ancey, C. and Meunier, M.},
journal = {J. Geophys. Res.},
pages = {F01004},
title = {{Estimating bulk rheological properties of flowing snow avalanches from field data}},
volume = {109},
year = {2004}
}
@article{Anderson1998,
abstract = {We review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. These models have been applied successfully to situations in which the physical phenomena of interest have a length scale commensurate with the thickness of the interfacial region (e.g. near-critical interfacial phenomena or small-scale flows such as those occurring near contact lines) and fluid flows involving large interface deformations and/or topological changes (e.g. breakup and coalescence events associated with fluid jets, droplets, and large-deformation waves). We discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, we address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, computational approaches to describe interfacial phenomena, and models of fully miscible fluids.},
author = {Anderson, D. M. and McFadden, G. B. and Wheeler, A. A.},
doi = {doi:10.1146/annurev.fluid.30.1.139},
journal = {Ann. Rev. Fluid Mech.},
pages = {139--165},
title = {{Diffuse-interface methods in fluid mechanics}},
volume = {30},
year = {1998}
}
@article{Ankiewicz2009,
abstract = {We study the effect of various perturbations on the fundamental rational solution of the nonlinear Schr{\"{o}}dinger equation (NLSE). This solution describes generic nonlinear wave phenomena in the deep ocean, including the notorious rogue waves. It also describes light pulses in optical fibres. We find that the solution can survive at least three types of perturbations that are often used in the physics of nonlinear waves. We show that the rational solution remains rational and localized in each direction, thus representing a modified rogue wave.},
author = {Ankiewicz, A. and Devine, N. and Akhmediev, N.},
journal = {Physics Letters A},
pages = {3997--4000},
title = {{Are rogue waves robust against perturbations?}},
volume = {373},
year = {2009}
}
@article{Ankiewicz2014,
abstract = {We consider an extended nonlinear Schr{\"{o}}dinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.},
author = {Ankiewicz, A. and Wang, Y. and Wabnitz, S. and Akhmediev, N.},
doi = {10.1103/PhysRevE.89.012907},
issn = {1539-3755},
journal = {Phys. Rev. E},
month = {jan},
number = {1},
pages = {012907},
title = {{Extended nonlinear Schr{\"{o}}dinger equation with higher-order odd and even terms and its rogue wave solutions}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.89.012907},
volume = {89},
year = {2014}
}
@article{Annenkov2006a,
abstract = {We present the results of direct numerical simulations (DNS) of the evolution of nonlinear random water wave fields. The aim of the work is to validate the hypotheses underlying the statistical theory of nonlinear dispersive waves and to clarify the role of exactly resonant, nearly resonant and non-resonant wave interactions. These basic questions are addressed by examining relatively simple wave systems consisting of a finite number of wave packets localized in Fourier space. For simulation of the long-term evolution of random water wave fields we employ an efficient DNS approach based on the integrodifferential Zakharov equation. The non-resonant cubic terms in the Hamiltonian are excluded by the canonical transformation. The proposed approach does not use a regular grid of harmonics in Fourier space. Instead, wave packets are represented by clusters of discrete Fourier harmonics.},
author = {Annenkov, S. Yu. and Shrira, V. I.},
doi = {10.1017/S0022112006000632},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {aug},
pages = {181--207},
title = {{Role of non-resonant interactions in the evolution of nonlinear random water wave fields}},
volume = {561},
year = {2006}
}
@article{Annenkov2006,
abstract = {By means of direct numerical simulations (DNS) based on the integrodifferential Zakharov equation, we study the long-term evolution of nonlinear random water wave fields. For the first time, formation of powerlike Kolmogorov-type spectra corresponding to weak-turbulent inverse cascade is demonstrated by DNS, and the evolution in time of the resulting spectra is quantitatively investigated. The predictions of the statistical theory for water waves, both qualitative (formation of the direct and inverse cascades, self-similar behavior) and quantitative (the spectra exponents, specific shape of self-similar functions, the rate of time evolution) are found to be in good agreement with the DNS results, except for the initial part of the evolution, where the established statistical theory is not applicable yet and the evolution has a much faster time scale.},
author = {Annenkov, S. Yu. and Shrira, V. I.},
institution = {Department of Mathematics, Keele University, Keele ST5 5BG, United Kingdom.},
journal = {Phys. Rev. Lett},
number = {20},
pages = {204501},
pmid = {16803176},
title = {{Direct numerical simulation of downshift and inverse cascade for water wave turbulence.}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.96.204501},
volume = {96},
year = {2006}
}
@techreport{Annunziato2005,
author = {Annunziato, A. and Best, C.},
institution = {Institute for the Protection and Security of the Citizen. Joint Research Centre. European Commission},
month = {jan},
title = {{The tsunami event analyses and models}},
year = {2005}
}
@article{AD2013,
author = {Antonopoulos, D. C. and Dougalis, V. A.},
journal = {Math. Comp.},
pages = {689--717},
title = {{Error estimates for Galerkin approximations of the ``classical'' Boussinesq system}},
volume = {82},
year = {2013}
}
@article{ADM1,
author = {Antonopoulos, D. C. and Dougalis, V. A. and Mitsotakis, D. E.},
journal = {Advances in Differential Equations},
pages = {27--53},
title = {{Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems}},
volume = {14},
year = {2009}
}
@article{Antonopoulos2010,
author = {Antonopoulos, D. C. and Dougalis, V. A. and Mitsotakis, D. E.},
journal = {Bulletin of Greek Math. Soc.},
pages = {13--30},
title = {{Galerkin approximations of the periodic solutions of Boussinesq systems}},
volume = {57},
year = {2010}
}
@article{ADM1,
author = {Antonopoulos, D. C. and Dougalis, V. A. and Mitsotakis, D. E.},
journal = {Advances in Differential Equations},
pages = {27--53},
title = {{Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems}},
volume = {14},
year = {2009}
}
@article{ADM2,
author = {Antonopoulos, D. C. and Dougalis, V. A. and Mitsotakis, D. E.},
journal = {Appl. Numer. Math.},
pages = {314--336},
title = {{Numerical solution of Boussinesq systems of the Bona-Smith family}},
volume = {30},
year = {2010}
}
@inproceedings{Antonopoulos2000,
author = {Antonopoulos, D. C. and Dougalis, V. D.},
booktitle = {Proceedings of the 5th International Conference on Mathematical and Numerical Aspects of Wave Propagation},
editor = {Bermudez, A},
pages = {265--269},
publisher = {SIAM, Philadelphia},
title = {{Numerical approximation of Boussinesq systems}},
year = {2000}
}
@article{AD3,
author = {Antonopoulos, D. C. and Dougalis, V. D.},
journal = {Math. Comp. Simul.},
pages = {984--1007},
title = {{Numerical solution of the `classical' Boussinesq system}},
volume = {82},
year = {2012}
}
@book{Antonsev1990,
author = {Antonsev, S. N. and Kazhikov, A. V. and Monakov, V. N.},
publisher = {North-Holland},
title = {{Boundary Value Problems in Mechanics of Nonhomogeneous Fluids}},
year = {1990}
}
@article{AntunesDoCarmo2013,
abstract = {The classical Boussinesq equations only incorporate weak dispersion and weak nonlinearity, and are valid only for long waves in shallow waters. The classical Serre equations (or Green and Naghdi) are fully-nonlinear and weakly dispersive. Thus, as for the classical Boussinesq models, Serre's equations are valid only for shallow water conditions. To allow applications in a greater range of depth to wavelength ratio, a new set of extended Serre equations with additional terms of dispersive origin is proposed in this work. The equations are solved using an efficient finite-difference method, which consistency and stability are tested by comparison with a closed-form solitary wave solution of these equations. It is shown that computed results agree closely with the analytical ones and test data. An equivalent form of the Boussinesq equations, also with improved linear dispersion characteristics, is solved using a numerical procedure similar to that used to solve the extended Serre equations. Numerical solutions of both approaches, in the case of waves generated by disturbances on the water surface, are compared to each other and with available data, testing different functions commonly used in modelling the generation and propagation of ship waves.},
author = {{Antunes Do Carmo}, J. S.},
doi = {10.1080/00221686.2013.814090},
issn = {0022-1686},
journal = {J. Hydr. Res.},
keywords = {Dispersion characteristics,improved Serre equations,intermediate waters,moving pressure,ship waves},
month = {dec},
number = {6},
pages = {719--727},
title = {{Boussinesq and Serre type models with improved linear dispersion characteristics: Applications}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00221686.2013.814090},
volume = {51},
year = {2013}
}
@article{Carmo2013,
author = {{Antunes Do Carmo}, J. S.},
doi = {10.2174/1874835X01306010016},
issn = {1874835X},
journal = {The Open Ocean Engineering Journal},
month = {aug},
number = {1},
pages = {16--25},
title = {{Extended Serre Equations for Applications in Intermediate Water Depths}},
url = {http://benthamscience.com/open/openaccess.php?tooej/articles/V006/16TOOEJ.htm},
volume = {6},
year = {2013}
}
@article{Antuono2010,
author = {Antuono, M. and Brocchini, M.},
journal = {J. Fluid Mech},
pages = {207--232},
title = {{Solving the nonlinear shallow-water equations in physical space}},
volume = {643},
year = {2010}
}
@article{Antuono2010a,
author = {Antuono, M. and Brocchini, M.},
doi = {10.1111/j.1467-9590.2009.00464.x},
issn = {00222526},
journal = {Studies in Applied Mathematics},
month = {jan},
number = {1},
pages = {85--103},
title = {{Analysis of the Nonlinear Shallow Water Equations Over Nonplanar Topography}},
url = {http://doi.wiley.com/10.1111/j.1467-9590.2009.00464.x},
volume = {124},
year = {2010}
}
@article{Antuono2007,
abstract = {We propose an approximate analytical solution of the boundary value problem (BVP) for the nonlinear shallow waters equations. Our work, based on the Carrier and Greenspan {\&}{\#}91; 1{\&}{\#}93; hodograph transformation, focuses on the propagation of nonlinear nonbreaking waves over a uniformly plane beach. Available results are briefly discussed with specific emphasis on the comparison between the Initial Value Problem and the BVP; the latter more completely representing the physical phenomenon of wave propagation on a beach. The solution of the BVP is achieved through a perturbation approach solely using the assumption of small waves incoming at the seaward boundary of the domain. The most significant results, i.e., the shoreline position estimation, the actual wave height and velocity at the seaward boundary, the reflected wave height and velocity at the seaward boundary are given for three specific input waves and compared with available solutions.},
author = {Antuono, M. and Brocchini, M.},
doi = {doi:10.1111/j.1365-2966.2007.00378.x},
journal = {Stud. Appl. Math.},
pages = {73--93},
title = {{The Boundary Value Problem for the Nonlinear Shallow Water Equations}},
volume = {119},
year = {2007}
}
@article{Antuono2009,
author = {Antuono, M. and Liapidevskii, V. Yu. and Brocchini, M.},
journal = {Studies in Applied Mathematics},
pages = {1--28},
title = {{Dispersive Nonlinear Shallow-Water Equations}},
volume = {122(1)},
year = {2009}
}
@article{Antuono2012,
abstract = {The behavior of the Chezy frictional term near the shoreline has been studied in detail. An asymptotic analysis valid for water depths going to zero clearly shows that the use of such a term implies a non-receding motion of the shoreline. This phenomenon is induced by a thin layer of water which, because of frictional forces, remains on the beach and keeps it wet seaward of the largest run-up. However, the influence of such a frictional layer of water on the global wave motion is very weak and practically negligible for most of the swash zone flow dynamics. The existence of a non-receding shoreline has led to some clarifications on the role of some ad-hoc tools used in numerical models for the prediction of the wet/dry interface.},
author = {Antuono, M. and Soldini, L. and Brocchini, M.},
doi = {10.1007/s00162-010-0220-8},
journal = {Theor. Comput. Fluid Dyn.},
number = {1-4},
pages = {105--116},
title = {{On the role of the Chezy frictional term near the shoreline}},
volume = {26},
year = {2012}
}
@article{Arai1980,
author = {Arai, M.},
journal = {Nucl. Sci. Eng.},
pages = {74--77},
title = {{Characteristic and stability analyses for two-phase flow equation system with viscous terms}},
volume = {74},
year = {1980}
}
@article{Arcas2012,
author = {Arcas, D. and Segur, H.},
journal = {Phil. Trans. R. Soc. A},
pages = {1505--1542},
title = {{Seismically generated tsunamis}},
volume = {370},
year = {2012}
}
@article{Archambeau2004,
author = {Archambeau, F. and Mehitoua, N. and Sakiz, M.},
journal = {International Journal On Finite Volumes},
pages = {1--62},
title = {{Code Saturne: A Finite Volume Code for the Computation of Turbulent Incompressible Flows - Industrial Applications}},
volume = {1},
year = {2004}
}
@article{Argyris1991,
abstract = {The paper presents a finite element algorithm for the numerical solution of the sine-Gordon equation in two spatial dimensions, as it arises, for example, in rectangular large-area Josephson junctions. The dispersive nonlinear partial differential equation of the system allows for soliton-type solutions, an ubiquitous phenomenon in a large variety of physical problems. A semidiscrete Galerkin approach based on simple four-noded bilinear finite elements in combination with a generalized Newmark integration scheme is used throughout the paper and is tested in a variety of cases. Comparisons with finite difference solutions show the superior performance of the proposed algorithm leading to very accurate, numerically stable and physically consistent solitary wave solutions. The results support the confidence in the present numerical model which should be capable to treat also more complex situations involving soliton-type interactions.},
author = {Argyris, J. and Haase, M. and Heinrich, J. C.},
doi = {10.1016/0045-7825(91)90136-T},
issn = {00457825},
journal = {Comput. Methods Appl. Mech. Engrg.},
month = {mar},
number = {1},
pages = {1--26},
title = {{Finite element approximation to two-dimensional sine-Gordon solitons}},
url = {http://linkinghub.elsevier.com/retrieve/pii/004578259190136T},
volume = {86},
year = {1991}
}
@article{Arnold1980,
author = {Arnold, D. N. and Winther, R.},
journal = {Mathematics of Computation},
number = {149},
pages = {23--43},
title = {{A conservative finite element method for the Korteweg-de Vries equation}},
volume = {34},
year = {1980}
}
@article{Arnold1965a,
author = {Arnold, V. I.},
journal = {C. R. Ac. Sci. Paris},
pages = {17--20},
title = {{Sur la topologie des {\'{e}}coulements stationnaires des fluides parfaits}},
volume = {261},
year = {1965}
}
@book{Arnold1996,
address = {New York},
author = {Arnold, V. I.},
pages = {351},
publisher = {Springer-Verlag},
title = {{Geometrical Methods in the Theory of Ordinary Differential Equations}},
year = {1996}
}
@article{Arnold1965,
author = {Arnold, V. I.},
journal = {C. R. Ac. Sci. Paris},
pages = {5668--5671},
title = {{Sur la courbure de Riemann des groupes de diff{\'{e}}omorphismes}},
volume = {260},
year = {1965}
}
@article{Arnold1966,
author = {Arnold, V. I.},
journal = {Ann. Inst. Fourier},
number = {1},
pages = {319--361},
title = {{Sur la g{\'{e}}ometrie diff{\'{e}}rentielle des groupes de Lie de dimension infinie et ses applications {\`{a}} l'hydrodynamique des fluides parfaits}},
volume = {16},
year = {1966}
}
@book{Arnol'd1989,
author = {Arnold, V. I.},
edition = {2nd edn},
publisher = {New York: Springer},
title = {{Mathematical methods of classical mechanics}},
year = {1989}
}
@book{Arnold1997,
abstract = {This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.},
address = {New York},
author = {Arnold, V. I.},
edition = {2nd},
isbn = {978-0387968902},
pages = {519},
publisher = {Springer},
title = {{Mathematical Methods of Classical Mechanics}},
year = {1997}
}
@article{Arnoux1991,
author = {Arnoux, P. and Rauzy, G.},
journal = {Bull. Soc. Math. France},
number = {2},
pages = {199--215},
title = {{Repr{\'{e}}sentation g{\'{e}}om{\'{e}}trique de suites de complexit{\'{e}} {\$}2n+1{\$}}},
url = {http://www.numdam.org/item?id=BSMF{\_}1991{\_}{\_}119{\_}2{\_}199{\_}0},
volume = {119},
year = {1991}
}
@article{Artiles2004,
abstract = {New nonlinear evolution equations are derived that generalize those presented in a Letter by Matsuno Phys. Rev. Lett. 69, 609 (1992) and a terrain-following Boussinesq system recently deduced by Nachbin SIAM J Appl. Math. 63, 905 (2003). The regime considers finite-amplitude surface gravity waves on a two-dimensional incompressible and inviscid fluid of, highly variable, finite depth. A Fourier-type operator is expanded in a wave steepness parameter. The novelty is that the topography can vary on a broad range of scales. It can also have a complex profile including that of a multiply valued function. The resulting evolution equations are variable coefficient Boussinesq-type equations. The formulation is over a periodically extended domain so that, as an application, it produces efficient Fourier (fast-Fourier-transform algorithm) solvers.},
author = {Artiles, W. and Nachbin, A.},
institution = {Instituto de Matem{\'{a}}tica Pura e Aplicada, Est. D Castorina 110, Jardim Bot{\^{a}}nico, Rio de Janeiro, RJ 22460-320, Brazil.},
journal = {Phys. Rev. Lett.},
number = {23},
pages = {234501},
pmid = {15601164},
title = {{Nonlinear evolution of surface gravity waves over highly variable depth.}},
volume = {93},
year = {2004}
}
@article{Arvanitis2006,
abstract = {In this work we consider finite volume schemes combined with dynamic spatial mesh redistribution. We study whether appropriate mesh redistribution is a satisfactory mechanism for increasing the resolution of numerical solutions for problems of scalar and systems of conservation laws (CL) in one space dimension, while being at the same time a stabilization mechanism for selecting the appropriate entropy solution. In order to increase the resolution around shock areas and keep the computational cost low, our redistribution policy is to reconstruct spatially the numerical solution on a new mesh, where the solution’s curvature is almost uniformly distributed, while the node’s cardinality is kept constant. We examine the stabilization properties of that redistribution process by adding it as a substep on the time evolution step of some classical schemes with known (unstable) characteristics. Testing the resulting method for several such schemes and on a large number of CL problems that have solutions with special characteristics (shocks, rarefaction areas, steady states) and comparing the results with those produced by schemes with extra stabilization mechanisms (like slope/flux limiters, entropy corrections), we conclude that indeed the proposed redistribution adds such stabilization properties while at the same time increasing the resolution.},
author = {Arvanitis, Ch. and Delis, A. I.},
doi = {10.1137/050632853},
issn = {1064-8275},
journal = {SIAM J. Sci. Comput.},
month = {jan},
number = {5},
pages = {1927--1956},
title = {{Behavior of Finite Volume Schemes for Hyperbolic Conservation Laws on Adaptive Redistributed Spatial Grids}},
volume = {28},
year = {2006}
}
@article{Arvanitis2006a,
abstract = {In this work we consider finite volume schemes combined with dynamic spatial mesh redistribution. We study whether appropriate mesh redistribution is a satisfactory mechanism for increasing the resolution of numerical solutions for problems of scalar and systems of conservation laws (CL) in one space dimension, while being at the same time a stabilization mechanism for selecting the appropriate entropy solution. In order to increase the resolution around shock areas and keep the computational cost low, our redistribution policy is to reconstruct spatially the numerical solution on a new mesh, where the solution’s curvature is almost uniformly distributed, while the node’s cardinality is kept constant. We examine the stabilization properties of that redistribution process by adding it as a substep on the time evolution step of some classical schemes with known (unstable) characteristics. Testing the resulting method for several such schemes and on a large number of CL problems that have solutions with special characteristics (shocks, rarefaction areas, steady states) and comparing the results with those produced by schemes with extra stabilization mechanisms (like slope/flux limiters, entropy corrections), we conclude that indeed the proposed redistribution adds such stabilization properties while at the same time increasing the resolution.},
author = {Arvanitis, Ch. and Delis, A. I.},
doi = {10.1137/050632853},
issn = {1064-8275},
journal = {SIAM J. Sci. Comput.},
month = {jan},
number = {5},
pages = {1927--1956},
title = {{Behavior of Finite Volume Schemes for Hyperbolic Conservation Laws on Adaptive Redistributed Spatial Grids}},
url = {http://epubs.siam.org/doi/abs/10.1137/050632853},
volume = {28},
year = {2006}
}
@article{Arvanitis2010,
abstract = {We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar problems and the system of elastodynamics.},
author = {Arvanitis, Ch. and Katsaounis, T. and Makridakis, Ch.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
number = {1},
pages = {17--33},
title = {{Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws}},
volume = {35},
year = {2010}
}
@book{ASCE2010,
author = {ASCE},
isbn = {9780784410851},
pages = {650},
publisher = {American Society of Civil Engineers},
title = {{Minimum Design Loads for Buildings and Other Structures}},
year = {2010}
}
@article{Ascher2005,
abstract = {We examine some symplectic and multisymplectic methods for the notorious Korteweg–de Vries equation, with the question whether the added structure preservation that these methods offer is key in providing high quality schemes for the long time integration of nonlinear, conservative partial differential equations. Concentrating on second order discretizations, several interesting schemes are constructed and studied. Our essential conclusions are that it is possible to design very stable, conservative difference schemes for the nonlinear, conservative KdV equation. Among the best of such schemes are methods which are symplectic or multisymplectic. Semi-explicit, symplectic schemes can be very effective in many situations. Compact box schemes are effective in ensuring that no artificial wiggles appear in the approximate solution. A family of box schemes is constructed, of which the multisymplectic box scheme is a prominent member, which are particularly stable on coarse space–time grids},
author = {Ascher, U. M. and McLachlan, R. I.},
doi = {10.1007/s10915-004-4634-6},
journal = {J. Sci. Comput.},
keywords = {Hamiltonian system,Korteweg-de Vries equation,Symplectic method,box scheme,multisymplectic method},
number = {1},
pages = {83--104},
title = {{On Symplectic and Multisymplectic Schemes for the KdV Equation}},
volume = {25},
year = {2005}
}
@article{Ascher2004,
author = {Ascher, U. M. and McLachlan, R. I.},
doi = {10.1016/j.apnum.2003.09.002},
issn = {01689274},
journal = {Applied Numerical Mathematics},
number = {3-4},
pages = {255--269},
title = {{Multisymplectic box schemes and the Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0168927403001545},
volume = {48},
year = {2004}
}
@article{Ascher1997,
author = {Ascher, U. M. and Ruuth, S. J. and Spiteri, R. J.},
journal = {Applied Numerical Mathematics},
pages = {151--167},
title = {{Implicit-Explicit Runge-Kutta methods for time-dependent partial differential equations}},
volume = {25},
year = {1997}
}
@article{Ascher1995,
author = {Ascher, U. M. and Ruuth, S. J. and Wetton, B. T. R.},
journal = {SIAM J. Numer. Anal.},
pages = {797--823},
title = {{Implicit-Explicit methods for time-dependent partial differential equations}},
volume = {32(3)},
year = {1995}
}
@article{Assier-Rzadkieaicz2000,
author = {Assier-Rzadkieaicz, S. and Heinrich, P. and Sabatier, P. C. and Savoye, B. and Bourillet, J. F.},
doi = {10.1007/PL00001057},
issn = {0033-4533},
journal = {Pure Appl. Geophys.},
month = {oct},
number = {10},
pages = {1707--1727},
title = {{Numerical Modelling of a Landslide-generated Tsunami: The 1979 Nice Event}},
url = {http://www.springerlink.com/index/10.1007/PL00001057},
volume = {157},
year = {2000}
}
@article{Athanassoulis1999,
author = {Athanassoulis, G. A. and Belibassakis, K. A.},
journal = {J. Fluid Mech},
pages = {275--301},
title = {{A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions}},
volume = {389},
year = {1999}
}
@article{Aubry1995,
abstract = {Pressurized water reactor (PWR) or liquid-metal fast breeder reactor cores or fuel assemblies, PWR steam generators, condensers, and tubular heat exchangers are basic components of a nuclear power plant that involve two-phase flows in tube or rod bundles. A deep knowledge of the detailed flow patterns on the shell side is necessary to evaluate departure from nucleate boiling (DNB) margins in reactor cores, singularity effects (grids, wire spacers, support plates, and baffles), corrosion on the steam generator tube sheet, bypass effects, and vibration risks. For that purpose, Electricit� de France has developed since 1986 a general purpose Thermal-HYdraulic Code (THYC) to study three-dimensional single- and two-phase flows in rod or tube bundles (PWR cores, steam generators, condensers, and heat exchangers). It considers the three-dimensional domain to contain two kinds of components : fluid and solids. The THYC model is obtained by space-time averaging of the instantaneous equations (mass, momentum, and energy) of each phase over control volumes including fluid and solids. The physical model of THYC is validated under several French and international experiments for single- and two-phase flows. The THYC is used for the calculation of transients such as steam-line break (coupled with a three-dimensional neutronics code), for DNB predictions, and for various steam generator or condenser studies.},
author = {Aubry, S. and Caremoli, C. and Olive, J. and Rascle, P.},
journal = {Nuclear technology},
pages = {331--345},
title = {{The THYC three-dimensional thermal-hydraulic code for rod bundles : recent developments and validation tests}},
volume = {112(3)},
year = {1995}
}
@phdthesis{Audusse2004a,
author = {Audusse, E.},
school = {Universit{\'{e}} Paris {\{}VI{\}}},
title = {{Mod{\'{e}}lisation hyperbolique et analyse num{\'{e}}rique pour les {\'{e}}coulements en eaux peu profondes}},
year = {2004}
}
@article{Audusse2004,
author = {Audusse, E. and Bouchut, F. and Bristeau, M.-O. and Klein, R. and Perthame, B.},
journal = {SIAM J. of Sc. Comp.},
pages = {2050--2065},
title = {{A Fast and Stable Well-balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows}},
volume = {25},
year = {2004}
}
@article{Audusse2005,
author = {Audusse, E. and Bristeau, M.-O.},
journal = {J. Comput. Phys},
pages = {311--333},
title = {{A well-balanced positivity preserving "second-order" scheme for shallow water flows on unstructured meshes}},
volume = {206},
year = {2005}
}
@article{Audusse2003,
author = {Audusse, E. and Bristeau, M.-O.},
doi = {10.1051/m2an:2003034},
issn = {0764-583X},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
month = {mar},
number = {2},
pages = {389--416},
title = {{Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method}},
url = {http://www.esaim-m2an.org/10.1051/m2an:2003034},
volume = {37},
year = {2003}
}
@article{Audusse2010,
abstract = {The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.},
author = {Audusse, E. and Bristeau, M.-O. and Perthame, B. and Sainte-Marie, J.},
doi = {10.1051/m2an/2010036},
issn = {0764-583X},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
month = {jun},
number = {1},
pages = {169--200},
title = {{A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation}},
url = {http://www.esaim-m2an.org/10.1051/m2an/2010036},
volume = {45},
year = {2010}
}
@article{Avila2011,
abstract = {Shear flows undergo a sudden transition from laminar to turbulent motion as the velocity increases, and the onset of turbulence radically changes transport efficiency and mixing properties. Even for the well-studied case of pipe flow, it has not been possible to determine at what Reynolds number the motion will be either persistently turbulent or ultimately laminar. We show that in pipes, turbulence that is transient at low Reynolds numbers becomes sustained at a distinct critical point. Through extensive experiments and computer simulations, we were able to identify and characterize the processes ultimately responsible for sustaining turbulence. In contrast to the classical Landau-Ruelle-Takens view that turbulence arises from an increase in the temporal complexity of fluid motion, here, spatial proliferation of chaotic domains is the decisive process and intrinsic to the nature of fluid turbulence.},
author = {Avila, K. and Moxey, D. and de Lozar, A. and Avila, M. and Barkley, D. and Hof, B.},
doi = {10.1126/science.1203223},
issn = {1095-9203},
journal = {Science},
month = {jul},
number = {6039},
pages = {192--196},
pmid = {21737736},
title = {{The onset of turbulence in pipe flow}},
volume = {333},
year = {2011}
}
@article{Avilez-Valente2009,
author = {Avilez-Valente, P. and Seabra-Santos, F. J.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {969--1010},
title = {{A high-order Petrov-Galerkin finite element method for the classical Boussinesq wave model}},
volume = {59},
year = {2009}
}
@article{Avolio2000,
author = {Avolio, M. V. and {Di Gregorio}, S. and Mantovani, F. and Pasuto, A. and Rongo, R. and Silvano, S. and Spataro, W.},
journal = {International Journal of Applied Earth Observation and Geoinformation},
pages = {41--50},
title = {{Simulation of the 1992 Tessina landslide by a cellular automata model and future hazard scenarios}},
volume = {2},
year = {2000}
}
@article{Azarenok2003,
abstract = {In this work, a detailed description for an efficent adaptive mesh redistribution algorithm based on the Godunov's scheme is presented. After each mesh iteration a second-order finite-volume flow solver is used to update the flow parameters at the new time level directly without using interpolation. Numerical experiments are perfomed to demonstrate the efficency and robustness of the proposed adaptive mesh algorithm in one and two dimensions.},
author = {Azarenok, B. N. and Ivanenko, S. A. and Tang, T.},
journal = {Commun. Math. Sci.},
number = {1},
pages = {152--179},
title = {{Adaptive Mesh Redistibution Method Based on Godunov's Scheme}},
volume = {1},
year = {2003}
}
@article{Baba2006,
author = {Baba, T. and Cummins, P. R. and Hori, T. and Kaneda, Y.},
journal = {Tectonophysics},
pages = {119--134},
title = {{High precision slip distribution of the 1944 Tonankai earthquake inferred from tsunami waveforms: Possible slip on a splay fault}},
volume = {426},
year = {2006}
}
@article{Babenko1987,
author = {Babenko, K. I.},
journal = {Sov. Math. Dokl.},
pages = {599--603},
title = {{Some remarks on the theory of surface waves of finite amplitude}},
volume = {35},
year = {1987}
}
@book{Babuska1995,
address = {New York, NY},
doi = {10.1007/978-1-4612-4248-2},
editor = {Babuska, I. and Henshaw, W. D. and Oliger, J. E. and Flaherty, J. E. and Hopcroft, J. E. and Tezduyar, T.},
isbn = {978-1-4612-8707-0},
pages = {450},
publisher = {Springer},
series = {The IMA Volumes in Mathematics and its Applications},
title = {{Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations}},
url = {http://link.springer.com/10.1007/978-1-4612-4248-2},
volume = {75},
year = {1995}
}
@article{Babuska1994,
abstract = {In the classical form of the finite element method called the hversion, piecewise polynomials of fixed degree p are used and the mesh size h is decreased for accuracy. In this paper, we discuss the fundamental theoretical ideas behind the relatively recent p version and h-p version. In the p version, a fixed mesh is used and p is allowed to increase. The h-p version combines both approaches. The authors describe and explain the basic properties and characteristics of these newer versions, especially in areas where their behavior is significantly different from that of the h version. Simplified proofs of key concepts are included and computational illustrations of several results are provided. A benchmark comparison between the various versions in included.},
author = {Babuska, I. and Suri, M.},
doi = {10.1137/1036141},
issn = {0036-1445},
journal = {SIAM Review},
month = {dec},
number = {4},
pages = {578--632},
title = {{The p and h-p Versions of the Finite Element Method, Basic Principles and Properties}},
url = {http://epubs.siam.org/doi/abs/10.1137/1036141},
volume = {36},
year = {1994}
}
@article{Backhaus2013,
abstract = {As our electrical grid systems become smarter and more autonomous, they require greater control technologies to protect them from failing.},
author = {Backhaus, S. and Chertkov, M.},
doi = {10.1063/PT.3.1979},
issn = {00319228},
journal = {Physics Today},
number = {5},
pages = {42},
title = {{Getting a grip on the electrical grid}},
url = {http://scitation.aip.org/content/aip/magazine/physicstoday/article/66/5/10.1063/PT.3.1979},
volume = {66},
year = {2013}
}
@techreport{Bae2012,
author = {Bae, H.},
institution = {Department of Mathematics, UC Davis},
pages = {9},
title = {{The viscous potential flows in a moving domain of infinite depth without surface tension}},
url = {https://www.math.ucdavis.edu/{~}hantaek/Note 2.pdf},
year = {2012}
}
@article{Baer1986a,
author = {Baer, M. R. and Gross, R. J. and Nunziato, J. W.},
journal = {Combust. Flame},
pages = {15--30},
title = {{An experimental and theoretical study of deflagration-to-detonation transition (DDT) in the granular explosive}},
volume = {65(1)},
year = {1986}
}
@article{Baer1986,
author = {Baer, M. R. and Nunziato, J. W.},
journal = {International journal of multiphase flow},
pages = {861--889},
title = {{A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials}},
volume = {12(6)},
year = {1986}
}
@techreport{Baez2005,
address = {Riverside},
author = {Baez, J. C. and Wise, D. K. and Smith, B.},
institution = {University of California},
pages = {1--70},
title = {{Lectures on Classical Mechanics}},
year = {2005}
}
@article{Bagnold1939,
author = {Bagnold, R. A.},
journal = {Proc. Inst. Civil Eng.},
pages = {201--226},
title = {{Interim report on wave pressure research}},
volume = {12},
year = {1939}
}
@article{Bai2007,
author = {Bai, Y.-C. and Xu, D.},
journal = {Journal of Hydrodynamics, Ser. B},
pages = {726--735},
title = {{Numerical simulation of two-dimensional dam-break flows in curved channels}},
volume = {19(6)},
year = {2007}
}
@article{Baiti1997,
author = {Baiti, P. and Jenssen, H. K.},
journal = {J. Diff. Eqns.},
pages = {161--185},
title = {{Well-posedness for a class of 2x2 conservation laws with L inf data}},
volume = {140},
year = {1997}
}
@article{Baiti1999,
author = {Baiti, P. and LeFloch, Ph. G. and Piccoli, B.},
journal = {Contemporary Mathematics},
pages = {1--25},
title = {{Nonclassical Shocks and the Cauchy Problem: General Conservation Laws}},
volume = {238},
year = {1999}
}
@article{Baker1982,
author = {Baker, G. R. and Meiron, D. I. and Orszag, S. A.},
journal = {J. Fluid Mech.},
pages = {477--501},
title = {{Generalized vortex methods for free-surface flow problems}},
volume = {123},
year = {1982}
}
@article{Bakhvalov1969,
author = {Bakhvalov, N. S.},
doi = {10.1016/0041-5553(69)90038-X},
issn = {00415553},
journal = {USSR Computational Mathematics and Mathematical Physics},
month = {jan},
number = {4},
pages = {139--166},
title = {{The optimization of methods of solving boundary value problems with a boundary layer}},
url = {http://linkinghub.elsevier.com/retrieve/pii/004155536990038X},
volume = {9},
year = {1969}
}
@article{Bakhvalov1973,
author = {Bakhvalov, N. S. and Eglit, M. E.},
journal = {Fluid Dynamics},
pages = {683--689},
title = {{Investigation of the one-dimensional motion of a snow avalanche along a flat slope}},
volume = {8},
year = {1973}
}
@article{Bakhvalov1975,
author = {Bakhvalov, N. S. and Kulikovskiy, A. G. and Kurkin, V. N. and Sveshnikova, Y. I. and Eglit, M. E.},
journal = {Soviet Hydrology: Selected Papers, Rocky Mountain Station},
title = {{Movement of snow avalanches}},
volume = {4},
year = {1975}
}
@article{Balk1996,
author = {Balk, A. M.},
journal = {Phys. Fluids},
pages = {416--419},
title = {{A Lagragian for water waves}},
volume = {8},
year = {1996}
}
@article{Ballestra2004,
author = {Ballestra, L. V. and Sacco, R.},
doi = {10.1016/j.jcp.2003.10.002},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {mar},
number = {1},
pages = {320--340},
title = {{Numerical problems in semiconductor simulation using the hydrodynamic model: a second-order finite difference scheme}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999103005345},
volume = {195},
year = {2004}
}
@article{Banner2014,
abstract = {Observed crest speeds of maximally steep, breaking water waves are much slower than expected. Our fully nonlinear computations of unsteadily propagating deep water wave groups show that each wave crest approaching its maximum height slows down significantly and either breaks at this reduced speed, or accelerates forward unbroken. This previously noted crest slowdown behavior was validated as generic in our extensive laboratory and field observations. It is likely to occur in unsteady dispersive nonlinear wave groups in other natural systems.},
author = {Banner, M. L. and Barthelemy, X. and Fedele, F. and Allis, M. and Benetazzo, A. and Dias, F. and Peirson, W. L.},
doi = {10.1103/PhysRevLett.112.114502},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {mar},
number = {11},
pages = {114502},
title = {{Linking Reduced Breaking Crest Speeds to Unsteady Nonlinear Water Wave Group Behavior}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.114502},
volume = {112},
year = {2014}
}
@article{Banner1993,
author = {Banner, M. L. and Peregrine, D. H.},
journal = {Ann. Rev. Fluid Mech.},
pages = {373--397},
title = {{Wave Breaking in Deep Water}},
volume = {25},
year = {1993}
}
@article{Barbeiro2005,
author = {Barbeiro, S. and Ferreira, J. A. and Grigorieff, R. D.},
doi = {10.1093/imanum/dri018},
issn = {0272-4979},
journal = {IMA J. Numer. Anal.},
month = {feb},
number = {4},
pages = {797--811},
title = {{Supraconvergence of a finite difference scheme for solutions in {\$}H{\^{}}s(0, L){\$}}},
url = {http://imanum.oxfordjournals.org/cgi/doi/10.1093/imanum/dri018},
volume = {25},
year = {2005}
}
@article{Bardet2003,
author = {Bardet, J.-P. and Synolakis, C. E. and Davies, H. L. and Imamura, F. and Okal, E. A.},
journal = {Pure Appl. Geophys.},
pages = {1793--1809},
title = {{Landslide Tsunamis: Recent Findings and Research Directions}},
volume = {160},
year = {2003}
}
@book{Barone1982,
abstract = {Comprehensive coverage of the Josephson effect, from a survey of underlying physical theory to actual and proposed engineering applications. Considers many macroscopic quantum effects with potential for technical development. Theoretical material is followed by relevant discussions of device applications. Includes 100 original figures and photographs.},
address = {Weinheim, FRG},
author = {Barone, A. and Patern{\`{o}}, G.},
doi = {10.1002/352760278X},
isbn = {9783527602780},
month = {jul},
publisher = {Wiley-VCH Verlag GmbH {\&} Co. KGaA},
title = {{Physics and Applications of the Josephson Effect}},
url = {http://doi.wiley.com/10.1002/352760278X},
year = {1982}
}
@article{Barth1994,
author = {Barth, T. J.},
journal = {Lecture series - van Karman Institute for Fluid Dynamics},
pages = {1--140},
title = {{Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations}},
volume = {5},
year = {1994}
}
@article{Barth1990,
author = {Barth, T. J. and Frederickson, P. O.},
journal = {AIAA},
title = {{Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction}},
volume = {90-0013},
year = {1990}
}
@article{Barth1989,
author = {Barth, T. J. and Jespersen, D. C.},
journal = {AIAA},
title = {{The Design and Application of Upwind Schemes on Unstructured Meshes}},
volume = {0366},
year = {1989}
}
@inbook{Barth2004,
abstract = {Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, meteorology, electromagnetics, semi conductor device simulation, models of biological processes, and many other engineering areas governed by conservative systems that can be written in integral control volume form.},
address = {Chichester, UK},
author = {Barth, T. J. and Ohlberger, M.},
booktitle = {Encyclopedia of Computational Mechanics},
doi = {10.1002/0470091355},
editor = {Stein, Erwin and de Borst, Ren{\"{\i}}¿½{\"{\i}}¿½ and Hughes, Thomas J R},
isbn = {0470846992},
keywords = {conservation laws,discrete maximum principles,finite volume methods,higher-order schemes,nonoscillatory approximation},
mendeley-tags = {conservation laws,discrete maximum principles,finite volume methods,higher-order schemes,nonoscillatory approximation},
month = {nov},
publisher = {John Wiley {\&} Sons, Ltd},
title = {{Finite Volume Methods: Foundation and Analysis}},
url = {http://doi.wiley.com/10.1002/0470091355},
year = {2004}
}
@article{Barthelemy2004,
author = {Barth{\'{e}}l{\'{e}}my, E.},
journal = {Surveys in Geophysics},
pages = {315--337},
title = {{Nonlinear shallow water theories for coastal waves}},
volume = {25},
year = {2004}
}
@book{Basdevant2007,
address = {New York},
author = {Basdevant, J.-L.},
pages = {183},
publisher = {Springer-Verlag},
title = {{Variational Principles in Physics}},
year = {2007}
}
@article{Basher2006,
author = {Basher, R.},
journal = {Philosophical Transactions: Mathematical, Physical and Engineering Sciences},
pages = {2167--2182},
title = {{Global Early Warning Systems for Natural Hazards: Systematic and People-Centred}},
volume = {364(1845)},
year = {2006}
}
@article{Bassin2000,
author = {Bassin, C. and Laske, G. and Masters, G.},
journal = {EOS Trans AGU},
pages = {F897},
title = {{The Current Limits of Resolution for Surface Wave Tomography in North America}},
volume = {81},
year = {2000}
}
@book{Batchelor1967,
abstract = {First published in 1967, Professor Batchelor's classic text on fluid dynamics is still one of the foremost texts in the subject. The careful presentation of the underlying theories of fluids is still timely and applicable, even in these days of almost limitless computer power. This re-issue should ensure that a new generation of graduate students see the elegance of Professor Batchelor's presentation.},
address = {Cambridge},
author = {Batchelor, G. K.},
isbn = {978-0521663960},
pages = {658},
publisher = {Cambridge University Press},
title = {{An Introduction to Fluid Dynamics}},
year = {1967}
}
@book{Batchelor2000,
abstract = {First published in 1967, Professor Batchelor's classic work is still one of the foremost texts on fluid dynamics. His careful presentation of the underlying theories of fluids is still timely and applicable, even in these days of almost limitless computer power. This reissue ensures that a new generation of graduate students experiences the elegance of Professor Batchelor's writing.},
author = {Batchelor, G. K.},
booktitle = {American Mathematical Monthly},
doi = {10.2307/2317984},
institution = {Inst Ciencies Mar; Colegio Oficial Biologos; Univ Politecn Catalunya; Univ Barcelona; Museu Ciencia Fundacio La Caixa},
isbn = {0521663962},
issn = {00319007},
number = {8},
pages = {615},
pmid = {15601019},
publisher = {Cambridge University Press},
series = {Cambridge mathematical library},
title = {{An introduction to fluid dynamics}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/18525475},
volume = {61},
year = {2000}
}
@article{Bateman1929,
abstract = {Variational principles for problems in fluid dynamics, plasma dynamics and elasticity are discussed in the context of the general problem of finding a variational principle for a given system of equations. In continuum mechanics, the difficulties arise...},
author = {Bateman, H.},
doi = {10.1098/rspa.1929.0189},
issn = {1364-5021},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
pages = {598--618},
title = {{Notes on a Differential Equation Which Occurs in the Two-Dimensional Motion of a Compressible Fluid and the Associated Variational Problems}},
volume = {125},
year = {1929}
}
@article{Bateman2001,
author = {Bateman, W. J. D. and Swan, C. and Taylor, P. H.},
doi = {10.1006/jcph.2001.6906},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {nov},
number = {1},
pages = {277--305},
title = {{On the Efficient Numerical Simulation of Directionally Spread Surface Water Waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999101969062},
volume = {174},
year = {2001}
}
@article{Batten1997,
author = {Batten, P. and Clarke, N. and Lambert, C. and Causon, D. M.},
journal = {SIAM J. Sci. Comput.},
number = {6},
pages = {1553--1570},
title = {{On the Choice of Wavespeeds for the HLLC Riemann Solver}},
volume = {18},
year = {1997}
}
@article{Bauer2011,
abstract = {Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium (ISM). Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium (IGM), which may substantially modify the thermodynamic structure of gas in virialized dark matter halos and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far systematic code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyze simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH quite badly fails in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. This casts doubt about the reliability of SPH for simulations of cosmic structure formation, especially if turbulence in clusters of galaxies is indeed significant. In contrast, SPH's performance is much better for supersonic turbulence, as here the flow is kinetically dominated and characterized by a network of strong shocks, which can be adequately captured with SPH. [Abridged]},
archivePrefix = {arXiv},
arxivId = {1109.4413},
author = {Bauer, A. and Springel, V.},
doi = {10.1111/j.1365-2966.2012.21058.x},
eprint = {1109.4413},
issn = {00358711},
journal = {Mon. Not. R. Astron. Soc.},
keywords = {Hydrodynamics,Methods: numerical,Shock waves,Turbulence},
number = {3},
pages = {2558--2578},
title = {{Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations}},
volume = {423},
year = {2012}
}
@book{Bautin2009,
address = {Novosibirsk},
author = {Bautin, S. P.},
pages = {368},
publisher = {Nauka},
title = {{Characteristic Cauchy Problem and its Applications in Gas Dynamics}},
year = {2009}
}
@book{Bautin2005,
address = {Novosibirsk},
author = {Bautin, S. P. and Deryabin, S. L.},
pages = {390},
publisher = {Nauka},
title = {{Mathematical Modelling of Ideal Gas Outflow into Vacuum}},
year = {2005}
}
@article{Bautin2011,
abstract = {Solutions to initial boundary value problems are constructed for the shallow water equations in the form of series locally convergent in the neighbourhood of a movable water-land boundary for an arbitrary bottom relief. The motion law and the velocity of this boundary are determined for various wave-shore interaction modes. The obtained results of analytic study of the solutions are used for the development of approximations of boundary conditions on the movable shoreline. Test problems are numerically solved using an explicit predictor-corrector scheme of the second order of approximation on adaptive grids retracing the position of the water-land boundary. The results of these calculations are presented.},
author = {Bautin, S. P. and Deryabin, S. L. and Sommer, A. F. and Khakimzyanov, G. S. and Shokina, N. Yu.},
doi = {10.1515/rjnamm.2011.020},
issn = {0927-6467},
journal = {Russ. J. Numer. Anal. Math. Modelling},
month = {jan},
number = {4},
pages = {353--377},
title = {{Use of analytic solutions in the statement of difference boundary conditions on a movable shoreline}},
volume = {26},
year = {2011}
}
@article{Beale1991,
abstract = {We prove the existence of solitary water waves of elevation, as exact solutions of the equations of steady inviscid flow, taking into account the effect of surface tension on the free surface. In contrast to the case without surface tension, a resonance occurs with periodic waves of the same speed. The wave form consists of a single crest on the elongated scale with a much smaller oscillation at infinity on the physical scale. We have not proved that the amplitude of the oscillation is actually nonzero; a formal calculation suggests that it is exponentially small.},
author = {Beale, J. T.},
doi = {10.1002/cpa.3160440204},
issn = {00103640},
journal = {Comm. Pure Appl. Math.},
month = {mar},
number = {2},
pages = {211--257},
title = {{Exact solitary water waves with capillary ripples at infinity}},
url = {http://doi.wiley.com/10.1002/cpa.3160440204},
volume = {44},
year = {1991}
}
@article{Beals1979,
author = {Beals, R.},
doi = {10.1016/0022-1236(79)90021-1},
issn = {00221236},
journal = {J. Func. Anal.},
month = {oct},
number = {1},
pages = {1--20},
title = {{An abstract treatment of some forward-backward problems of transport and scattering}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0022123679900211},
volume = {34},
year = {1979}
}
@article{Beals1983,
abstract = {Half-range completeness theorems are proved for eigenfunctions associated to the one-dimensional Fokker-Planck equation in a semi-infinite medium. Existence and uniqueness results for perfectly absorbing, partially absorbing, and purely specularly reflecting boundary conditions are deduced for the stationary and time-dependent problems. Similar results are obtained for a slab geometry.},
author = {Beals, R. and Protopopescu, V.},
doi = {10.1007/BF01008957},
issn = {0022-4715},
journal = {J. Stat. Phys.},
month = {sep},
number = {3},
pages = {565--584},
title = {{Half-range completeness for the Fokker-Planck equation}},
url = {http://link.springer.com/10.1007/BF01008957},
volume = {32},
year = {1983}
}
@article{Beals2001,
abstract = {Explicit formulas are given for the multi-peakon-antipeakon solutions of the Camassa-Holm equation, and a detailed analysis is made of both short-term and long-term aspects of the interaction between a single peakon and single anti-peakon.},
author = {Beals, R. and Sattinger, D. H. and Szmigielski, J.},
doi = {10.2991/jnmp.2001.8.s.5},
issn = {1402-9251},
journal = {J. Nonlinear Math. Phys.},
month = {jan},
number = {sup1},
pages = {23--27},
title = {{Peakon-Antipeakon Interaction}},
url = {http://www.tandfonline.com/doi/abs/10.2991/jnmp.2001.8.s.5},
volume = {8},
year = {2001}
}
@article{Beck1996,
abstract = {The sediments of the two largest post-Riss and post-W{\"{u}}rm lakes, in the northwestern Alps and southern Jura, contain possible records of seismo-tectonic instability: earthquake triggering of gravity reworking, and direct stratification disturbance. In Lake Annecy, the lacustrine s.s. (non-proglacial) part of a 40 meters-thick rhythmic sediment pile has been investigated for this purpose by CLIMASILAC coring. For the last 15,000 to 20,000 years, 50 sedimentary “events” have been detected, with the most frequent time-recurrence intervals from 1 to 5 centuries. These events appear to have been concentrated during the deglaciation period. Thus, different factors could be responsible for the subsequent decrease: change of sediment composition and properties, modification of slope instability related to the latter and to modification in the catchment area, and decrease of regional seismic activity. Following the third possibility, the period of high reworking frequency, coeval with the main glacial melting, should be related to a glacio-isostatic rebound. On the other hand, the scarce “events” registered for the Holocene could represent the record of a longer term (tectonic) seismicity.},
author = {Beck, C. and Manalt, F. and Chapron, E. and {Van Rensbergen}, P. and {De Batist}, M.},
doi = {10.1016/0264-3707(96)00001-4},
journal = {Journal of Geodynamics},
number = {1-2},
pages = {155--171},
title = {{Enhanced seismicity in the early post-glacial period: Evidence from the post-w{\"{u}}rm sediments of lake Annecy, northwestern Alps}},
volume = {22},
year = {1996}
}
@phdthesis{Beghin1979,
author = {Beghin, P.},
school = {Institut National Polytechnique de Grenoble},
title = {{Etude des bouff{\'{e}}es bidimensionnelles de densit{\'{e}} en {\'{e}}coulement sur pente avec application aux avalanches de neige poudreuse}},
year = {1979}
}
@article{Beghin1983,
author = {Beghin, P. and Brugnot, G.},
journal = {Cold Review Science and Technology},
pages = {63--73},
title = {{Contribution of theoretical and experimental results to powder-snow avalanche dynamics}},
volume = {8},
year = {1983}
}
@techreport{Beghin1990,
author = {Beghin, P. and Closet, J.-F.},
institution = {Cemagref},
title = {{Effet d'une digue sur l'{\'{e}}coulement d'une avalanche poudreuse}},
year = {1990}
}
@article{Beghin1991,
author = {Beghin, P. and Olagne, X.},
journal = {Cold Regions Science and Technology},
pages = {317--326},
title = {{Experimental and theoretical study of the dynamics of powder snow avalanches}},
volume = {19},
year = {1991}
}
@article{Beisel2009,
author = {Beisel, S. A. and Chubarov, L. B. and Didenkulova, I. and Kit, E. and Levin, A. and Pelinovsky, E. N. and Shokin, Yu. I. and Sladkevich, M.},
doi = {10.1029/2008JC005262},
journal = {Journal of Geophysical Research - Oceans},
pages = {C09002},
title = {{The 1956 Greek tsunami recorded at Yafo, Israel, and its numerical modeling}},
volume = {114},
year = {2009}
}
@article{Beisel2012,
author = {Beisel, S. A. and Chubarov, L. B. and Dutykh, D. and Khakimzyanov, G. S. and Shokina, N. Yu.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {6},
pages = {539--558},
title = {{Simulation of surface waves generated by an underwater landslide in a bounded reservoir}},
volume = {27},
year = {2012}
}
@article{Beisel2011,
author = {Beisel, S. A. and Chubarov, L. B. and Khakimzyanov, G. S.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {1},
pages = {17--38},
title = {{Simulation of surface waves generated by an underwater landslide moving over an uneven slope}},
volume = {26},
year = {2011}
}
@incollection{Beisel2011a,
address = {Berlin, Heidelberg},
author = {Beisel, S. A. and Chubarov, L. B. and Shokin, Yu. I.},
booktitle = {Notes on Numerical Fluid Mechanics and Multidisciplinary Design},
editor = {et Al., E Krause},
pages = {137--148},
publisher = {Springer Verlag},
title = {{Some features of the landslide mechanism of surface waves generation in real basins}},
year = {2011}
}
@article{Beisel2010,
author = {Beisel, S. A. and Khakimzyanov, G. S. and Chubarov, L. B.},
journal = {Computational Technologies},
number = {3},
pages = {39--51},
title = {{Surface wave modeling generated by an underwater landslide moving along a nonuniform slope}},
volume = {15},
year = {2010}
}
@article{Beji1994,
author = {Beji, S. and Battjes, J. A.},
doi = {10.1016/0378-3839(94)90012-4},
issn = {03783839},
journal = {Coastal Engineering},
month = {may},
number = {1-2},
pages = {1--16},
title = {{Numerical simulation of nonlinear wave propagation over a bar}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0378383994900124},
volume = {23},
year = {1994}
}
@article{Beji1996,
abstract = {A formal derivation of the improved Boussinesq equations of Madsen and Sorens (1992) is presented to provide the correct forms of the depth-gradient related terms. Linear shoaling characteristics of the new equations are investigated by the method of Madsen and Sorensen (1992) and by the energy flux concept separately and found to agree perfectly, whereas these approaches give conflicting results for the equations derived by Madsen and Sorensen (1992). Furthermore, Nwogu's (1993) modified Boussinesq model is found to produce a linear shoaling-gradient identical with the present work. Numerical modelling of the derived equations for directional waves is carried out by three-time-level finite-difference approximations. A higher-order radiation condition is implemented for effective absorption of the outgoing waves. Several test cases are included to demonstrate the performance of the model.},
author = {Beji, S. and Nadaoka, K.},
doi = {10.1016/0029-8018(96)84408-8},
issn = {00298018},
journal = {Ocean Engineering},
month = {nov},
number = {8},
pages = {691--704},
title = {{A formal derivation and numerical modelling of the improved Boussinesq equations for varying depth}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0029801896844088},
volume = {23},
year = {1996}
}
@article{Belanger1828,
author = {B{\'{e}}langer, J.-B.},
journal = {Carilian-Goeury, Paris, France},
pages = {38},
title = {{Essai sur la Solution Num{\'{e}}rique de quelques Probl{\`{e}}mes Relatifs au Mouvement Permanent des Eaux Courantes}},
year = {1828}
}
@article{Belanger1828,
author = {B{\'{e}}langer, J.-B.},
journal = {Carilian-Goeury, Paris, France},
pages = {38},
title = {{Essai sur la Solution Num{\'{e}}rique de quelques Probl{\`{e}}mes Relatifs au Mouvement Permanent des Eaux Courantes}},
year = {1828}
}
@article{Belibassakis2006,
author = {Belibassakis, K. A. and Athanassoulis, G. A.},
doi = {10.1016/j.apor.2005.12.003},
issn = {01411187},
journal = {Applied Ocean Research},
month = {feb},
number = {1},
pages = {59--76},
title = {{A coupled-mode technique for weakly nonlinear wave interaction with large floating structures lying over variable bathymetry regions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0141118706000265},
volume = {28},
year = {2006}
}
@article{Belibassakis2002,
author = {Belibassakis, K. A. and Athanassoulis, G. A.},
journal = {J. Fluid Mech},
pages = {35--80},
title = {{Extension of second-order Stokes theory to variable bathymetry}},
volume = {464},
year = {2002}
}
@article{Bellos2004,
author = {Bellos, C. V.},
journal = {European Water},
pages = {3--15},
title = {{Experimental Measurements of Flood Wave Created by a Dam Break}},
volume = {7/8},
year = {2004}
}
@article{Bellotti2001,
author = {Bellotti, G. and Brocchini, M.},
journal = {Int. J. Num. Meth. in Fluids},
number = {4},
pages = {479--500},
title = {{On the shoreline boundary conditions for Boussinesq-type models}},
volume = {37},
year = {2001}
}
@article{Bellotti2002,
author = {Bellotti, G. and Brocchini, M.},
journal = {Ocean Engineering},
pages = {1569--1575},
title = {{On using Boussinesq-type equations near the soreline: a note of caution}},
volume = {29},
year = {2002}
}
@article{Ben-M,
author = {Ben-Menahem, A. and Rosenman, M.},
journal = {J. Geophys. Res.},
pages = {3097--3128},
title = {{Amplitude patterns of tsunami waves from submarine earthquakes}},
volume = {77},
year = {1972}
}
@article{ben1,
author = {Ben-Menahem, A. and Singh, S. J. and Solomon, F.},
journal = {Bull. Seism. Soc. Am.},
pages = {813--853},
title = {{Static deformation of a spherical earth model by internal dislocations}},
volume = {59},
year = {1969}
}
@article{ben2,
author = {Ben-Menahem, A. and Singh, S. J. and Solomon, F.},
journal = {Rev. Geophys. Space Phys.},
pages = {591--632},
title = {{Deformation of an homogeneous earth model finite by dislocations}},
volume = {8},
year = {1970}
}
@article{Benabdallah2002,
author = {Benabdallah, A. and Caputo, J.-G.},
doi = {10.1063/1.1503856},
issn = {00218979},
journal = {Journal of Applied Physics},
number = {7},
pages = {3853},
title = {{Influence of the passive region on zero field steps for window Josephson junctions}},
url = {http://link.aip.org/link/JAPIAU/v92/i7/p3853/s1{\&}Agg=doi},
volume = {92},
year = {2002}
}
@article{Benilov1993,
author = {Benilov, E. S. and Grimshaw, R. and Kuznetsova, E. P.},
doi = {10.1016/0167-2789(93)90091-E},
issn = {01672789},
journal = {Phys. D},
month = {dec},
number = {3-4},
pages = {270--278},
title = {{The generation of radiating waves in a singularly-perturbed Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/016727899390091E},
volume = {69},
year = {1993}
}
@article{Benjamin2010,
author = {Benjamin, A. T. and Walton, D.},
doi = {10.1016/j.jspi.2010.01.012},
issn = {03783758},
journal = {Journal of Statistical Planning and Inference},
keywords = {Chebyshev polynomials,Combinatorial proof,Tiling},
month = {aug},
number = {8},
pages = {2161--2167},
title = {{Combinatorially composing Chebyshev polynomials}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378375810000236},
volume = {140},
year = {2010}
}
@article{Benjamin1968,
author = {Benjamin, T. B.},
journal = {J. Fluid Mech.},
pages = {209--248},
title = {{Gravity Currents and Related Phenomenon}},
volume = {31},
year = {1968}
}
@article{Benjamin1967,
author = {Benjamin, T. B.},
journal = {Proc. R. Soc. London, Ser. A},
title = {{Instability of periodic wavetrains in nonlinear dispersive systems}},
volume = {299(59)},
year = {1967}
}
@article{Benjamin1972,
abstract = {The Korteweg-de Vries equation, which describes the unidirectional propagation of long waves in a wide class of nonlinear dispersive systems, is well known to have solutions representing solitary waves. The present analysis establishes that these solutions are stable, confirming a property that has for a long time been presumed. The demonstration of stability hinges on two nonlinear functionals which for solutions of the Korteweg-de Vries equation are invariant with time: these are introduced in section 2, where it is recalled that Boussinesq recognized their significance in relation to the stability of solitary waves. The principles upon which the stability theory is based are explained in section 3, being supported by a few elementary ideas from functional analysis. A proof that solitary wave solutions are stable is completed in section 4, the most exacting steps of which are accomplished by means of spectral theory. In appendix A a method deriving from the calculus of variations is presented, whereby results needed for the proof of stability may be obtained independently of spectral theory as used in section 4. In appendix B it is shown how the stability analysis may readily be adapted to solitary-wave solutions of the 'regularized long-wave equation' that has recently been advocated by Benjamin, Bona {\&} Mahony as an alternative to the Korteweg-de Vries equation. In appendix C a variational principle is demonstrated relating to the exact boundary-value problem for solitary waves in water: this is a counterpart to a principle used in the present work (introduced in section 2) and offers some prospect of proving the stability of exact solitary waves.},
author = {Benjamin, T. B.},
doi = {10.1098/rspa.1972.0074},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {may},
number = {1573},
pages = {153--183},
title = {{The Stability of Solitary Waves}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1972.0074},
volume = {328},
year = {1972}
}
@inbook{Benjamin1974,
author = {Benjamin, T. B.},
chapter = {Lectures o},
pages = {3--47},
publisher = {Amer. Math. Soc., Providence, RI},
title = {{Lectures in Appl. Math.}},
volume = {15},
year = {1974}
}
@article{Benjamin1967b,
author = {Benjamin, T. B.},
journal = {J. Fluid Mech},
pages = {559--562},
title = {{Internal waves of permanent form in fluids of great depth}},
volume = {29},
year = {1967}
}
@article{bona,
author = {Benjamin, T. B. and Bona, J. L. and Mahony, J. J.},
journal = {Philos. Trans. Royal Soc. London Ser. A},
pages = {47--78},
title = {{Model equations for long waves in nonlinear dispersive systems}},
volume = {272},
year = {1972}
}
@article{Benjamin1967a,
author = {Benjamin, T. B. and Feir, J. E.},
journal = {J. Fluid Mech.},
number = {417},
title = {{The disintegration of wavetrains in deep water. Part 1}},
volume = {27},
year = {1967}
}
@article{Benjamin1954,
author = {Benjamin, T. B. and Lighthill, J.},
journal = {Proc. R. Soc. London, Ser. A},
pages = {448--460},
title = {{On cnoidal waves and bores}},
volume = {224},
year = {1954}
}
@article{Benjamin1982,
author = {Benjamin, T. B. and Olver, P. J.},
journal = {J. Fluid Mech},
pages = {137--185},
title = {{Hamiltonian structure, symmetries and conservation laws for water waves}},
volume = {125},
year = {1982}
}
@article{Benkhaldoun2006,
author = {Benkhaldoun, F. and Quivy, L.},
journal = {Flow, Turbulence and Combustion},
pages = {391--402},
title = {{A Non Homogeneous Riemann Solver for shallow water and two phase flows}},
volume = {76},
year = {2006}
}
@article{Benkhaldoun2009a,
abstract = {We present a finite volume method for the numerical solution of the sediment transport equations in one and two space dimensions. The numerical fluxes are reconstructed using a modified Roe scheme that incorporates, in its reconstruction, the sign of the Jacobian matrix in the sediment transport system. A well-balanced discretization is used for the treatment of source terms. The method is well balanced, nonoscillatory, and suitable for both structured and unstructured triangular meshes. An adaptive procedure is also considered for the two-dimensional problems to update the bed-load accounting for the interaction between the bed-load and the water flow. The proposed method is applied to several sediment transport problems in one and two space dimensions. The numerical results demonstrate high resolution of the proposed finite volume method and confirm its capability to provide accurate simulations for sediment transport problems under flow regimes with strong shocks.},
author = {Benkhaldoun, F. and Sahmim, S. and Sea{\"{\i}}d, M.},
doi = {10.1137/080727634},
journal = {SIAM J. Sci. Comput.},
keywords = {finite volume method,sediment transport problems,shallow water equations,unstructured mesh,well-balanced discretization},
number = {4},
pages = {2866--2889},
title = {{Solution of the Sediment Transport Equations Using a Finite Volume Method Based on Sign Matrix}},
url = {http://dx.doi.org/10.1137/080727634},
volume = {31},
year = {2009}
}
@article{Benkhaldoun2009,
abstract = {We discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics.},
author = {Benkhaldoun, F. and Sahmim, S. and Sea{\"{\i}}d, M.},
journal = {Int. J. Num. Meth. Fluids},
number = {11},
pages = {1296--1327},
publisher = {John Wiley},
title = {{A two-dimensional finite volume morphodynamic model on unstructured triangular grids}},
url = {http://dx.doi.org/10.1002/fld.2129},
volume = {63},
year = {2010}
}
@article{Benkhaldoun2011,
abstract = {We propose a new numerical method for solving the equations of coupled sediment transport and bed morphology by free-surface water flows. The mathematical formulation of these models consists of the shallow water equations for the hydraulics, an advection equation for the transport of sediment species, and an Exner equation for the bedload transport. The coupled problem forms a one-dimensional hyperbolic system of conservation laws with geometric source terms. The proposed numerical method combines the method of characteristics with a finite volume discretization of the system. The combined method is simple to implement and accurately resolves the governing equations without relying on Riemann problem solvers. Numerical results are presented for several test examples on sediment transport and bed morphology by free-surface water flows.},
author = {Benkhaldoun, F. and Sea{\"{\i}}d, M.},
doi = {http://dx.doi.org/10.1016/j.matcom.2010.12.025},
journal = {Mathematics and Computers in Simulation},
keywords = {Bed morphology,Finite volume scheme,Method of characteristics,Sediment transport,Shallow water equations},
number = {10},
pages = {2073--2086},
title = {{Combined characteristics and finite volume methods for sediment transport and bed morphology in surface water flows}},
volume = {81},
year = {2011}
}
@article{Benkhaldoun2008,
author = {Benkhaldoun, F. and Sea{\"{\i}}d, M.},
journal = {Commun. Comput. Phys.},
pages = {820--837},
title = {{New finite-volume relaxation methods for the third-order differential equations}},
volume = {4},
year = {2008}
}
@book{Bennett2006,
abstract = {The emergence of observing systems such as acoustically-tracked floats in the deep ocean, and surface drifters navigating by satellite has seen renewed interest in Lagrangian fluid dynamics. Starting from the foundations of elementary kinematics and assuming some familiarity of Eulerian fluid dynamics, this book reviews the classical and new exact solutions of the Lagrangian framework, and then addresses the general solvability of the resulting general equations of motion. A unified account of turbulent diffusion and dispersion is offered, with applications among others to plankton patchiness in the ocean.},
address = {Cambridge},
author = {Bennett, A.},
pages = {310},
publisher = {Cambridge University Press},
title = {{Lagrangian Fluid Dynamics}},
year = {2006}
}
@article{Benney1966,
author = {Benney, D. J.},
journal = {J. Math. Phys.},
pages = {52--63},
title = {{Long non-linear waves in fluid flows}},
volume = {45},
year = {1966}
}
@inbook{Benney1974,
author = {Benney, D. J.},
chapter = {Nonlinear},
editor = {Newell, A C},
publisher = {Amer. Math. Soc., Providence, RI},
title = {{Nonlinear wave motion}},
year = {1974}
}
@article{Benney1967,
author = {Benney, D. J. and Newell, A. C.},
journal = {J. Math. and Physics},
pages = {133--139},
title = {{The propagation of nonlinear wave envelopes}},
volume = {46},
year = {1967}
}
@book{Benoit2006,
annote = {M�moire d{\&}{\#}039;habilitation � diriger des recherches},
author = {Benoit, M.},
institution = {Universit{\'{e}} du Sud Toulon Var},
title = {{Contribution {\`{a}} l'{\'{e}}tude des {\'{e}}tats de mer et des vagues, depuis l'oc{\'{e}}an jusqu'aux ouvrages c{\^{o}}tiers}},
type = {Habilitation {\`{a}} Diriger des Recherches},
year = {2006}
}
@techreport{Berg1970,
author = {Berg, E.},
institution = {Hawaii Institute of Geophysics, University of Hawaii, Honolulu},
title = {{Field survey of the Tsunamis of 28 March 1964 in Alaska, and conclusions as to the origin of the major Tsunami}},
year = {1970}
}
@article{Berger2003,
abstract = {The weak- or wave-turbulence problemconsists of finding statistical states of a large number of interacting waves. These states are obtained by forcing and dissipating a conservative dispersive wave equation at disparate scales to model physical forcing and dissipation, and by predicting the spectrum, often as a Kolmogorov-like power law, at intermediate scales. The mechanism for energy transfer in such systems is usually triads or quartets of waves. Here, we first derive a small-amplitude nonlinear dispersive equation (a finite-depth Benney-Luke-type equation), which we validate, analytically and numerically, by showing that it correctly captures the main deterministic aspects of gravity wave interactions: resonant quartets, Benjamin-Feir-type wave-packet stability, and wave-mean flow interactions. Numerically, this equation is easier to integrate than either the full problem or the Zakharov integral equation. Some additional features of wave interaction are discussed such as harmonic generation in shallow water. We then perform long time computations on the forced-dissipated model equation and compute statistical quantities of interest, which we compare to existing predictions. The forward cascade yields a spectrum close to the prediction of Zakharov, and the inverse cascade does not.},
author = {Berger, K. M. and Milewski, P. A.},
journal = {SIAM Journal on Applied Mathematics},
keywords = {finite depth,quartets,water waves,wave turbulence},
number = {4},
pages = {1121--1140},
title = {{Simulation of wave interactions and turbulence in one-dimensional water waves}},
volume = {63},
year = {2003}
}
@article{Berger1989,
abstract = {The aim of this work is the development of an automatic, adaptive mesh refinement strategy for solving hyperbolic conservation laws in two dimensions. There are two main difficulties in doing this. The first problem is due to the presence of discontinuities in the solution and the effect on them of discontinuities in the mesh. The second problem is how to organize the algorithm to minimize memory and CPU overhead. This is an important consideration and will continue to be important as more sophisticated algorithms that use data structures other than arrays are developed for use on vector and parallel computers.},
author = {Berger, M. J. and Colella, P.},
doi = {10.1016/0021-9991(89)90035-1},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {may},
number = {1},
pages = {64--84},
title = {{Local adaptive mesh refinement for shock hydrodynamics}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999189900351},
volume = {82},
year = {1989}
}
@article{Berger1984,
abstract = {An adaptive method based on the idea of multiple component grids for the solution of hyperbolic partial differential equations using finite difference techniques is presented. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. The approach is recursive in that fine grids can contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. We present the algorithm, error estimation procedure, and the data structures, and conclude with numerical examples in one and two space dimensions.},
author = {Berger, M. J. and Oliger, J.},
doi = {10.1016/0021-9991(84)90073-1},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {mar},
number = {3},
pages = {484--512},
title = {{Adaptive mesh refinement for hyperbolic partial differential equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999184900731},
volume = {53},
year = {1984}
}
@article{Berger1998,
abstract = {The standard two-dimensional shallow water equation formulation assumes a mild bed slope and no curvature effect. These assumptions limit the applicability of these equations for some important classes of problems. In particular, flow over a spillway is affected by the bed curvature via a decidedly non-hydrostatic pressure distribution. A detailed derivation of a more general equation set is given here in Part I. The method relies upon a perturbation expansion to simplify a bed-fitted co-ordinate configuration of the three-dimensional Euler equations. The resulting equations are essentially the equivalent of the two-dimensional shallow water equations but with curvature included and without the mild slope assumption. A finite element analysis and flume result are given in Part II.},
author = {Berger, R. C. and Carey, G. F.},
journal = {Int. J. Num. Meth. Fluids},
keywords = {curved surface,finite element,non-hydrostatic,s hallow water,spillway},
pages = {191--200},
title = {{Free-surface flow over curved surfaces: Part I: Perturbation analysis}},
volume = {28},
year = {1998}
}
@article{Berkooz1993,
author = {Berkooz, G. and Holmes, P. and Lumley, J. L.},
doi = {10.1146/annurev.fl.25.010193.002543},
issn = {0066-4189},
journal = {Ann. Rev. Fluid Mech.},
month = {jan},
number = {1},
pages = {539--575},
title = {{The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows}},
url = {http://www.annualreviews.org/doi/abs/10.1146/annurev.fl.25.010193.002543},
volume = {25},
year = {1993}
}
@article{Bermudez1998,
author = {Bermudez, A. and Dervieux, A. and Desideri, J.-A. and Vazquez, M. E.},
journal = {Computer Methods in Applied Mechanics and Engineering},
pages = {49--72},
title = {{Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes}},
volume = {155},
year = {1998}
}
@article{Bernard2007,
abstract = {Tsunamis are an ever-present threat to lives and property along the coasts of most of the world's oceans. The Sumatra tsunami of 26 December 2004, which killed over 230,000 people, compels us to be more proactive in developing ways to reduce tsunami impact on our global society. Since 1997, the United States has used a joint state/federal partnership to reduce tsunami hazards along US coastlines - the National Tsunami Hazard Mitigation Program. By integrating hazard assessment, warning guidance and mitigation activities, the program has created a roadmap and a set of tools to make communities more resilient to local and distant tsunamis. Among the tools are forecasting, educational programs, and design guidance for communities to become tsunami resilient. This article focuses on the technology required to produce accurate, reliable tsunami forecasts.},
author = {Bernard, E. N. and Titov, V. V.},
journal = {Mar. Technol. Soc. J.},
pages = {23--26},
title = {{Improving tsunami forecast skill using deep ocean observations}},
volume = {40(4)},
year = {2007}
}
@article{Berry,
author = {Berry, M. V.},
journal = {Proc. R. Soc. A},
pages = {3055--3071},
title = {{Focused tsunami waves}},
volume = {463},
year = {2007}
}
@article{Berthe2004,
author = {Berth{\'{e}}, V. and Tijdeman, R.},
doi = {10.1016/j.tcs.2004.02.016},
issn = {03043975},
journal = {Theoretical Computer Science},
month = {jun},
number = {1-3},
pages = {177--202},
title = {{Lattices and multi-dimensional words}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S030439750400101X},
volume = {319},
year = {2004}
}
@article{Berthe2000,
abstract = {We study a two-dimensional generalization of Sturmian sequences corresponding to an approximation of a plane: these sequences are defined on a three-letter alphabet and code a two-dimensional tiling obtained by projecting a discrete plane. We show that these sequences code a Z2-action generated by two rotations on the unit circle. We first deduce a new way of computing the rectangle complexity function. Then we provide an upper bound on the number of frequencies of rectangular factors of given size.},
author = {Berth{\'{e}}, V. and Vuillon, L.},
doi = {10.1016/S0012-365X(00)00039-X},
issn = {0012365X},
journal = {Discrete Mathematics},
keywords = {Combinatorics on words,Discrete plane,Generalized Sturmian sequences,Symbolic dynamics},
month = {aug},
number = {1-3},
pages = {27--53},
title = {{Tilings and rotations on the torus: a two-dimensional generalization of Sturmian sequences}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0012365X0000039X},
volume = {223},
year = {2000}
}
@phdthesis{Berthet-Rambaud2004,
author = {Berthet-Rambaud, Ph.},
school = {Universit$\backslash$'e Joseph Fourier},
title = {{Structures rigides soumises aux avalanches et chutes de blocs: mod{\{}{\'{e}}{\}}lisation du comportement m{\{}{\'{e}}{\}}canique et caract{\{}{\`{e}}{\}}risation de l'interaction ''ph{\{}{\'{e}}{\}}nom{\{}{\`{e}}{\}}ne-ouvrage''}},
year = {2004}
}
@phdthesis{Berthet-Rambaud2004,
author = {Berthet-Rambaud, Ph.},
school = {Universit$\backslash$'e Joseph Fourier},
title = {{Structures rigides soumises aux avalanches et chutes de blocs: mod{\'{e}}lisation du comportement m{\'{e}}canique et caract{\`{e}}risation de l'interaction ''ph{\'{e}}nom{\`{e}}ne-ouvrage''}},
year = {2004}
}
@article{Bespalov1966,
author = {Bespalov, V. I. and Talanov, V. I.},
journal = {JETP Lett.},
pages = {307},
title = {{Filamentary Structure of Light Beams in Nonlinear Liquids}},
volume = {3},
year = {1966}
}
@article{Bestion1990,
author = {Bestion, D.},
journal = {Nuclear Engineering and Design},
pages = {229--245},
title = {{The physical closure laws in the CATHARE code}},
volume = {124},
year = {1990}
}
@article{Bestion2005,
author = {Bestion, D. and Guelfi, A.},
journal = {Nuclear Engineering and Technology},
pages = {511--524},
title = {{Status and perspective of two-phase flow modelling in the NEPTUNE multi-scale thermal-hydraulic platform for nuclear reactor simulation}},
volume = {37(6)},
year = {2005}
}
@article{Bhat2006,
author = {Bhat, H. S. and Fetecau, R. C.},
doi = {10.1007/s00332-005-0712-7},
issn = {0938-8974},
journal = {J. Nonlinear Sci.},
month = {dec},
number = {6},
pages = {615--638},
title = {{A Hamiltonian Regularization of the Burgers Equation}},
url = {http://link.springer.com/10.1007/s00332-005-0712-7},
volume = {16},
year = {2006}
}
@article{Bhat2007,
author = {Bhat, H. S. and Fetecau, R. C. and Goodman, J.},
doi = {10.1088/0951-7715/20/9/001},
issn = {0951-7715},
journal = {Nonlinearity},
month = {sep},
number = {9},
pages = {2035--2046},
title = {{A Leray-type regularization for the isentropic Euler equations}},
url = {http://stacks.iop.org/0951-7715/20/i=9/a=001?key=crossref.7398ebdbe4fd304b2789d00ce255d6ad},
volume = {20},
year = {2007}
}
@article{Bianchini2005,
author = {Bianchini, S. and Bressan, A.},
journal = {Annals of Mathematics},
number = {1},
pages = {223--342},
title = {{Vanishing Viscosity Solutions of Nonlinear Hyperbolic Systems}},
volume = {161},
year = {2005}
}
@article{Bibikov2009,
abstract = {The free scalar field is studied on the Y-junction of three semi-infinite axes which is the simplest example of a non-manifold space. It is shown that the transition rules for this system uniquely follow from conservation of energy and charge. A discrete version of the model gives the same result.},
author = {Bibikov, P. N. and Prokhorov, L. V.},
doi = {10.1088/1751-8113/42/4/045302},
issn = {1751-8113},
journal = {J. Phys. A: Math. Gen},
month = {jan},
number = {4},
pages = {045302},
title = {{Mechanics not on a manifold}},
url = {http://stacks.iop.org/1751-8121/42/i=4/a=045302?key=crossref.40fba2fc28c5634ec0b0e9c45e15ad05},
volume = {42},
year = {2009}
}
@article{Bilham2005,
author = {Bilham, R.},
journal = {Science},
pages = {1126--1127},
title = {{A flying start, then a slow slip}},
volume = {308},
year = {2005}
}
@book{Billingham2001,
address = {Cambridge},
author = {Billingham, J. and King, A.},
editor = {Billingham, J. and King, A.},
publisher = {Cambridge University Press},
title = {{Wave motion}},
year = {2001}
}
@article{Birman2005,
author = {Birman, V. K. and Martin, J. E. and Meiburg, E.},
journal = {J. Fluid Mech.},
pages = {125--144},
title = {{The non-Boussinesq lock-exchange problem. Part 2. High-resolution simulations}},
volume = {537},
year = {2005}
}
@article{Blagovechshenskiy2002,
author = {Blagovechshenskiy, V. and Eglit, M. and Naaim, M.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {217--220},
title = {{The calibration of an avalanche mathematical model using field data}},
volume = {2},
year = {2002}
}
@article{Blaise2000,
author = {Blaise, N. and Debiane, K. and Piau, J.-M.},
journal = {J. Hydr. Res.},
title = {{Bed slope effect on the dam break problem}},
volume = {38(6)},
year = {2000}
}
@book{BleisHandel,
author = {Bleistein, N. and Handelsman, R. A.},
isbn = {0486650820},
publisher = {Courier Dover Publications},
title = {{Asymptotic Expansions of Integrals}},
year = {1986}
}
@book{Boccotti2000,
address = {Oxford},
author = {Boccotti, P.},
pages = {496},
publisher = {Elsevier Sciences},
title = {{Wave Mechanics for Ocean Engineering}},
year = {2000}
}
@article{Bogacki1989,
author = {Bogacki, P. and Shampine, L. F.},
journal = {Appl. Math. Lett.},
pages = {321--325},
title = {{A 3(2) pair of Runge-Kutta formulas}},
volume = {2(4)},
year = {1989}
}
@article{Boger2015,
author = {Boger, M. and Jaegle, F. and Klein, R. and Munz, C. D.},
doi = {10.1002/mma.3081},
issn = {01704214},
journal = {Math. Meth. Appl. Sci.},
month = {feb},
number = {3},
pages = {458--477},
title = {{Coupling of compressible and incompressible flow regions using the multiple pressure variables approach}},
url = {http://doi.wiley.com/10.1002/mma.3081},
volume = {38},
year = {2015}
}
@article{Bogolubsky1977,
abstract = {An analogue of the Boussinesq equation is presented which is exact for ion-sound (s) waves in the linear limit and which is correct in the sense of the Cauchy problem. This equation can be used to study by computer the dynamics of various wave processes when weak nonlinearities and dispersive effects are taken into account. An equation is obtained to describe the hydrodynamic velocity of small amplitude s-waves. Properties of solitons and processes of their formation are investigated analytically and by computer. It is demonstrated that soliton interactions described by these equations are inelastic and that the coefficient of inelasticity increases with an increase of amplitude of the interacting solitons.},
author = {Bogolubsky, I. L.},
doi = {10.1016/0010-4655(77)90009-1},
issn = {00104655},
journal = {Computer Physics Communications},
month = {sep},
number = {3},
pages = {149--155},
title = {{Some examples of inelastic soliton interaction}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0010465577900091},
volume = {13},
year = {1977}
}
@article{Bohorquez2010,
author = {Bohorquez, P. and Rentschler, M.},
doi = {10.1007/s10915-010-9444-4},
issn = {0885-7474},
journal = {J. Sci. Comput.},
month = {dec},
number = {1-3},
pages = {3--15},
title = {{Hydrodynamic Instabilities in Well-Balanced Finite Volume Schemes for Frictional Shallow Water Equations. The Kinematic Wave Case}},
url = {http://link.springer.com/10.1007/s10915-010-9444-4},
volume = {48},
year = {2010}
}
@article{Bohr1920,
author = {Bohr, N.},
doi = {10.1007/BF01329978},
issn = {1434-6001},
journal = {Zeitschrift f{\"{u}}r Physik},
month = {oct},
number = {5},
pages = {423--469},
title = {{{\"{U}}ber die Serienspektra der Element}},
url = {http://link.springer.com/10.1007/BF01329978},
volume = {2},
year = {1920}
}
@article{Bookhove2005,
author = {Bokhove, O.},
journal = {J. Sci. Comput.},
pages = {47--82},
title = {{Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations of Shallow-Water Equations. Part 1: One Dimension}},
volume = {22-23},
year = {2005}
}
@book{Bolibrukh2002,
address = {Moscow},
author = {Bolibrukh, A. A.},
pages = {24},
publisher = {MCCME},
title = {{Maxwell equations and differential forms}},
year = {2002}
}
@article{Bona1975,
abstract = {Improvements are made on the theory for the stability of solitary waves developed by T. B. Benjamin. The results apply equally to the Kortewegde Vries equation and to an alternative model equation for the propagation of long waves in nonlinear dispersive media.},
author = {Bona, J. L.},
doi = {10.1098/rspa.1975.0106},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A A},
month = {jul},
number = {1638},
pages = {363--374},
title = {{On the Stability Theory of Solitary Waves}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1975.0106},
volume = {344},
year = {1975}
}
@article{Bona1980a,
author = {Bona, J. L.},
journal = {Fluid Dynam. Trans.},
pages = {77--111},
title = {{Solitary waves and other phenomena associated with model equations for long waves}},
volume = {10},
year = {1980}
}
@article{Bona2008,
author = {Bona, J. L. and Cascaval, R.},
journal = {Canadian Applied Mathematics Quarterly},
number = {1},
pages = {1--18},
title = {{Nonlinear dispersive waves on trees}},
volume = {16},
year = {2008}
}
@article{BC,
author = {Bona, J. L. and Chen, M.},
journal = {Physica D},
pages = {191--224},
title = {{A Boussinesq system for two-way propagation of nonlinear dispersive waves}},
volume = {116},
year = {1998}
}
@article{BCS,
author = {Bona, J. L. and Chen, M. and Saut, J.-C.},
journal = {J. Nonlinear Sci.},
pages = {283--318},
title = {{Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory}},
volume = {12},
year = {2002}
}
@article{Bona2004,
author = {Bona, J. L. and Chen, M. and Saut, J.-C.},
journal = {Nonlinearity},
pages = {925--952},
title = {{Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory}},
volume = {17},
year = {2004}
}
@article{BCL,
author = {Bona, J. L. and Colin, T. and Lannes, D.},
journal = {Arch. Rational Mech. Anal.},
pages = {373--410},
title = {{Long wave approximations for water waves}},
volume = {178},
year = {2005}
}
@article{BoDo,
author = {Bona, J. L. and Dougalis, V. A.},
journal = {J. Math. Anal. and Applics.},
pages = {503--522},
title = {{An initial- and boundary value problem for a model equation for propagation of long waves}},
volume = {75},
year = {1980}
}
@article{BDKM1995,
author = {Bona, J. L. and Dougalis, V. A. and Karakashian, O. A. and McKinney, W. R.},
journal = {Philos. Trans. Royal Soc. London A},
pages = {107--164},
title = {{Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation}},
volume = {351},
year = {1995}
}
@article{BDKMc,
author = {Bona, J. L. and Dougalis, V. A. and Karakashian, O. A. and McKinney, W. R.},
journal = {Phil. Trans. R. Soc. London A},
pages = {107--164},
title = {{Conservative high-order numerical schemes for the generalized Korteweg-deVries equation}},
volume = {351},
year = {1995}
}
@article{BDM2,
author = {Bona, J. L. and Dougalis, V. A. and Mitsotakis, D. E.},
journal = {Nonlinearity},
pages = {2825--2848},
title = {{Numerical solution of Boussinesq systems of KdV-KdV type II. Evolution of radiating solitary waves}},
volume = {21},
year = {2008}
}
@article{Bona2007,
author = {Bona, J. L. and Dougalis, V. A. and Mitsotakis, D. E.},
journal = {Mat. Comp. Simul.},
pages = {214--228},
title = {{Numerical solution of KdV-KdV systems of Boussinesq equations: I. The numerical scheme and generalized solitary waves}},
volume = {74},
year = {2007}
}
@article{Bona1985,
author = {Bona, J. L. and Pritchard, W. G. and Scott, L. R.},
journal = {J. Comput. Phys.},
pages = {167--186},
title = {{Numerical schemes for a model for nonlinear dispersive waves}},
volume = {60},
year = {1985}
}
@article{Bona1981,
author = {Bona, J. L. and Pritchard, W. G. and Scott, L. R.},
journal = {Phil. Trans. R. Soc. Lond. A},
pages = {457--510},
title = {{An Evaluation of a Model Equation for Water Waves}},
volume = {302},
year = {1981}
}
@article{Bona1980,
author = {Bona, J. L. and Pritchard, W. G. and Scott, L. R.},
journal = {Phys. Fluids},
pages = {438--441},
title = {{Solitary-wave interaction}},
volume = {23},
year = {1980}
}
@article{BS,
author = {Bona, J. L. and Smith, R.},
journal = {Math. Proc. Camb. Phil. Soc.},
pages = {167--182},
title = {{A model for the two-way propagation of water waves in a channel}},
volume = {79},
year = {1976}
}
@article{Bona2009,
author = {Bona, J. L. and Tzvetkov, N.},
journal = {Discrete Contin. Dyn. Syst.},
pages = {1241--1252},
title = {{Sharp well-posedness results for the BBM equation}},
volume = {23},
year = {2009}
}
@article{Bona2005,
author = {Bona, J. L. and Varlamov, V.},
journal = {Nonlinear partial differential equations and related analysis},
pages = {41--71},
title = {{Wave generation by a moving boundary}},
volume = {371},
year = {2005}
}
@article{Bongolan-Walsh2007,
author = {Bo{\~{n}}golan-Walsh, V. P. and Duan, J. and Fischer, P. and {\"{O}}zg{\"{o}}kmen, T. and Iliescu, T.},
journal = {Applied Mathematical Modelling},
pages = {1338--1350},
title = {{Impact of boundary conditions on entrainment and transport in gravity currents}},
volume = {31},
year = {2007}
}
@article{BCLMT2010,
author = {Bonneton, P. and Chazel, F. and Lannes, D. and Marche, F. and Tissier, M.},
journal = {J. Comp. Phys.},
pages = {1479--1498},
title = {{A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model}},
volume = {230},
year = {2010}
}
@article{Bonneton2011,
author = {Bonneton, P. and Chazel, F. and Lannes, D. and Marche, F. and Tissier, M.},
journal = {J. Comput. Phys.},
pages = {1479--1498},
title = {{A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model}},
volume = {230},
year = {2011}
}
@article{Boris1992,
author = {Boris, J. P.},
journal = {Fluid Dynamics Research},
pages = {199--229},
title = {{New insights into Large Eddy Simulations}},
volume = {10},
year = {1992}
}
@article{Boris1973,
author = {Boris, J. P. and Book, D. L.},
journal = {J. Comp. Phys.},
pages = {38--69},
title = {{Flux corrected transport: Shasta, a fluid transport algorithm that works}},
volume = {11},
year = {1973}
}
@book{Borisenko1979,
address = {New York},
author = {Borisenko, A. I. and Tarapov, I. E.},
isbn = {978-0486638331},
pages = {288},
publisher = {Dover Publications},
title = {{Vector and Tensor Analysis with Applications}},
year = {1979}
}
@article{Borrero2006,
author = {Borrero, J. C. and Uslu, B. and Synolakis, C. E. and Titov, V. V.},
doi = {10.1142/9789812709554{\_}0133},
journal = {Coastal Engineering},
pages = {1566--1578},
title = {{Modeling far field tsunamis for California Ports and Harbors}},
year = {2006}
}
@article{Borsche2014,
abstract = {In this article we present a method to extend high order finite volume schemes to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if stated by the coupling conditions. Several numerical examples confirm the benefits of a high order coupling procedure for high order accuracy and stable shock capturing.},
author = {Borsche, R. and Kall, J.},
doi = {10.1016/j.jcp.2014.05.042},
issn = {00219991},
journal = {J. Comp. Phys.},
keywords = {ADER,Coupling,Generalized Riemann problem,Hyperbolic conservation law,Network,WENO},
month = {sep},
pages = {658--670},
title = {{ADER schemes and high order coupling on networks of hyperbolic conservation laws}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999114004070},
volume = {273},
year = {2014}
}
@article{Bouche2003,
author = {Bouche, D. and Bonnaud, G. and Ramos, D.},
doi = {10.1016/S0893-9659(03)80024-1},
issn = {08939659},
journal = {Applied Mathematics Letters},
month = {feb},
number = {2},
pages = {147--154},
title = {{Comparison of numerical schemes for solving the advection equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0893965903800241},
volume = {16},
year = {2003}
}
@article{Bouchut2003,
author = {Bouchut, F. and Mangeney-Castelnau, A. and Perthame, B. and Vilotte, J.-P.},
journal = {C. R. Acad. Sci. Paris I},
pages = {531--536},
title = {{A new model of Saint-Venant and Savage-Hutter type for gravity driven shallow water flows}},
volume = {336},
year = {2003}
}
@phdthesis{Boucker1998,
author = {Boucker, M.},
school = {ENS-Cachan},
title = {{Mod{\'{e}}lisation num{\'{e}}rique multidimensionnelle d'{\'{e}}coulements diphasiques liquide-gaz en r{\'{e}}gimes transitoires et permanents : m{\'{e}}thodes et applications}},
year = {1998}
}
@article{Bourdarias2007,
abstract = {We present a one-dimensional model for compressible flows in a deformable pipe which is an alternative to the Allievi equations and is intended to be coupled in a "natural way" with the shallow water equations to simulate mixed flows. The numerical simulation is performed using a second-order linearly implicit scheme adapted from the Roe scheme. The validation is performed in the case of water hammer in a rigid pipe: we compare the numerical results provided by an industrial code with those of our spatial second-order implicit scheme. It appears that the maximum value of the pressure within the pipe for large CFL numbers and a coarse discretisation is accurately computed.},
author = {Bourdarias, C. and Gerbi, S.},
doi = {10.1016/j.compfluid.2007.09.007},
issn = {00457930},
journal = {Comput. {\&} Fluids},
month = {dec},
number = {10},
pages = {1225--1237},
title = {{A conservative model for unsteady flows in deformable closed pipes and its implicit second-order finite volume discretisation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0045793008000042},
volume = {37},
year = {2008}
}
@article{Bourdarias2007a,
author = {Bourdarias, C. and Gerbi, S.},
journal = {J. Comp. Appl. Math.},
number = {1},
pages = {109--131},
title = {{A finite volume scheme for a model coupling free surface and pressurised flows in pipes}},
volume = {209},
year = {2007}
}
@inbook{Boure1982,
author = {Boure, J. A. and Delhaye, J.-M.},
chapter = {General eq},
editor = {Hestroni, G},
publisher = {Hemisphere},
title = {{Handbook of Multiphase Systems}},
year = {1982}
}
@article{Boussinesq1871,
author = {Boussinesq, J. V.},
journal = {C. R. Acad. Sc. Paris},
pages = {256--260},
title = {{Th{\'{e}}orie g{\'{e}}n{\'{e}}rale des mouvements qui sont propag{\'{e}}s dans un canal rectangulaire horizontal}},
volume = {73},
year = {1871}
}
@article{Boussinesq1872,
author = {Boussinesq, J. V.},
journal = {J. Math. Pures Appl.},
pages = {55--108},
title = {{Th{\'{e}}orie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond}},
volume = {17},
year = {1872}
}
@article{Boussinesq1877,
author = {Boussinesq, J. V.},
journal = {M{\'{e}}moires pr{\'{e}}sent{\'{e}}s par divers savants {\`{a}} l'Acad. des Sci. Inst. Nat. France},
pages = {1--680},
title = {{Essai sur la theorie des eaux courantes}},
volume = {XXIII},
year = {1877}
}
@article{Boussinesq1895,
author = {Boussinesq, J. V.},
journal = {C. R. Acad. Sci. Paris},
pages = {15--20},
title = {{Lois de l'extinction de la houle en haute mer}},
volume = {121},
year = {1895}
}
@article{bouss,
author = {Boussinesq, J. V.},
journal = {C.R. Acad. Sci. Paris S{\'{e}}r. A-B},
pages = {755--759},
title = {{Th{\'{e}}orie de l'intumescence liquide appel{\'{e}}e onde solitaire ou de translation se propageant dans un canal rectangulaire}},
volume = {72},
year = {1871}
}
@phdthesis{Boutin2009,
abstract = {This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization {\`{a}} la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in {\$}L{\^{}}\backslashinfty{\$}. The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples.},
author = {Boutin, B.},
keywords = {Dafermos regularization,coupling of equations,finite volume methods,hyperbolic equations,nonclassical solutions,resonance},
pages = {290},
school = {Universit{\'{e}} Pierre et Marie Curie - Paris VI},
title = {{Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks}},
year = {2009}
}
@article{Boyd1997,
author = {Boyd, J. P.},
doi = {10.1016/0096-3003(95)00326-6},
issn = {00963003},
journal = {Applied Mathematics and Computation},
month = {feb},
number = {2-3},
pages = {173--187},
title = {{Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0096300395003266},
volume = {81},
year = {1997}
}
@article{Boyd2007,
author = {Boyd, J. P.},
doi = {10.1016/j.matcom.2006.10.001},
issn = {03784754},
journal = {Math. Comp. Simul.},
month = {mar},
number = {2-3},
pages = {72--81},
title = {{Why Newton's method is hard for travelling waves: Small denominators, KAM theory, Arnold's linear Fourier problem, non-uniqueness, constraints and erratic failure}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378475406002746},
volume = {74},
year = {2007}
}
@book{Boyd2000,
abstract = {Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more. Includes 7 appendices and over 160 text figures.},
address = {New York},
author = {Boyd, J. P.},
edition = {2nd},
editor = {{Dover Publications}},
pages = {688},
title = {{Chebyshev and Fourier Spectral Methods}},
year = {2000}
}
@article{Boyd2002a,
author = {Boyd, J. P.},
journal = {J. Comput. Phys.},
pages = {118--160},
title = {{A comparison of numerical algorithms for Fourier extension of the first, second and third kinds}},
volume = {178},
year = {2002}
}
@article{Boyd1986,
author = {Boyd, J. P.},
journal = {Physica D},
pages = {227--246},
title = {{Solitons from sine waves: analytical and numerical methods for non-integrable solitary and cnoidal waves}},
volume = {21},
year = {1986}
}
@article{Boyd2002b,
author = {Boyd, J. P.},
journal = {J. Comput. Phys.},
pages = {216--237},
title = {{Deleted residuals, the QR-factored Newton iteration, and other methods for formally overdetermined determinate discretizations of nonlinear eigenproblems for solitary, cnoidal, and shock waves}},
volume = {179},
year = {2002}
}
@techreport{Bozhinskiy1998,
author = {Bozhinskiy, N. and Losev, K. S.},
institution = {EISFL, Davos},
title = {{The fundamentals of avalanche science}},
year = {1998}
}
@article{bradd,
author = {Braddock, R. D. and van den Driessche, P. and Peady, G. W.},
journal = {J. Fluid Mech.},
number = {4},
pages = {817--828},
title = {{Tsunamis generation}},
volume = {59},
year = {1973}
}
@article{Bradford1999,
abstract = {A mathematical model is developed for unsteady, two-dimensional, single-layer, depth-averaged turbid underflows driven by nonuniform, noncohesive sediment. The numerical solution is obtained by a high-resolution, total variation diminishing, finite-volume numerical model, which is known to capture sharp fronts accurately. The monotone upstream scheme for conservation laws is used in conjunction with predictor-corrector time-stepping to provide a second-order accurate solution. Flux-limiting is implemented to prevent the development of spurious oscillations near discontinuities. The model also possesses the capability to track the evolution and development of an erodible bed, due to sediment entrainment and deposition. This is accomplished by solving a bed-sediment conservation equation at each time step, independent of the hydrodynamic equations, with a predictor-corrector method. The model is verified by comparison to experimental data for currents driven by uniform and nonuniform sediment.},
author = {Bradford, S. F. and Katopodes, N. D.},
doi = {10.1061/(ASCE)0733-9429(1999)125:10(1006)},
issn = {07339429},
journal = {Journal of Hydraulic Engineering},
number = {10},
pages = {1006--1015},
title = {{Hydrodynamics of Turbid Underflows. I: Formulation and Numerical Analysis}},
url = {http://link.aip.org/link/JHEND8/v125/i10/p1006/s1{\&}Agg=doi},
volume = {125},
year = {1999}
}
@article{Bradshaw1967,
author = {Bradshaw, P. and Ferriss, D. H. and Atwell, N. P.},
doi = {10.1017/S0022112067002319},
issn = {00221120},
journal = {Journal of Fluid Mechanics},
number = {03},
pages = {593--616},
title = {{Calculation of boundary-layer development using the turbulent energy equation}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112067002319},
volume = {28},
year = {1967}
}
@inproceedings{Braeunig2009,
address = {Osaka, Japan},
author = {Braeunig, J. P. and Brosset, L. and Dias, F. and Ghidaglia, J.-M.},
booktitle = {Proceedings of the 19th International Offshore and Polar Engineering Conference (ISOPE)},
title = {{Phenomenological Study of Liquid Impacts through 2D Compressible Two-fluid Numerical Simulations}},
year = {2009}
}
@book{Brebbia1984,
address = {Berlin and New York},
author = {Brebbia, C. A. and Telles, J. C. F. and Wrobel, L. C.},
isbn = {0387124845},
keywords = {Boundary element methods,Engineering mathematics},
pages = {464},
publisher = {Springer-Verlag},
title = {{Boundary element techniques: Theory and applications in engineering}},
year = {1984}
}
@techreport{Bredmose2005,
author = {Bredmose, H.},
title = {{Flair: A finite volume solver for aerated flows}},
year = {2005}
}
@article{Bredmose2009,
author = {Bredmose, H. and Peregrine, D. H. and Bullock, G. N.},
journal = {J. Fluid Mech},
pages = {389--430},
title = {{Violent breaking wave impacts. Part 2: modelling the effect of air}},
volume = {641},
year = {2009}
}
@inproceedings{Bredmose1,
author = {Bredmose, H. and Peregrine, D. H. and Bullock, G. N. and Obhrai, C. and Muller, G. and Wolters, G.},
booktitle = {Int. Workshop on Water Waves and Floating Bodies, Cortona, Italy},
title = {{Extreme wave impact pressures and the effect of aeration}},
year = {2004}
}
@article{Brenier1998,
abstract = {Multivalued solutions with a limited number of branches of the inviscid Burgers equation can be obtained by solving closed systems of moment equations. For this purpose, a suitable concept of entropy multivalued solutions with K branches is introduced.},
author = {Brenier, Y. and Corrias, L.},
doi = {10.1016/S0294-1449(97)89298-0},
issn = {02941449},
journal = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
month = {mar},
number = {2},
pages = {169--190},
title = {{A kinetic formulation for multi-branch entropy solutions of scalar conservation laws}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0294144997892980},
volume = {15},
year = {1998}
}
@article{Brenier2000,
author = {Brenier, Y. and Levy, D.},
doi = {10.1016/S0167-2789(99)00190-6},
journal = {Physica D},
number = {3-4},
pages = {277--294},
title = {{Dissipative behavior of some fully non-linear KdV-type of equations}},
volume = {137},
year = {2000}
}
@article{Brenner2005a,
author = {Brenner, H.},
journal = {Physica A},
pages = {60--132},
title = {{Navier-Stokes revisited}},
volume = {349},
year = {2005}
}
@article{Brenner2005,
author = {Brenner, H.},
journal = {Physica A},
pages = {11--59},
title = {{Kinematics of volume transport}},
volume = {349},
year = {2005}
}
@article{Brenner2006,
author = {Brenner, H.},
journal = {Physica A},
pages = {190--224},
title = {{Fluid mechanics revisited}},
volume = {370},
year = {2006}
}
@article{Bresch2007a,
author = {Bresch, D. and Desjardins, B.},
journal = {Journal de Math{\'{e}}matiques Pures et Appliqu{\'{e}}s},
number = {1},
pages = {57--90},
title = {{On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids}},
volume = {87},
year = {2007}
}
@article{Bresch2003,
author = {Bresch, D. and Desjardins, B.},
journal = {Communications in Mathematical Physics},
pages = {211--223},
title = {{Existence of Global Weak Solutions for a 2D Viscous Shallow Water Equations and Convergence to the Quasi-Geostrophic Model}},
volume = {238},
year = {2003}
}
@article{Bresch2006,
author = {Bresch, D. and Desjardins, B.},
journal = {Journal de Math{\'{e}}matiques Pures et Appliqu{\'{e}}es},
pages = {362--368},
title = {{On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier-Stokes models}},
volume = {86(4)},
year = {2006}
}
@article{Bresch2007b,
author = {Bresch, D. and Desjardins, B. and G{\'{e}}rard-Varet, D.},
journal = {J. Math. Pures Appl.},
number = {2},
pages = {227--235},
title = {{On compressible Navier-Stokes equations with density dependent viscosities in bounded domains}},
volume = {87},
year = {2007}
}
@article{Bresch2008,
author = {Bresch, D. and Desjardins, B. and Ghidaglia, J.-M. and Grenier, E.},
journal = {To appear in Archive for Rational Mechanics and Analysis},
title = {{On global weak solutions to a generic two-fluid model}},
year = {2009}
}
@article{Bresch2007,
author = {Bresch, D. and Desjardins, B. and Ghidaglia, J.-M. and Grenier, E.},
journal = {In preparation},
title = {{Mathematical properties of the basic two fluid model}},
year = {2007}
}
@article{Bresch2003a,
author = {Bresch, D. and Desjardins, B. and Lin, C.-K.},
journal = {Communications in Partial Differential Equations},
pages = {843--868},
title = {{On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems}},
volume = {28},
year = {2003}
}
@article{Bresch2002,
author = {Bresch, D. and Essoufi, E. and Sy, M.},
journal = {C.R. Acad. Sci. Paris Ser. I},
pages = {973--978},
title = {{Some new Kazhikhov-Smagulov type systems: pollutant spread and low Mach number combustion models}},
volume = {335},
year = {2002}
}
@article{Bresch2007c,
author = {Bresch, D. and Essoufi, E. and Sy, M.},
journal = {J. Math. Fluid Mech.},
pages = {377--397},
title = {{Effect of Density Dependent Viscosities on Multiphasic Incompressible Fluid Models}},
volume = {9},
year = {2007}
}
@article{Noble2007,
author = {Bresch, D. and Noble, P.},
journal = {Submitted},
title = {{Mathematical justification of a shallow water model}},
year = {2007}
}
@techreport{Bressan2009,
address = {State College, PA},
author = {Bressan, A.},
institution = {Penn State University},
pages = {84},
title = {{Lecture Notes on Hyperbolic Conservation Laws}},
url = {http://php.math.unifi.it/users/cimeCourses/2009/01/200912-Notes.pdf},
year = {2009}
}
@article{Bressan2014,
abstract = {The broad research thematic of flows on networks was addressed in recent years by many researchers, in the area of applied mathematics, with new models based on partial differential equations. The latter brought a significant innovation in a field previously dominated by more classical techniques from discrete mathematics or methods based on ordinary differential equations. In particular, a number of results, mainly dealing with vehicular traffic, supply chains and data networks, were collected in two monographs: Traffic flow on networks, AIMSciences, Springfield, 2006, and Modeling, simulation, and optimization of supply chains, SIAM, Philadelphia, 2010. The field continues to flourish and a considerable number of papers devoted to the subject is published every year, also because of the wide and increasing range of applications: from blood flow to air traffic management. The aim of the present survey paper is to provide a view on a large number of themes, results and applications related to this broad research direction. The authors cover different expertise (modeling, analysis, numeric, optimization and other) so to provide an overview as extensive as possible. The focus is mainly on developments which appeared subsequently to the publication of the aforementioned books.},
author = {Bressan, A. and Cani{\'{c}}, S. and Garavello, M. and Herty, M. and Piccoli, B.},
doi = {10.4171/EMSS/2},
issn = {2308-2151},
journal = {EMS Surveys in Mathematical Sciences},
keywords = {Networks,balance laws,control problems},
number = {1},
pages = {47--111},
title = {{Flows on networks: recent results and perspectives}},
url = {http://www.ems-ph.org/doi/10.4171/EMSS/2},
volume = {1},
year = {2014}
}
@article{Bretti2007,
abstract = {We introduce a simulation algorithm based on a fluid-dynamic model for traffic flows on road networks, which are considered as graphs composed by arcs that meet at some junctions. The approximation of scalar conservation laws along arcs is made by three velocities Kinetic schemes with suitable boundary conditions at junctions. Here we describe the algorithm and we give an example.},
author = {Bretti, G. and Natalini, R. and Piccoli, B.},
doi = {10.1016/j.cam.2006.10.057},
issn = {03770427},
journal = {J. Comp. Appl. Math.},
keywords = {Boundary conditions,Finite difference schemes,Fluid-dynamic models,Scalar conservation laws,Traffic flow},
month = {dec},
number = {1-2},
pages = {71--77},
title = {{Numerical algorithms for simulations of a traffic model on road networks}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377042706006492},
volume = {210},
year = {2007}
}
@article{Breuss2004,
abstract = {We discuss the numerical stability of the classical Lax-Friedrichs method. The scheme features well-established properties, especially it is TVD and monotone. However, it turns out that oscillations can occur at data extrema which seems to be in severe contrast to the large numerical diffusion the scheme exhibits. We briefly explain the phenomenon by use of a simple model problem and we give a short theoretical discussion.},
author = {Breuss, M.},
doi = {10.1002/pamm.200410299},
issn = {1617-7061},
journal = {PAMM},
month = {dec},
number = {1},
pages = {636--637},
title = {{About the Lax-Friedrichs scheme for the numerical approximation of hyperbolic conservation laws}},
url = {http://doi.wiley.com/10.1002/pamm.200410299},
volume = {4},
year = {2004}
}
@article{Bridges1997,
abstract = {A Hamiltonian structure is presented, which generalizes classical Hamiltonian structure, by assigning a distinct symplectic operator for each unbounded space direction and time, of a Hamiltonian evolution equation on one or more space dimensions. This generalization, called multi-symplectic structures, is shown to be natural for dispersive wave propagation problems. Application of the abstract properties of the multi-symplectic structures framework leads to a new variational principle for space-time periodic states reminiscent of the variational principle for invariant tori, a geometric reformulation of the concepts of action and action flux, a rigorous proof of the instability criterion predicted by the Whitham modulation equations, a new symplectic decomposition of the Noether theory, generalization of the concept of reversibility to space-time and a proof of Lighthill's geometric criterion for instability of periodic waves travelling in one space dimension. The nonlinear Schr{\"{o}}dinger equation and the water-wave problem are characterized as Hamiltonian systems on a multi-symplectic structure for example. Further ramifications of the generalized symplectic structure of theoretical and practical interest are also discussed.},
author = {Bridges, T. J.},
doi = {10.1017/S0305004196001429},
issn = {03050041},
journal = {Math. Proc. Camb. Phil. Soc.},
month = {jan},
number = {1},
pages = {147--190},
title = {{Multi-symplectic structures and wave propagation}},
url = {http://www.journals.cambridge.org/abstract{\_}S0305004196001429},
volume = {121},
year = {1997}
}
@article{Bridges1996,
author = {Bridges, T. J.},
journal = {Phil. Trans. Royal Soc. London A},
pages = {533--574},
title = {{Periodic patterns, linear instability, symplectic structure and mean-flow dynamics for three-dimensional surface waves}},
volume = {354},
year = {1996}
}
@article{Bridges2002,
author = {Bridges, T. J. and Derks, G. and Gottwald, G.},
doi = {10.1016/S0167-2789(02)00655-3},
issn = {01672789},
journal = {Phys. D},
month = {nov},
number = {1-4},
pages = {190--216},
title = {{Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278902006553},
volume = {172},
year = {2002}
}
@article{Bridges2007,
author = {Bridges, T. J. and Dias, F.},
journal = {Phys. Fluids},
pages = {104104},
title = {{Enhancement of the Benjamin-Feir instability with dissipation}},
volume = {19},
year = {2007}
}
@article{Bridges2010,
author = {Bridges, T. J. and Donaldson, N. M.},
doi = {10.1112/S0025579310001233},
issn = {0025-5793},
journal = {Mathematika},
month = {nov},
number = {01},
pages = {147--173},
title = {{Variational principles for water waves from the viewpoint of a time-dependent moving mesh}},
url = {http://www.journals.cambridge.org/abstract{\_}S0025579310001233},
volume = {57},
year = {2010}
}
@article{Bridges2005,
author = {Bridges, T. J. and Donaldson, N. M.},
doi = {10.1103/PhysRevLett.95.104301},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {sep},
number = {10},
pages = {104301},
title = {{Degenerate Periodic Orbits and Homoclinic Torus Bifurcation}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.95.104301},
volume = {95},
year = {2005}
}
@article{Bridges2001,
author = {Bridges, T. J. and Reich, S.},
doi = {10.1016/S0375-9601(01)00294-8},
journal = {Phys. Lett. A},
number = {4-5},
pages = {184--193},
title = {{Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity}},
volume = {284},
year = {2001}
}
@article{Bridges2006,
author = {Bridges, T. J. and Reich, S.},
journal = {J. Phys. A: Math. Gen},
pages = {5287--5320},
title = {{Numerical methods for Hamiltonian PDEs}},
volume = {39},
year = {2006}
}
@article{Brizard2009,
author = {Brizard, A. J.},
doi = {10.1088/1742-6596/169/1/01200},
journal = {Journal of Physics: Conference Series},
pages = {1--24},
title = {{Variational principles for reduced plasma physics}},
volume = {169},
year = {2009}
}
@article{Brocchini2013,
author = {Brocchini, M.},
doi = {10.1098/rspa.2013.0496},
issn = {1364-5021},
journal = {Proc. R. Soc. A},
month = {oct},
number = {2160},
pages = {20130496},
title = {{A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2013.0496},
volume = {469},
year = {2013}
}
@article{Brocchini2001,
author = {Brocchini, M. and Bernetti, R. and Mancinelli, A. and Albertini, G.},
journal = {Coastal Engineering},
pages = {105--129},
title = {{An efficient solver for nearshore flows based on the WAF method}},
volume = {43},
year = {2001}
}
@article{Brocchini1996,
author = {Brocchini, M. and Peregrine, D. H.},
journal = {J. Fluid Mech},
pages = {241--273},
title = {{Integral flow properties of the swash zone and averaging}},
volume = {317},
year = {1996}
}
@article{Broer1974,
abstract = {It is shown that the classical theory of gravity driven waves on the surface of a non-viscous liquid can be derived from a set nf canonical equations. Various approximate equations then can be found by introducing suitable approximations to the kinetic and potential energy functionals. The stability of these approximate equations then can be insured beforehand by using positive definite approximate energy functionals. For fairly long, fairly low waves a stable equation of Boussinesq type is derived in this way. This equation is also valid for waves which are not approximately simple.},
author = {Broer, L. J. F.},
journal = {Applied Sci. Res.},
pages = {430--446},
title = {{On the Hamiltonian theory of surface waves}},
volume = {29(6)},
year = {1974}
}
@article{Bronski2010,
author = {Bronski, J. C. and Johnson, M. A.},
doi = {10.1007/s00205-009-0270-5},
issn = {0003-9527},
journal = {Archive for Rational Mechanics and Analysis},
month = {dec},
number = {2},
pages = {357--400},
title = {{The Modulational Instability for a Generalized Korteweg-de Vries Equation}},
url = {http://link.springer.com/10.1007/s00205-009-0270-5},
volume = {197},
year = {2010}
}
@article{Bronski2011,
abstract = {We consider the stability of periodic travelling-wave solutions to a generalized Korteweg-de Vries (gKdV) equation and prove an index theorem relating the number of unstable and potentially unstable eigenvalues to geometric information on the classical mechanics of the travelling-wave ordinary differential equation. We illustrate this result with several examples, including the integrable KdV and modified KdV equations, the L2-critical KdV-4 equation that arises in the study of blow-up and the KdV-1/2 equation, which is an idealized model for plasmas.},
author = {Bronski, J. C. and Johnson, M. A. and Kapitula, T.},
doi = {10.1017/S0308210510001216},
issn = {0308-2105},
journal = {Proc. R. Soc. Edinburgh Sect. A},
month = {nov},
number = {06},
pages = {1141--1173},
title = {{An index theorem for the stability of periodic travelling waves of Korteweg-de Vries type}},
url = {http://www.journals.cambridge.org/abstract{\_}S0308210510001216},
volume = {141},
year = {2011}
}
@article{Brugnot1981,
author = {Brugnot, G. and Pochat, R.},
journal = {Journal of Glaciology},
pages = {77--88},
title = {{Numerical simulation study of avalanches}},
volume = {27},
year = {1981}
}
@inproceedings{Bruhl2014,
abstract = {Hydraulic model tests and numerical simulations show that long sinusoidal waves that are generated in very shallow waters are not stable but show modifications of the free surface as function of propagation in time and space. First, with increasing distance from the wave maker the wave becomes asymmetric and develops into a bore-shaped wave. Second, with further increasing distance more and more additional wave crests appear from the front of the bore (undular bore). The shallower the water depth, the more additional wave components can be observed. In extremely shallow water, the periodic sine waves completely disintegrate into periodic trains of solitons. At Leichtweiss-Institute for Hydraulic Engineering and Water Resources (LWI), TU Braunschweig, a nonlinear Fourier transform based on the Korteweg-deVries equation (KdV-NLFT) is implemented and successfully applied in Br{\"{u}}hl [1] that provides an explanation for this nonlinear phenomenon and allows the prediction of the dispersion and propagation of long sinusoidal waves in shallow water.},
address = {San Francisco, California, USA, June 8-13, 2014},
author = {Br{\"{u}}hl, M. and Oumeraci, H.},
booktitle = {Volume 8B: Ocean Engineering},
doi = {10.1115/OMAE2014-24165},
isbn = {978-0-7918-4551-6},
month = {jun},
pages = {V08BT06A040},
publisher = {ASME},
title = {{Analysis of Propagation of Long Waves in Shallow Water Using the KdV-Based Nonlinear Fourier Transform (KdV-NLFT)}},
year = {2014}
}
@article{Bruun1977,
author = {Bruun, P. and Gunb{\"{a}}k, A. R.},
journal = {Coastal Engineering},
pages = {287--322},
title = {{Stability of sloping structures in relation to $\backslash$xi = $\backslash$tan $\backslash$alpha/$\backslash$sqrt{\{}H/L{\_}0{\}} risk criteria in design}},
volume = {1},
year = {1977}
}
@techreport{Bruun1974,
author = {Bruun, P. and Johannesson, P.},
institution = {The Norwegian Institute of Technology Trondheim},
title = {{A critical review of the hydraulics of rubble mound structures}},
year = {1974}
}
@article{Bryn2005,
abstract = {The StoreggaSlide occurred 8200 years ago and was the last megaslide in this region where similar slides have occurred with intervals of approximately 100 ky since the onset of continental shelf glaciations at 0.5 Ma. A geological model for the Plio-Pleistocene of the area explains the large scale sliding as a response to climatic variability, and the seismic stratigraphy indicates that sliding occurs at the end of a glaciation or soon after the deglaciation. The slides are in general translational with the failure planes related to strain softening behaviour of marine clay layers. The destabilisation prior to the slide is related to rapid loading from glacial deposits with generation of excess pore pressure and reduction of the effective shear strength in the underlying clays. Basin modelling has shown that excess pore pressure generated in the North Sea Fan area is transferred to the Storegga area with reduction of the slope stability in the old escarpments in distal parts of the StoreggaSlide. The slide was most likely triggered by a strong earthquake in an area 150 km downslope from the Ormen Lange gas field and developed as a retrogressive slide. The unstable sediments in the area disappeared with the slide 8200 years ago. A new ice age with infilling of glacial sediments on top of marine clays in the slide scar would be needed to create a new unstable situation at Ormen Lange.},
author = {Bryn, P. and Berg, K. and Forsberg, C. F. and Solheim, A. and Kvalstad, T. J.},
doi = {10.1016/j.marpetgeo.2004.12.003},
issn = {02648172},
journal = {Marine and Petroleum Geology},
keywords = {Erosion cycle,Risk assessment,Sediment load,Slope stability},
month = {jan},
number = {1-2},
pages = {11--19},
title = {{Explaining the Storegga Slide}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0264817204001771},
volume = {22},
year = {2005}
}
@article{Budd2001b,
author = {Budd, C. J. and Leimkuhler, B. and Piggott, M. D.},
doi = {10.1016/S0168-9274(00)00036-2},
issn = {01689274},
journal = {Appl. Numer. Math.},
month = {dec},
number = {3-4},
pages = {261--288},
title = {{Scaling invariance and adaptivity}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0168927400000362},
volume = {39},
year = {2001}
}
@article{Budd2001a,
abstract = {This review paper examines a synthesis of adaptive mesh methods with the use of symmetry to solve ordinary and partial differential equations. It looks at the effectiveness of numerical methods in preserving geometric structures of the underlying equations such as scaling invariance, conservation laws and solution orderings. Studies are made of a series of examples including the porous medium equation and the nonlinear Schr{\"{o}}dinger equation.},
author = {Budd, C. J. and Piggott, M. D.},
doi = {10.1016/S0377-0427(00)00521-5},
issn = {03770427},
journal = {J. Comp. Appl. Math.},
keywords = {Conservation laws,Equidistribution,Maximum principles,Mesh adaption,Scaling invariance,Self-similar solution},
month = {mar},
number = {1-2},
pages = {399--422},
title = {{The geometric integration of scale-invariant ordinary and partial differential equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377042700005215},
volume = {128},
year = {2001}
}
@article{Budd2001,
author = {Budd, Ch. and Dorodnitsyn, V.},
doi = {10.1088/0305-4470/34/48/305},
issn = {0305-4470},
journal = {J. Phys. A: Math. Gen.},
month = {dec},
number = {48},
pages = {10387--10400},
title = {{Symmetry-adapted moving mesh schemes for the nonlinear Schr{\"{o}}dinger equation}},
url = {http://stacks.iop.org/0305-4470/34/i=48/a=305?key=crossref.5be3bca77d33cffc64fa1ba7ff96c4d0},
volume = {34},
year = {2001}
}
@article{Buffoni1996,
author = {Buffoni, B. and Champneys, A. R. and Toland, J. F.},
doi = {10.1007/BF02218892},
issn = {1040-7294},
journal = {Journal of Dynamics and Differential Equations},
month = {apr},
number = {2},
pages = {221--279},
title = {{Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system}},
url = {http://link.springer.com/10.1007/BF02218892},
volume = {8},
year = {1996}
}
@article{Buffoni2000,
author = {Buffoni, B. and Dancer, E. N. and Toland, J. F.},
doi = {10.1007/s002050000086},
issn = {0003-9527},
journal = {Archive for Rational Mechanics and Analysis},
month = {jun},
number = {3},
pages = {207--240},
title = {{The Regularity and Local Bifurcation of Steady Periodic Water Waves}},
url = {http://link.springer.com/10.1007/s002050000086},
volume = {152},
year = {2000}
}
@article{Buffoni1996a,
abstract = {This paper considers the existence of solitary-wave solutions of the classical water-wave problem in the presence of surface tension. A region of Bond number-Froude number parameter space close to ({\$}\backslashfrac{\{}1{\}}{\{}3{\}}{\$}, 1) is identified, at each point of which there are infinitely many distinct multi-troughed solitary waves of depression. The method is to study a Hamiltonian formulation of the mathematical problem for solitary waves using a centre-manifold technique valid near Bond number {\$}\backslashfrac{\{}1{\}}{\{}3{\}}{\$} and Froude number 1. The problem is thus replaced by an equivalent problem posed on a four-dimensional manifold. In a certain region of parameter space near ({\$}\backslashfrac{\{}1{\}}{\{}3{\}}{\$}, 1), there is a Smale horseshoe in the dynamics on the centre manifold and therefore infinitely many distinct homoclinic orbits.},
author = {Buffoni, B. and Groves, M. D. and Toland, J. F.},
doi = {10.1098/rsta.1996.0020},
issn = {1364-503X},
journal = {Phil. Trans. R. Soc. Lond. A},
month = {mar},
number = {1707},
pages = {575--607},
title = {{A Plethora of Solitary Gravity-Capillary Water Waves with Nearly Critical Bond and Froude Numbers}},
url = {http://rsta.royalsocietypublishing.org/cgi/doi/10.1098/rsta.1996.0020},
volume = {354},
year = {1996}
}
@article{Bukreev2004,
author = {Bukreev, V. I. and Gusev, A. V. and Malysheva, A. A. and Malysheva, I. A.},
journal = {Fluid Dynamics},
number = {5},
pages = {801--809},
title = {{Experimental Verification of the Gas-Hydraulic Analogy with Reference to the Dam-Break Problem}},
volume = {39},
year = {2004}
}
@article{Bullock2001,
author = {Bullock, G. N. and Crawford, A. R. and Hewson, P. J. and Walkden, M. J. A. and Bird, P. A. D.},
journal = {Coastal Engineering},
pages = {291--312},
title = {{The influence of air and scale on wave impact pressures}},
volume = {42},
year = {2001}
}
@article{Bullock2007,
author = {Bullock, G. N. and Obhrai, C. and Peregrine, D. H. and Bredmose, H.},
journal = {Coastal Engineering},
pages = {602--617},
title = {{Violent breaking wave impacts. Part 1: Results from large-scale regular wave tests on vertical and sloping walls}},
volume = {54},
year = {2007}
}
@article{Burchard1995,
author = {Burchard, H. and Baumert, H.},
journal = {J. Geophys. Res.},
pages = {8523--8540},
title = {{On the performance of a mixed layer model based on the k-e turbulence closure}},
volume = {100},
year = {1995}
}
@article{Burchard2004,
author = {Burchard, H. and Beckers, J.-M.},
journal = {Ocean Modelling},
number = {1},
pages = {51--81},
title = {{Non-uniform adaptive vertical grids in one-dimensional numerical ocean models}},
volume = {6},
year = {2004}
}
@article{Burchard2009,
author = {Burchard, H. and Janssen, F. and Bolding, K. and Umlauf, L. and Rennau, H.},
journal = {Cont. Shelf Res.},
pages = {205--220},
title = {{Model simulations of dense bottom currents in the Western Baltic Sea}},
volume = {29},
year = {2009}
}
@article{Burchard2008,
author = {Burchard, H. and Rennau, H.},
journal = {Ocean Modelling},
pages = {293--311},
title = {{Comparative quantification of physically and numerically induced mixing in ocean models}},
volume = {20},
year = {2008}
}
@techreport{Burger2004,
abstract = {The aim of this lecture is to give an overview on modern numerical methods for the computation of incompressible flows. We start with a short introduction to fluid mechanics, including the derivation and discussion of the most important models and equations. The numerical methods discussed in the subsequent part are ordered due to the model they solve, i.e., we start with the stationary Stokes problem, a linear saddlepoint problem, then proceed to stationary Navier-Stokes, which adds the complication of a nonlinear equation, and finally discuss the instationary Navier-Stokes equations, which adds time discretizations. In all cases, we shall discuss modern discretization strategies, their major properties, and the solution of the discretized equations.},
address = {Los Angeles},
author = {Burger, M.},
institution = {UCLA},
pages = {86},
title = {{Numerical methods for incompressible flow}},
year = {2004}
}
@article{Burgers1948,
author = {Burgers, J. M.},
journal = {Advances in Applied Mechanics},
pages = {171--199},
title = {{A mathematical model illustrating the theory of turbulence}},
volume = {1},
year = {1948}
}
@article{Burschka1982,
abstract = {We study stationary solutions of the Fokker-Planck equation for velocity and position of a Brownian particle in the presence of a constant external field and a completely or selectively absorbing plane wall. Adapting a procedure used earlier for the field-free case, we determine analytically a set of boundary layer solutions and combine them numerically with the Chapman-Enskog solutions to satisfy various boundary conditions at the wall, albeit approximately. Various aspects of the solutions so obtained are presented, in particular the profiles of the density and the kinetic energy density in the boundary layer. The most important quantity that can be extracted from them is the effective absorption rate at the wall corresponding to complete or partial absorption of particles hitting the wall. This quantity is noticeably increased by the presence of the external field; as in the field-free case it also depends on the reflection mechanism adopted for the non-absorbed particles. The trends in the absorption rate, and even their numerical values, are predicted remarkably well by a simple analytical approximation, a self-consistent modification of the usual transition state theory for chemical reactions.},
author = {Burschka, M. A. and Titulaer, U. M.},
doi = {10.1016/0378-4371(82)90222-9},
issn = {03784371},
journal = {Phys. A},
month = {may},
number = {1-2},
pages = {315--330},
title = {{The kinetic boundary layer for the Fokker-Planck equation: A Brownian particle in a uniform field}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0378437182902229},
volume = {112},
year = {1982}
}
@article{Bustamante2009a,
author = {Bustamante, M. D. and Kartashova, E.},
doi = {10.1209/0295-5075/85/34002},
issn = {0295-5075},
journal = {EPL},
month = {feb},
number = {3},
pages = {34002},
title = {{Effect of the dynamical phases on the nonlinear amplitudes' evolution}},
volume = {85},
year = {2009}
}
@article{Bustamante2009,
abstract = {It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonances consists of independent clusters of resonantly interacting modes, described by a few low-dimensional dynamical systems. We formulate and prove a new theorem on integrability which allows us to show that most frequently met clusters are described by integrable dynamical systems. We argue that construction of clusters can be used as the base for the Clipping method, substantially more effective for these systems than the Galerkin method. The results can be used directly for systems with cubic Hamiltonian.},
author = {Bustamante, M. D. and Kartashova, E.},
doi = {10.1209/0295-5075/85/14004},
issn = {0295-5075},
journal = {EPL},
month = {jan},
number = {1},
pages = {14004},
title = {{Dynamics of nonlinear resonances in Hamiltonian systems}},
volume = {85},
year = {2009}
}
@article{Byatt-Smith1988,
author = {Byatt-Smith, J. G. B.},
journal = {J. Fluid Mech.},
pages = {503--521},
title = {{The reflection of a solitary wave by a vertical wall}},
volume = {197},
year = {1988}
}
@article{Byatt-Smith1971a,
author = {Byatt-Smith, J. G. B.},
journal = {J. Fluid Mech.},
pages = {33--40},
title = {{The effect of laminar viscosity on the solution of the undular bore}},
volume = {48},
year = {1971}
}
@article{Byatt-Smith1971,
author = {Byatt-Smith, J. G. B.},
journal = {J. Fluid Mech},
pages = {625--633},
title = {{An integral equation for unsteady surface waves and a comment on the Boussinesq equation}},
volume = {49},
year = {1971}
}
@article{Byatt-Smith1970,
abstract = {An exact integral equation is found for inviscid steady surface waves. Existing known approximations are all derived from the one equation. A numerical solution is attempted in the case of the solitary wave. From the numerical solution the amplitude of the solitary wave of maximum height is estimated. The numerical solution is also compared with the existing approximations and the implications drawn from the comparison are discussed.},
author = {Byatt-Smith, J. G. B.},
doi = {10.1098/rspa.1970.0051},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {mar},
number = {1522},
pages = {405--418},
title = {{An Exact Integral Equation for Steady Surface Waves}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1970.0051},
volume = {315},
year = {1970}
}
@article{Caflisch1998,
author = {Caflisch, R. E.},
doi = {10.1017/S0962492900002804},
journal = {Acta Numerica},
pages = {1--49},
title = {{Monte Carlo and quasi-Monte Carlo methods}},
volume = {7},
year = {1998}
}
@article{Caflisch1983,
abstract = {We consider a suspension of particles in a fluid settling under the influence of gravity and dispersing by Brownian motion. A mathematical description is provided by the Stokes equations and a Fokker-Planck equation for the one-particle phase space density. This is a nonlinear system that depends on a number of parametric functions of the spatial concentration of the particles. These functions are known only empirically or for dilute suspensions. We analyze the system, its stability, its asymptotic behavior under different scalings and its validity from more microscopic description. We summarize our conclusions at the end.},
author = {Caflisch, R. and Papanicolaou, G. C.},
doi = {10.1137/0143057},
issn = {0036-1399},
journal = {SIAM J. Appl. Math},
month = {aug},
number = {4},
pages = {885--906},
title = {{Dynamic Theory of Suspensions with Brownian Effects}},
url = {http://epubs.siam.org/doi/abs/10.1137/0143057},
volume = {43},
year = {1983}
}
@article{Cai2001,
author = {Cai, D. and Majda, A. J. and McLaughlin, D. W. and Tabak, E. G.},
doi = {10.1016/S0167-2789(01)00193-2},
issn = {01672789},
journal = {Physica D: Nonlinear Phenomena},
keywords = {dispersive wave,one dimension,turbulence,weak turbulence theory},
number = {1-2},
pages = {551--572},
title = {{Dispersive wave turbulence in one dimension}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278901001932},
volume = {152-153},
year = {2001}
}
@article{Calini2002,
abstract = {We numerically investigate dispersive perturbations of the nonlinear Schr{\"{o}}dinger (NLS) equation, which model waves in deep water. We observe that a chaotic regime greatly increases the likelihood of rogue wave formation. These large amplitude waves are well modeled by higher order homoclinic solutions of the NLS equation for which the spatial excitations have coalesced to produce a wave of maximal amplitude. Remarkably, a Melnikov analysis of the conditions for the onset of chaos identifies the observed maximal amplitude homoclinic solutions as the persistent hyperbolic structures throughout the perturbed dynamics.},
author = {Calini, A. and Schober, C. M.},
journal = {Physics Letters A},
pages = {335--349},
title = {{Homoclinic chaos increases the likelihood of rogue wave formation}},
volume = {298},
year = {2002}
}
@book{Callen1985,
author = {Callen, H. B.},
pages = {512},
publisher = {Wiley},
title = {{Thermodynamics and an Introduction to Thermostatistics}},
year = {1985}
}
@book{Calogero1982,
author = {Calogero, F. and Degasperis, A.},
publisher = {North-Holland Publ.},
title = {{Spectral transform and solitons I}},
year = {1982}
}
@incollection{Calvo1993,
address = {Singapore},
author = {Calvo, M. P. and Sanz-Serna, J.-M.},
booktitle = {Physics Computing 92},
pages = {153--160},
publisher = {World Scientific},
title = {{Symplectic numerical methods for Hamiltonian problems}},
year = {1993}
}
@article{Camassa1993,
author = {Camassa, R. and Holm, D.},
journal = {Phys. Rev. Lett.},
pages = {1661--1664},
title = {{An integrable shallow water equation with peaked solitons}},
volume = {71(11)},
year = {1993}
}
@article{Camassa1991,
author = {Camassa, R. and Wu, T. Y.},
journal = {Phil. Trans. R. Soc. Lond. A},
pages = {429--466},
title = {{Stability of forced steady solitary waves}},
volume = {337},
year = {1991}
}
@article{Cammarano2010,
author = {Cammarano, A. and Burrow, S. G. and Barton, D. A. W. and Carrella, A. and Clare, L. R.},
doi = {10.1088/0964-1726/19/5/055003},
issn = {0964-1726},
journal = {Smart Mater. Struct.},
month = {may},
number = {5},
pages = {055003},
title = {{Tuning a resonant energy harvester using a generalized electrical load}},
volume = {19},
year = {2010}
}
@book{Canuto1988,
address = {New York},
author = {Canuto, C. and Hussaini, M. Y. and Quarteroni, A. and Zang, T. A.},
pages = {369},
publisher = {Springer},
title = {{Spectral Methods in Fluid Dynamics}},
year = {1988}
}
@book{Canuto2006,
abstract = {Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988.The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms. A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.},
author = {Canuto, C. and Hussaini, M. Y. and Quarteroni, A. and Zang, T. A.},
booktitle = {New York},
isbn = {9783540307259},
pages = {563},
publisher = {Springer-Verlag Berlin Heidelberg},
series = {Scientific Computation},
title = {{Spectral Methods Fundamentals in Single Domains}},
url = {http://www.amazon.com/Spectral-Methods-Fundamentals-Scientific-Computation/dp/3540307257/sr=1-1/qid=1172681680/ref=sr{\_}1{\_}1/002-9880249-7216022?ie=UTF8{\&}s=books},
year = {2006}
}
@article{Caputo2014,
archivePrefix = {arXiv},
arxivId = {1402.6446},
author = {Caputo, J.-G. and Dutykh, D.},
doi = {10.1103/PhysRevE.90.022912},
eprint = {1402.6446},
journal = {Phys. Rev. E},
pages = {022912},
title = {{Nonlinear waves in networks: model reduction for sine-Gordon}},
url = {http://hal.archives-ouvertes.fr/hal-00951705},
volume = {90},
year = {2014}
}
@article{Caputo2011,
abstract = {We analyze the 1D focusing nonlinear Schr{\"{o}}dinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long-term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally, these equations elucidate the unique role of the zero mode for the Neumann boundary conditions.},
author = {Caputo, J.-G. and Efremidis, N. K. and Hang, C.},
doi = {10.1103/PhysRevE.84.036601},
issn = {1539-3755},
journal = {Phys. Rev. E},
month = {sep},
number = {3},
pages = {036601},
title = {{Fourier-mode dynamics for the nonlinear Schr{\"{o}}dinger equation in one-dimensional bounded domains}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.84.036601},
volume = {84},
year = {2011}
}
@article{Caputo2013,
abstract = {To describe the flow of a miscible quantity on a network, we consider the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. The structure of the graph influences strongly the dynamics. Assuming the graph is forced and damped at specific nodes, we derive the amplitude equations using a basis of eigenvectors of the graph Laplacian. These lead us to introduce the notion of soft nodes. We give sufficient conditions for their existence in general graphs. They can cause several effects as we show on small graphs, for example the ineffectiveness of damping applied to them. Soft nodes may be of critical importance for complex physical networks and engineering networks like power grids.},
author = {Caputo, J.-G. and Knippel, A. and Simo, E.},
doi = {10.1088/1751-8113/46/3/035101},
issn = {1751-8113},
journal = {J. Phys. A: Math. Gen.},
month = {jan},
number = {3},
pages = {035101},
title = {{Oscillations of networks: the role of soft nodes}},
url = {http://stacks.iop.org/1751-8121/46/i=3/a=035101?key=crossref.64d8f7075386bee34e6bf75157b2e8a5},
volume = {46},
year = {2013}
}
@article{Carbone2013,
abstract = {Wave impact and runup onto vertical obstacles are among the most important phenomena which must be taken into account in the design of coastal structures. From linear wave theory, we know that the wave amplitude on a vertical wall is twice the incident wave amplitude with weakly nonlinear theories bringing small corrections to this result. In this present study, however, we show that certain simple wave groups may produce much higher runups than previously predicted, with particular incident wave frequencies resulting in runup heights exceeding the initial wave amplitude by a factor of 5, suggesting that the notion of the design wave used in coastal structure design may need to be revisited. The results presented in this study can be considered as a note of caution for practitioners, on one side, and as a challenging novel material for theoreticians who work in the field of extreme wave-coastal structure interaction.},
author = {Carbone, F. and Dutykh, D. and Dudley, J. M. and Dias, F.},
journal = {Geophys. Res. Lett.},
keywords = {Serre-Green-Naghdi equation,long waves,wave run-up},
number = {12},
pages = {3138--3143},
title = {{Extreme wave run-up on a vertical cliff}},
volume = {40},
year = {2013}
}
@article{Carrier1966a,
author = {Carrier, G. F.},
journal = {J. Fluid Mech.},
number = {04},
pages = {641--659},
title = {{Gravity waves on water of variable depth}},
volume = {24},
year = {1966}
}
@article{Carrier1966,
author = {Carrier, G. F.},
journal = {J. Fluid Mech},
number = {04},
pages = {641--659},
title = {{Gravity waves on water of variable depth}},
volume = {24},
year = {1966}
}
@article{carrier,
author = {Carrier, G. F.},
journal = {Mathematical Problems in the Geophysical Sciences. Lectures in Applied Mathematics},
pages = {157--187},
title = {{The dynamics of tsunamis}},
volume = {13},
year = {1971}
}
@article{CG58,
author = {Carrier, G. F. and Greenspan, H. P.},
journal = {J. Fluid Mech.},
pages = {97--109},
title = {{Water waves of finite amplitude on a sloping beach}},
volume = {2},
year = {1958}
}
@article{CWY,
author = {Carrier, G. F. and Wu, T. T. and Yeh, H.},
journal = {J. Fluid Mech.},
pages = {79--99},
title = {{Tsunami run-up and draw-down on a plane beach}},
volume = {475},
year = {2003}
}
@article{Carrillo2006,
abstract = {We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.},
author = {Carrillo, J. and Goudon, T.},
doi = {10.1080/03605300500394389},
issn = {0360-5302},
journal = {Comm. Partial Diff. Eqns.},
month = {sep},
number = {9},
pages = {1349--1379},
title = {{Stability and Asymptotic Analysis of a Fluid-Particle Interaction Model}},
url = {http://www.informaworld.com/openurl?genre=article{\&}doi=10.1080/03605300500394389{\&}magic=crossref||D404A21C5BB053405B1A640AFFD44AE3},
volume = {31},
year = {2006}
}
@phdthesis{Carter2001,
author = {Carter, J. D.},
school = {University of Colorado at Boulder},
title = {{Stability and existence of traveling-wave solutions of the two-dimensional nonlinear Schr{\"{o}}dinger equation and its higher-order generalizations}},
year = {2001}
}
@article{Carter2011,
author = {Carter, J. D. and Cienfuegos, R.},
journal = {Eur. J. Mech. B/Fluids},
pages = {259--268},
title = {{The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations}},
volume = {30},
year = {2011}
}
@article{Cartwright1992,
abstract = {The first step in investigating the dynamics of a continuous-time system described by an ordinary differential equation is to integrate to obtain trajectories. In this paper, we attempt to elucidate the dynamics of the most commonly used family of numerical integration schemes, Runge--Kutta methods, by the application of the techniques of dynamical systems theory to the maps produced in the numerical analysis.},
author = {Cartwright, J. H. E. and Piro, O.},
journal = {Int. J. Bifurcation and Chaos},
pages = {427--449},
title = {{The Dynamics of Runge-Kutta Methods}},
volume = {2},
year = {1992}
}
@article{Cash1990,
author = {Cash, J. R. and Karp, A. H.},
doi = {10.1145/79505.79507},
issn = {00983500},
journal = {ACM Transactions on Mathematical Software},
month = {sep},
number = {3},
pages = {201--222},
title = {{A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides}},
url = {http://portal.acm.org/citation.cfm?doid=79505.79507},
volume = {16},
year = {1990}
}
@article{Castro-Orgaz2015,
author = {Castro-Orgaz, O. and Hager, W. H.},
doi = {10.1080/00221686.2015.1012655},
issn = {0022-1686},
journal = {J. Hydraulic Res.},
month = {mar},
number = {2},
pages = {282--284},
title = {{''Boussinesq- and Serre-type models with improved linear dispersion characteristics: applications''}},
url = {http://www.tandfonline.com/doi/full/10.1080/00221686.2015.1012655},
volume = {53},
year = {2015}
}
@article{Castro2005,
author = {Castro, M. J. and Ferreiro, A. M. and Garcia-Rodriguez, J. A. and Gonzalez-Vida, J. M. and Macias, J. and Pares, C. and Vazquez-Cendon, M. E.},
journal = {Mathematical and Computer Modelling},
pages = {419--439},
title = {{The numerical treatment of Wet/Dry Fronts in Shallow Flows: Application to one-layer and two-layer systems}},
volume = {42},
year = {2005}
}
@article{Castro2006,
author = {Castro, M. J. and Gonzalez-Vida, J. M. and Pares, C.},
journal = {Mathematical Models and Methods in Applied Sciences},
number = {6},
pages = {97--931},
title = {{Numerical Treatment of Wet/dry fronts in shallow flows with a modified Roe scheme}},
volume = {16},
year = {2006}
}
@article{Casulli1990,
author = {Casulli, V.},
journal = {Journal of Computational Physics},
pages = {56--74},
title = {{Semi-implicit finite difference methods for the two-dimensional shallow water equation}},
volume = {86},
year = {1990}
}
@article{Casulli2012,
abstract = {Blood flow in arterial systems is described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the viscoelasticity of the arterial walls. These equations are simplified by assuming cylindrical geometry, axially symmetric flow, and hydrostatic equilibrium in the radial direction. In this paper, an efficient semi-implicit method is formulated in such a fashion that numerical stability is obtained at a minimal computational cost. The resulting computer model is relatively simple, robust, accurate, and extremely efficient. These features are illustrated on nontrivial test cases where the exact analytical solution is known and by an example of a realistic flow through a complex arterial system.},
author = {Casulli, V. and Dumbser, M. and Toro, E. F.},
doi = {10.1002/cnm.1464},
issn = {20407939},
journal = {Int. J. Numer. Methods Biomed. Eng.},
keywords = {axially symmetric flow,blood flow,compliant arteries,finite difference,finite volume,hydrostatic equilibrium,moving boundaries,semi-implicit method},
month = {feb},
number = {2},
pages = {257--272},
title = {{Semi-implicit numerical modeling of axially symmetric flows in compliant arterial systems}},
url = {http://doi.wiley.com/10.1002/cnm.1464},
volume = {28},
year = {2012}
}
@article{Cauchy1827,
author = {Cauchy, A.-L.},
journal = {M{\{}{\'{e}}{\}}m. Pr{\{}{\'{e}}{\}}sent{\{}{\'{e}}{\}}s Divers Savans Acad. R. Sci. Inst. France},
pages = {3--312},
title = {{M{\{}{\'{e}}{\}}moire sur la th{\{}{\'{e}}{\}}orie de la propagation des ondes {\{}{\`{a}}{\}} la surface d'un fluide pesant d'une profondeur ind{\{}{\'{e}}{\}}finie}},
volume = {1},
year = {1827}
}
@article{Cauchy1827,
author = {Cauchy, A.-L.},
journal = {M{\'{e}}m. Pr{\'{e}}sent{\'{e}}s Divers Savans Acad. R. Sci. Inst. France},
pages = {3--312},
title = {{M{\'{e}}moire sur la th{\'{e}}orie de la propagation des ondes {\`{a}} la surface d'un fluide pesant d'une profondeur ind{\'{e}}finie}},
volume = {1},
year = {1827}
}
@article{Causon2000,
author = {Causon, D. M. and Ingram, D. M. and Mingham, C. G. and Yang, G. and Pearson, R. V.},
journal = {Advances in Water Resources},
pages = {545--562},
title = {{Calculation of shallow water flows using a Cartesian cut cell approach}},
volume = {23},
year = {2000}
}
@article{Cea2004,
author = {Cea, L. and Ferreiro, A. and Vazquez-Cendon, M. E. and Puertas, J.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {793--813},
title = {{Experimental and numerical analysis of solitary waves generated by bed and boundary movement}},
volume = {46},
year = {2004}
}
@book{Cercignani1969,
address = {Boston, MA},
author = {Cercignani, C.},
doi = {10.1007/978-1-4899-5409-1},
edition = {2},
isbn = {978-1-4899-5411-4},
pages = {227},
publisher = {Springer US},
title = {{Mathematical Methods in Kinetic Theory}},
url = {http://link.springer.com/10.1007/978-1-4899-5409-1},
year = {1969}
}
@article{Cercignani1992,
abstract = {This paper deals with a generalization of a classical result obtained by R. Beals and V. Protopopescu for the Fokker-Planck equations to the case in which a constant external force is present.},
author = {Cercignani, C. and Sgarra, C.},
doi = {10.1007/BF01054434},
issn = {0022-4715},
journal = {J. Stat. Phys.},
month = {mar},
number = {5-6},
pages = {1575--1582},
title = {{Half-range completeness for the Fokker-Planck equation with an external force}},
url = {http://link.springer.com/10.1007/BF01054434},
volume = {66},
year = {1992}
}
@article{Cerpa2007,
author = {Cerpa, E.},
journal = {SIAM Journal on Control and Optimization},
pages = {877--899},
title = {{Exact controllability of a nonlinear Korteweg-de Vries equation on a critical spatial domain}},
volume = {46},
year = {2007}
}
@article{Cerpa2009,
author = {Cerpa, E. and Crepeau, E.},
journal = {Ann. I. H. Poincar{\'{e}}},
pages = {457--475},
title = {{Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain}},
volume = {26},
year = {2009}
}
@article{Chabchoub2012,
author = {Chabchoub, A. and Akhmediev, N. N. and Hoffmann, N. P.},
journal = {Phys. Rev. E},
pages = {016311},
title = {{Experimental study of spatiotemporally localized surface gravity water waves}},
volume = {86},
year = {2012}
}
@article{Chabchoub2011,
author = {Chabchoub, A. and Hoffmann, N. P. and Akhmediev, N. N.},
journal = {Phys. Rev. Lett.},
pages = {204502},
title = {{Rogue wave observation in a water wave tank}},
volume = {106},
year = {2011}
}
@article{Chakrabarti1984,
author = {Chakrabarti, S. K.},
journal = {Applied Ocean Research},
pages = {175--176},
title = {{On the formulation of Jonswap spectrum}},
volume = {6},
year = {1984}
}
@article{Chambarel2009,
author = {Chambarel, J. and Kharif, C. and Touboul, J.},
journal = {Nonlin. Processes Geophys.},
pages = {111--122},
title = {{Head-on collision of two solitary waves and residual falling jet formation}},
volume = {16},
year = {2009}
}
@article{Champneys1997,
abstract = {The model equation arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravity-capillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts for the model equation. At the time of writing two major open problems for steady water waves are attracting particular attention. The first concerns the possible existence of solitary waves of elevation as local bifurcation phenomena in a particular parameter regime; the second, larger, issue is the determination of the global bifurcation picture for solitary waves. Given that the above equation is a good model for solitary waves of depression, it seems natural to study the above issues for this equation; they are comprehensively treated in this article. The equation is found to have branches of solitary waves of elevation bifurcating from the trivial solution in the appropriate parameter regime, one of which is described by an explicit solution. Numerical and analytical investigations reveal a rich global bifurcation picture including multi-modal solitary waves of elevation and depression together with interactions between the two types of wave. There are also new orbit-flip bifurcations and associated multi-crested solitary waves with non-oscillatory tails.},
author = {Champneys, A. R. and Groves, M. D.},
doi = {10.1017/S0022112097005193},
issn = {00221120},
journal = {J. Fluid Mech.},
month = {jul},
pages = {199--229},
title = {{A global investigation of solitary-wave solutions to a two-parameter model for water waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112097005193},
volume = {342},
year = {1997}
}
@article{Champneys2002,
author = {Champneys, A. R. and Vanden-Broeck, J.-M. and Lord, G. J.},
doi = {10.1017/S0022112001007200},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
pages = {403--417},
title = {{Do true elevation gravity-capillary solitary waves exist? A numerical investigation}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112001007200},
volume = {454},
year = {2002}
}
@article{Chan1970,
author = {Chan, R. K.-C and Street, R. L.},
doi = {10.1016/0021-9991(70)90005-7},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {aug},
number = {1},
pages = {68--94},
title = {{A computer study of finite-amplitude water waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999170900057},
volume = {6},
year = {1970}
}
@book{Chandrasekhar1981,
author = {Chandrasekhar, S.},
publisher = {Dover Publications},
title = {{Hydrodynamic and Hydromagnetic Stability}},
year = {1981}
}
@article{Chang2008,
author = {Chang, W.-Y. and Lee, L.-C. and Lien, H.-C. and Lai, J.-S.},
journal = {Journal of Mechanics},
pages = {391--403},
title = {{Simulations of dam-break flows using free surface capturing method}},
volume = {24(4)},
year = {2008}
}
@article{Chanson05,
author = {Chanson, H.},
journal = {La Houille Blanche},
pages = {25--32},
title = {{Le tsunami du 26 d{\'{e}}cembre 2004: un ph{\'{e}}nom{\`{e}}ne hydraulique d'ampleur internationale. Premiers constats}},
volume = {2},
year = {2005}
}
@book{Chanson2004,
address = {Amsterdam},
author = {Chanson, H.},
edition = {2},
isbn = {978-0-7506-5978-9},
pages = {650},
publisher = {Elsevier},
title = {{Hydraulics of Open Channel Flow}},
year = {2004}
}
@article{Chapman1899,
author = {Chapman, D. L.},
journal = {Philosophical Magazine},
pages = {90--104},
title = {{On the rate of explosion in gases}},
volume = {47},
year = {1899}
}
@book{Chapman1995,
author = {Chapman, S. and Cowling, T. G.},
publisher = {Cambridge University Press, Cambridge, England},
title = {{The Mathematical Theory of Non-Uniform Gases}},
year = {1995}
}
@article{Chapron1999,
abstract = {High-resolution textural signatures of an earthquake-induced historical ‘homogenite’ layer are presented, as well as its 3D distribution. This homogeneous deposit is correlated with the ad 1822 event (VII-VIII MSK intensity), the main historical earthquake of the French outer Alps, using 210Pb dating and historical chronicles. During this earthquake a violent lake water oscillation was reported (seiche effect). In the present study we discuss the influence of lake water oscillations during earthquake-induced subaqueous slide, through a pluridisciplinary analysis of subbottom sediments including high-resolution seismic, sidescan sonar and short gravity coring.},
author = {Chapron, E. and Beck, C. and Pourchet, M. and Deconinck, J.-F.},
doi = {10.1046/j.1365-3121.1999.00230.x},
journal = {Terra Nova},
number = {2-3},
pages = {86--92},
title = {{1822 earthquake-triggered homogenite in Lake Le Bourget (NW Alps)}},
volume = {11},
year = {1999}
}
@article{Chapron2004,
abstract = {The north-western corner of Lake Le Bourget is situated along an active fault zone and accommodated a large sediment supply from the Rhone River until the end of the Late Glacial period. On the delta slope, the Holocene sheet drape that covers the largest buried mass wasting deposit (the HDU) shows undulations, small fractures and discontinuities that are attributed to downslope creep. Evidence for episodes of vigorous fluid expulsion is found in association with these discontinuities. All these features are rooted at the top of the HDU and occur along two specific isobaths. These observations indicate a close link between fractures and focused fluid flow. We suggest that focused fluid flow triggered by earthquakes facilitates the formation of small-scale faults that accommodate part of the downslope movement and eventually link up to form a head-scarp of a large slide (c. 10{\^{}}7 m3).},
author = {Chapron, E. and {Van Rensbergen}, P. and {De Batist}, M. and Beck, C. and Henriet, J. P.},
doi = {10.1111/j.1365-3121.2004.00566.x},
journal = {Terra Nova},
number = {5},
pages = {305--311},
title = {{Fluid-escape features as a precursor of a large sublacustrine sediment slide in Lake Le Bourget, NW Alps, France}},
volume = {16},
year = {2004}
}
@article{Chardard2007,
author = {Chardard, F.},
doi = {10.1016/j.crma.2007.11.003},
issn = {1631073X},
journal = {C. R. Acad. Sci. Paris, Ser. I},
month = {dec},
number = {12},
pages = {689--694},
title = {{Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1631073X07004608},
volume = {345},
year = {2007}
}
@article{Chardard2009,
author = {Chardard, F. and Dias, F. and Bridges, T. J.},
doi = {10.1098/rspa.2009.0155},
issn = {1364-5021},
journal = {Proc. R. Soc. A},
month = {jul},
number = {2109},
pages = {2897--2910},
title = {{On the Maslov index of multi-pulse homoclinic orbits}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2009.0155},
volume = {465},
year = {2009}
}
@article{Chardard2011,
author = {Chardard, F. and Dias, F. and Nguyen, H. Y. and Vanden-Broeck, J.-M.},
journal = {J. Eng. Math.},
pages = {175--189},
title = {{Stability of some stationary solution to the forced KdV equation with one or two bumps}},
volume = {70},
year = {2011}
}
@article{Chazel2007,
author = {Chazel, F.},
journal = {M2AN},
pages = {771--799},
title = {{Influence of bottom topography on long water waves}},
volume = {41},
year = {2007}
}
@article{Chazel2009,
author = {Chazel, F. and Benoit, M. and Ern, A. and Piperno, S.},
doi = {10.1098/rspa.2008.0508},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {may},
number = {2108},
pages = {2319--2346},
title = {{A double-layer Boussinesq-type model for highly nonlinear and dispersive waves}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2008.0508},
volume = {465},
year = {2009}
}
@article{ChazelLannes2010,
author = {Chazel, F. and Lannes, D. and Marche, F.},
journal = {J. Sci. Comput.},
pages = {105--116},
title = {{Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model}},
volume = {48},
year = {2011}
}
@inbook{Chechkin2009,
author = {Chechkin, G. A. and Goritsky, A. Yu.},
chapter = {S.{\{}N{\}}. {\{}K{\}}},
editor = {Emmrich, E and Wittbold, P},
title = {{Analytical and Numerical Aspects of Partial Differential Equations}},
year = {2009}
}
@article{Chehab2011,
author = {Chehab, J.-P. and Sadaka, G.},
doi = {10.3934/cpaa.2013.12.519},
issn = {1534-0392},
journal = {Communications on Pure and Applied Analysis},
month = {sep},
number = {1},
pages = {519--546},
title = {{Numerical study of a family of dissipative KdV equations}},
url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=7626},
volume = {12},
year = {2013}
}
@article{Chen1996,
author = {Chen, G.-Q. and Glimm, J.},
doi = {10.1007/BF02101185},
issn = {0010-3616},
journal = {Comm. Math. Phys.},
month = {sep},
number = {1},
pages = {153--193},
title = {{Global solutions to the compressible Euler equations with geometrical structure}},
url = {http://link.springer.com/10.1007/BF02101185},
volume = {180},
year = {1996}
}
@article{Chen1999,
author = {Chen, G. and Kharif, C. and Zaleski, S. and Li, J.},
journal = {Physics of Fluids},
pages = {121--133},
title = {{Two-dimensional Navier-Stokes simulation of breaking waves}},
volume = {11(1)},
year = {1999}
}
@article{Chen2007,
author = {Chen, H. and Chen, M. and Nguyen, N.},
journal = {Nonlinearity},
pages = {1443--1461},
title = {{Cnoidal Wave Solutions to Boussinesq Systems}},
volume = {20},
year = {2007}
}
@article{Chen2000a,
author = {Chen, M.},
doi = {10.1080/00036810008840844},
issn = {0003-6811},
journal = {Applicable Analysis},
month = {jun},
number = {1-2},
pages = {213--240},
title = {{Solitary-wave and multi-pulsed traveling-wave solutions of boussinesq systems}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00036810008840844},
volume = {75},
year = {2000}
}
@article{Chen1998,
author = {Chen, M.},
journal = {International Journal of Theoretical Physics},
pages = {1547--1567},
title = {{Exact Traveling-Wave Solutions to Bidirectional Wave Equations}},
volume = {37},
year = {1998}
}
@article{Chen2000,
author = {Chen, M.},
journal = {Applic. Analysis.},
pages = {213--240},
title = {{Solitary-wave and multi pulsed traveling-wave solution of Boussinesq systems}},
volume = {7},
year = {2000}
}
@article{Chen2010,
author = {Chen, M. and Dumont, S. and Dupaigne, L. and Goubet, O.},
doi = {doi:10.3934/dcds.2010.27.1473},
journal = {Discrete Contin. Dyn. Syst.},
pages = {1473--1492},
title = {{Decay of solutions to a water wave model with a nonlocal viscous dispersive term}},
volume = {27(4)},
year = {2010}
}
@article{CG,
author = {Chen, M. and Goubet, O.},
journal = {Discrete and Continuous Dynamical Systems},
pages = {61--80},
title = {{Long-time asymptotic behaviour of dissipative Boussinesq systems}},
volume = {17},
year = {2007}
}
@article{Chen2005,
abstract = {In this paper, we prove the existence of a large family of nontrivial bifurcating standingwaves for amodelsystem which describes two-way propagation of waterwaves in a channel of finite depth or in the near shore zone. In particular, it is shown that, contrary to the classical standing gravity wave problem on a fluid layer of finite depth, the Lyapunov–Schmidt method applies to find the bifurcation equation. The bifurcation set is formed with the discrete union of Whitney's umbrellas in the three-dimensional space formed with 3 parameters representing the time-period and the wave length, and the average of wave amplitude.},
author = {Chen, M. and Iooss, G.},
doi = {10.1016/j.euromechflu.2004.07.002},
issn = {09977546},
journal = {European Journal of Mechanics - B/Fluids},
month = {jan},
number = {1},
pages = {113--124},
title = {{Standing waves for a two-way model system for water waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754604000822},
volume = {24},
year = {2005}
}
@article{Chen2008,
author = {Chen, M. and Iooss, G.},
doi = {10.1016/j.physd.2008.03.016},
issn = {01672789},
journal = {Physica D: Nonlinear Phenomena},
keywords = {Asymmetric periodic wave patterns,Bifurcation of traveling waves,Boussinesq systems,Lyapunov–Schmidt method,Three-dimensional water waves},
month = {jul},
number = {10-12},
pages = {1539--1552},
title = {{Asymmetric periodic traveling wave patterns of two-dimensional Boussinesq systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278908001061},
volume = {237},
year = {2008}
}
@article{Chen2006,
abstract = {We prove the existence of a large family of two-dimensional travelling wave patterns for a Boussinesqsystem which describes three-dimensional water waves. This model equation results from full Euler equations in assuming that the depth of the fluid layer is small with respect to the horizontal wave length, and that the flow is potential, with a free surface without surface tension. Our proof uses the Lyapunov–Schmidt method which may be managed here, contrary to the case of gravity waves with full Euler equations. Our results are in a good qualitative agreement with experimental results.},
author = {Chen, M. and Iooss, G.},
doi = {10.1016/j.euromechflu.2005.11.004},
issn = {09977546},
journal = {European Journal of Mechanics - B/Fluids},
keywords = {Bifurcation of travelling waves,Boussinesq systems,Periodic two-dimensional pattern,Water waves},
month = {jul},
number = {4},
pages = {393--405},
title = {{Periodic wave patterns of two-dimensional Boussinesq systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754606000057},
volume = {25},
year = {2006}
}
@article{Chen1999a,
author = {Chen, S. and Foias, C. and Holm, D. D. and Olson, E. and Titi, E. S. and Wynne, S.},
journal = {Phys. D},
pages = {49--65},
title = {{The Camassa-Holm equations and turbulence in pipes and channels}},
volume = {133},
year = {1999}
}
@book{Chen2003,
author = {Chen, W. and Scawthorn, C.},
isbn = {978-1-4200-4244-3},
publisher = {CRC Press},
title = {{Earthquake Engineering Handbook}},
year = {2003}
}
@article{Chen2011,
abstract = {In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov-Kuznetsov (ZK) equation and the Kadomtsev-Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method.},
author = {Chen, Y. and Song, S. and Zhu, H.},
doi = {10.1016/j.cam.2011.08.023},
issn = {03770427},
journal = {J. Comp. Appl. Math.},
keywords = {Fourier pseudospectral method,Hamiltonian PDE,Kadomtsev-Petviashvili equation,Multi-symplectic,Zakharov-Kuznetsov equation},
month = {oct},
number = {6},
pages = {1354--1369},
title = {{The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377042711004699},
volume = {236},
year = {2011}
}
@misc{Cheng2010,
abstract = {We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylindrical algebraic decomposition use sub-resultant sequences and computations with polynomials with algebraic coefficients. A novelty of our approach is to replace these tools by Gr{\"{o}}bner basis computations and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition also induces a new approach for computing an arrangement of polylines isotopic to the input curve. We also present an analysis of the complexity of our algorithm. An implementation of our algorithm demonstrates its efficiency, in particular on high-degree non-generic curves.},
author = {Cheng, J. and Lazard, S. and Pe{\~{n}}aranda, L. and Pouget, M. and Rouillier, F. and Tsigaridas, E.},
booktitle = {Mathematics in Computer Science},
doi = {10.1007/s11786-010-0044-3},
issn = {16618270},
pages = {1--25},
title = {{On the Topology of Real Algebraic Plane Curves}},
year = {2010}
}
@article{Chertock2006,
author = {Chertock, A. and Kurganov, A. and Petrova, G.},
doi = {10.1007/s10915-005-9060-x},
issn = {0885-7474},
journal = {J. Sci. Comput.},
month = {jun},
number = {1-3},
pages = {189--199},
title = {{Finite-Volume-Particle Methods for Models of Transport of Pollutant in Shallow Water}},
url = {http://link.springer.com/10.1007/s10915-005-9060-x},
volume = {27},
year = {2006}
}
@article{Chester1968,
author = {Chester, W.},
journal = {Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences},
number = {1484},
pages = {5--22},
title = {{Resonant Oscillations of Water Waves. I. Theory}},
volume = {306},
year = {1968}
}
@article{Cheung1989,
author = {Cheung, Y. K. and Jin, W. G. and Zienkiewicz, O. C.},
journal = {Comm. Appl. Num. Meth.},
pages = {159--169},
title = {{Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions}},
volume = {5},
year = {1989}
}
@phdthesis{Chhay2008,
author = {Chhay, M.},
pages = {183},
school = {Universit{\'{e}} de La Rochelle},
title = {{Int{\'{e}}grateurs g{\'{e}}om{\'{e}}triques: application {\`{a}} la m{\'{e}}canique des fluides}},
year = {2008}
}
@article{Chhay2016,
author = {Chhay, M. and Dutykh, D. and Clamond, D.},
journal = {J. Phys. A: Math. Gen.},
title = {{On the multi-symplectic structure of the Serre-Green-Naghdi equations}},
volume = {Accepted},
year = {2016}
}
@article{Chhay2015,
author = {Chhay, M. and Dutykh, D. and Gisclon, M. and Ruyer-Quil, C.},
journal = {Submitted},
pages = {1--24},
title = {{Asymptotic heat transfer model in thin liquid films}},
year = {2015}
}
@article{Chhay2011a,
author = {Chhay, M. and Hamdouni, A.},
journal = {Commun. Pure Appl. Anal.},
number = {2},
pages = {761--783},
title = {{On accuracy of invariant numerical schemes}},
volume = {10},
year = {2011}
}
@article{Chhay2010,
author = {Chhay, M. and Hamdouni, A.},
journal = {C. R. Acad. Sci. Meca.},
pages = {97--101},
title = {{A new construction for invariant numerical schemes using moving frames}},
volume = {338},
year = {2010}
}
@article{Chhay2010a,
abstract = {Invariant numerical schemes possess properties that may overcome the numerical properties of most of classical schemes. When they are constructed with moving frames, invariant schemes can present more stability and accuracy. The cornerstone is to select relevant moving frames. We present a new algorithmic process to do this. The construction of invariant schemes consists in parametrizing the scheme with constant coefficients. These coefficients are determined in order to satisfy a fixed order of accuracy and an equivariance condition. Numerical applications with the Burgers equation illustrate the high performances of the process.},
author = {Chhay, M. and Hamdouni, A.},
doi = {10.3390/sym2020868},
journal = {Symmetry},
keywords = {Lie symmetry,finite differences scheme,invariant scheme,moving frames},
number = {2},
pages = {868--883},
title = {{Lie symmetry preservation by finite difference schemes for the Burgers equation}},
volume = {2},
year = {2010}
}
@article{Chhay2011,
author = {Chhay, M. and Hoarau, E. and Hamdouni, A. and Sagaut, P.},
journal = {J. Comp. Phys.},
pages = {2174--2188},
title = {{Comparison of some Lie-symmetry-based integrators}},
volume = {230(5)},
year = {2011}
}
@article{chin,
author = {Chinnery, M. A.},
journal = {Bull. Seism. Soc. Am.},
pages = {921--932},
title = {{The stress changes that accompany strike-slip faulting}},
volume = {53},
year = {1963}
}
@article{Chiocci2008,
abstract = {In order to monitor the Stromboli submarine slope after the 30 December 2002 landslide and tsunami, repeated marine surveys were carried out offshore of Sciara del Fuoco. The morphological changes and depositionalprocesses that brought to the gradual filling of the slide scar have been studied in detail. Thirteen surveys in a period of little more than 4 years provided a unique opportunity to reconstruct the morpho-sedimentary evolution of the submarine slope and its recovery after the mass-wasting event. The scar has been progressively filled with lava and volcanoclastic debris; in the first month and a half, the filling rate was very high due to the entrance of lava flows into the sea and to the morphological readjustment of the slope; in the following months/years the rate dramatically decreased when the eruptive vents moved upwards and the eruption finally stopped. After 4 years (February 2007) more than 40{\%} of the scar was already filled. In early 2007, a new eruption occurred and a lava delta was constructed in the 2002 scar, influencing the natural readjustment of the slope; therefore, our reconstruction only encompasses the period between the 2002 and 2007 eruptions. The swath bathymetry reconstruction of geometry and volume of scar filling during the period 2002–2007 evidenced a punctuated and fast shift of depocenters and debris emplacement through avalanching processes. This process quickly obliterated the features produced by the 2002 tsunamigenic landslide so that a major question about the preservation potential of mass-wasting features on active volcanic flanks emerges.},
author = {Chiocci, F. L. and Romagnoli, C. and Bosman, A.},
doi = {10.1016/j.geomorph.2008.01.008},
issn = {0169555X},
journal = {Geomorphology},
keywords = {Multibeam monitoring,Scar infilling,Stromboli volcano,Submarine landslide},
month = {aug},
number = {3-4},
pages = {356--365},
title = {{Morphologic resilience and depositional processes due to the rapid evolution of the submerged Sciara del Fuoco (Stromboli Island) after the December 2002 submarine slide and tsunami}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0169555X08000123},
volume = {100},
year = {2008}
}
@article{Choi2003,
abstract = {Long surface gravity waves of finite amplitude in uniform shear flows are considered by using an asymptotic model derived under the assumption that the aspect ratio between wavelength and water depth is small. Since its derivation requires no assumption on wave amplitude, the model can be used to describe arbitrary amplitude waves. It is shown that the simple model captures the interesting features of strongly nonlinear solitary waves observed in previous numerical solutions. When compared with the case of zero vorticity, the solitary wave in uniform shear flows is wider when propagating upstream (opposite to the direction of surface drift), while it is narrower when propagating downstream. For the upstream-propagating solitary wave, a stationary recirculating eddy appears at the bottom when wave amplitude exceeds the critical value. For the case of downstream propagation, no eddy forms at the bottom but the solitary wave becomes more peaked, yielding a cusp at the critical wave amplitude, beyond which the solitary wave has a round wave profile. Although the appearance of the derivative singularity is inconsistent with the long-wave assumption in the model, round wave profiles away from the singularity are qualitatively similar to numerical solutions and observation.},
author = {Choi, W.},
doi = {10.1103/PhysRevE.68.026305},
issn = {1063-651X},
journal = {Phys. Rev. E},
month = {aug},
number = {2},
pages = {026305},
title = {{Strongly nonlinear long gravity waves in uniform shear flows}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.68.026305},
volume = {68},
year = {2003}
}
@article{Choi2009a,
abstract = {To describe the evolution of fully nonlinear surface gravity waves in a linear shear current, a closed system of exact evolution equations for the free surface elevation and the free surface velocity potential is derived using a conformal mapping technique. Traveling wave solutions of the system are obtained numerically and it is found that the maximum wave amplitude for a positive shear current is much smaller than that in the absence of any shear while the opposite is true for a negative shear current. The new evolution equations are also solved numerically using a pseudo-spectral method to study the Benjamin-Feir instability of a modulated wave train in both positive and negative shear currents. With a fixed wave slope, compared with the irrotational case, the envelope of the modulated wave train grows faster in a positive shear current and slower in a negative shear current.},
author = {Choi, W.},
journal = {Math. Comp. Simul.},
number = {1},
pages = {29--36},
title = {{Nonlinear surface waves interacting with a linear shear current}},
volume = {80},
year = {2009}
}
@article{Choi2009,
author = {Choi, W. and Barros, R. and Jo, T.-E.},
journal = {J. Fluid Mech},
pages = {73--85},
title = {{A regularized model for strongly nonlinear internal solitary waves}},
volume = {629},
year = {2009}
}
@article{Choi1999,
abstract = {This paper considers surface gravity-capillary waves in an ideal fluid of finite depth and generalizes exact evolution equations for free gravity waves obtained by Dyachenko et al. to those for forced gravity-capillary waves. The model derived here describes the time evolution of the free surface and the velocity potential evaluated at the free surface under external pressure forcing. Two integro-differential equations are written explicitly in terms of these two dependent variables, and no extra step is required to close the system. These equations are solved numerically for the particular case of stationary periodic waves, and the results compared with analogous ones available in the literature.},
author = {Choi, W. and Camassa, R.},
doi = {10.1061/(ASCE)0733-9399(1999)125:7(756)},
issn = {07339399},
journal = {J. Eng. Mech.},
number = {7},
pages = {756},
title = {{Exact Evolution Equations for Surface Waves}},
volume = {125},
year = {1999}
}
@article{Chorin1968,
abstract = {A finite-difference method for solving the time-dependent NavierStokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an application to a three-dimensional convection problem is presented.},
author = {Chorin, A.},
journal = {Math. Comp.},
pages = {745--762},
title = {{Numerical solution of the Navier-Stokes equations}},
volume = {22},
year = {1968}
}
@book{Chorin1993,
author = {Chorin, A. and Marsden, J.},
edition = {3rd},
isbn = {978-0387979182},
pages = {172},
publisher = {Springer},
title = {{A Mathematical Introduction to Fluid Mechanics}},
year = {1993}
}
@book{Chow1959,
author = {Chow, V. T.},
isbn = {0070107769},
pages = {680},
publisher = {Mcgraw-Hill College},
title = {{Open-Channel Hydraulics}},
year = {1959}
}
@article{Christov2001,
author = {Christov, C. I.},
journal = {Wave Motion},
pages = {161--174},
title = {{An energy-consistent dispersive shallow-water model}},
volume = {34},
year = {2001}
}
@article{Chu1970,
abstract = {A WKB-perturbation technique is applied to study the slow modulation of a Stokes wave train on the surface of water. It is found that new terms directly representing modulation rates must be included to extend the scope of validity of Whitham's theory based on an averaged Lagrangian. Two examples are discussed. In the first, a monochromatic wave normally incident on a mild beach is studied and the local rate of depth variation is found to affect the wave phase. In the second, the ‘side-band instability’ problem of Benjamin {\&} Feir is discussed from both linear and non-linear points of view.},
author = {Chu, V. H. and Mei, C. C.},
doi = {10.1017/S0022112070000988},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
pages = {873--887},
title = {{On slowly-varying Stokes waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112070000988},
volume = {41},
year = {1970}
}
@article{Chubarov2005,
author = {Chubarov, L. B. and Eletsky, S. V. and Fedotova, Z. I. and Khakimzyanov, G. S.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {5},
pages = {425--437},
title = {{Simulation of surface waves by an underwater landslide}},
volume = {20},
year = {2005}
}
@incollection{Chubarov2011,
address = {Berlin, Heidelberg},
author = {Chubarov, L. B. and Khakimzyanov, G. S. and Shokina, N. Yu.},
booktitle = {Notes on Numerical Fluid Mechanics and Multidisciplinary Design: Computational Science and High Performance Computing IV},
edition = {Vol. 115},
pages = {75--91},
publisher = {Springer-Verlag},
title = {{Numerical modelling of surface water waves arising due to movement of underwater landslide on irregular bottom slope}},
year = {2011}
}
@article{Chueh1977,
author = {Chueh, K. and Conley, C. and Smoller, J.},
journal = {Ind. U. Math. J.},
pages = {373--392},
title = {{Positively invariant regions for systems of nonlinear equations}},
volume = {26},
year = {1977}
}
@phdthesis{Cibura2007,
abstract = {Geometric Algebra is an extension to the linear algebra usually used to describe geometric spaces. It unites Grassmann's inner and outer product into the associative geometric product and allows for the description of geometric objects and transformations like projections and rotations without referring to matrices. Also, algebraic objects described with Geometric Algebra often encode additional information like direction, handedness etc. and have other useful properties. While Geometric Algebra methods have been successfully applied to a variety of problems in the recent past, including computer vision, robotics and relativistic electro-magnetic field theory, its applications to the field of fluid dynamics have been restricted to isolated subjects or specialized problem descriptions. The systematic development of a comprehensive fluid dynamics calculus using Geometric Algebra methods is still an open task. This work will derive the Navier-Stokes equations, which describe a general fluid flow, out of basic physical principles like conservation of mass, balance of momentum and conservations of energy, thus preparing the ground for more in-depth research. While Geometric Algebra does not add greatly to purely scalar equations, it does facilitate their derivation, often making it quicker, easier to understand and, above all, valid in arbitrary dimensions and spaces. Promising results are also achieved in the description of vorticity and rotation as well as the stream function, which can be formulated in higherdimensional and less restricted spaces employing Geometric Algebra.},
author = {Cibura, C.},
keywords = {fluid dynamics,geometric algebra,introduction,mathematics,physics},
pages = {76},
school = {TU Darmstadt},
title = {{Derivation of fluid dynamics basics using geometric algebra}},
url = {http://publica.fraunhofer.de/documents/N-62336.html},
year = {2007}
}
@article{CBB2,
author = {Cienfuegos, R. and Barth{\'{e}}l{\'{e}}my, E. and Bonneton, P.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {1423--1455},
title = {{A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: Boundary conditions and model validation}},
volume = {53},
year = {2007}
}
@article{CBB1,
author = {Cienfuegos, R. and Barth{\'{e}}l{\'{e}}my, E. and Bonneton, P.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {1217--1253},
title = {{A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: Model development and analysis}},
volume = {51},
year = {2006}
}
@article{Clamond2003,
abstract = {Two-dimensional potential flows due to progressive surface waves in deep water are considered. For periodic waves, only gravity is included in the dynamic boundary condition, but both gravity and surface tension are taken into account for solitary waves. The validity of the steady first-order cnoidal wave approximation, i.e. the periodic solution of KdV, is extended to infinite depth by renormalizations. This renormalized cnoidal wave (RCW) solution is expressed as a Fourier–Pad{\'{e}} approximation. It is analytically simpler and more accurate than fifth-order Stokes approximations. It is also capable of describing the recently discovered sharp-crested wave. A sharp-crested wave is obtained when the fluid velocity at the crest is larger than the phase speed. When the wavelength is infinite, RCW yields an algebraic solitary wave. Depending on the surface tension, the solitary wave involves one or two interfaces: a wave of depression; a wave of depression with a pocket of air; a wave of elevation with a pocket of air. Solitary waves are found for all values of the surface tension. However, this does not necessarily mean that these waves are solutions of the exact equations. Moreover, RCW approximate solitary waves always present a dipole singularity. It is also shown that a cnoidal wave in deep water can be rewritten as a periodic distribution of dipoles, each dipole representing an algebraic solitary wave. This provides a new paradigm for descriptions of water wave phenomena.},
author = {Clamond, D.},
doi = {10.1017/S0022112003005111},
issn = {00221120},
journal = {J. Fluid Mech},
month = {jul},
pages = {101--120},
title = {{Cnoidal-type surface waves in deep water}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112003005111},
volume = {489},
year = {2003}
}
@article{Clamond2012a,
abstract = {The velocity and other fields of steady two-dimensional surface gravity waves in irrotational motion are investigated numerically. Only symmetric waves with one crest per wavelength are considered, i.e. Stokes waves of finite amplitude, but not the highest waves, nor subharmonic and superharmonic bifurcations of Stokes waves. The numerical results are analysed, and several conjectures are made about the velocity and acceleration fields.},
author = {Clamond, D.},
doi = {10.1098/rsta.2011.0470},
issn = {1364-503X},
journal = {Phil. Trans. R. Soc. A},
month = {apr},
number = {1964},
pages = {1572--1586},
pmid = {22393109},
title = {{Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/22393109},
volume = {370},
year = {2012}
}
@article{Clamond1999,
abstract = {From shallow-water gravity wave theories it is shown that the velocity field in the whole fluid domain can be reconstructed using an analytic transformation (a renormalization). The resulting velocity field satisfies the Laplace equation exactly, which is not the case for shallow-water approximations. Applying the renormalization to the first-order shallow-water solution of limited accuracy, gives accurate simple solutions for both long and short waves, even for large amplitudes. The KdV and Airy solutions are special limiting cases.},
author = {Clamond, D.},
doi = {10.1017/S0022112099006151},
issn = {00221120},
journal = {J. Fluid Mech},
month = {nov},
pages = {45--60},
title = {{Steady finite-amplitude waves on a horizontal seabed of arbitrary depth}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112099006151},
volume = {398},
year = {1999}
}
@article{Clamond1995,
author = {Clamond, D. and Barth{\'{e}}l{\'{e}}my, E.},
journal = {C.R. Acad. Sci. Paris Ser. II},
number = {6},
pages = {277--280},
title = {{Experimental determination of the phase shift in the Stokes wave-solitary wave interaction}},
volume = {320},
year = {1995}
}
@article{Clamond2012b,
abstract = {In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a fixed domain using the conformal mapping technique. Second, the problem is reduced to a single equation for the free surface. Third, this equation is solved using Petviashvili’s iterations together with pseudo-spectral discretisation. This method has a super-linear complexity, since the most demanding operations can be performed using a FFT algorithm. Moreover, when this algorithm is combined with the multi-precision floating point computations, the results can be obtained to any arbitrary accuracy.},
author = {Clamond, D. and Dutykh, D.},
doi = {10.1016/j.compfluid.2013.05.010},
issn = {00457930},
journal = {Comput. {\&} Fluids},
keywords = {Fully nonlinear water wave equations,Petviashvili method,Solitary gravity waves},
month = {jun},
pages = {35--38},
title = {{Fast accurate computation of the fully nonlinear solitary surface gravity waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0045793013001965},
volume = {84},
year = {2013}
}
@article{Clamond2009,
abstract = {This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a ‘relaxed’ variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving a variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact traveling wave solutions are constructed when possible.},
archivePrefix = {arXiv},
arxivId = {1002.3019},
author = {Clamond, D. and Dutykh, D.},
doi = {10.1016/j.physd.2011.09.015},
eprint = {1002.3019},
journal = {Phys. D},
keywords = {Approximations,Hamiltonian,Lagrangian,Relaxation,Variational principle,Water waves},
number = {1},
pages = {25--36},
title = {{Practical use of variational principles for modeling water waves}},
volume = {241},
year = {2012}
}
@misc{Clamond2012,
author = {Clamond, D. and Dutykh, D.},
keywords = {Euler equations,Free surface hydrodynamics,Solitary waves},
title = {http://www.mathworks.com/matlabcentral/fileexchange/39189-solitary-water-wave},
year = {2012}
}
@article{Clamond2015a,
archivePrefix = {arXiv},
arxivId = {1411.5519},
author = {Clamond, D. and Dutykh, D. and Dur{\'{a}}n, A.},
eprint = {1411.5519},
journal = {J. Fluid Mech.},
pages = {664--680},
title = {{A plethora of generalised solitary gravity-capillary water waves}},
url = {https://hal.archives-ouvertes.fr/hal-01081798/},
volume = {784},
year = {2015}
}
@inproceedings{Clamond2015,
author = {Clamond, D. and Dutykh, D. and Galligo, A.},
booktitle = {Proceedings of ISSAC 2015},
publisher = {ACM},
title = {{Computer algebra applied to a solitary waves study}},
year = {2015}
}
@article{Clamond2015c,
author = {Clamond, D. and Dutykh, D. and Mitsotakis, D.},
journal = {Submitted},
pages = {1--15},
title = {{Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics}},
year = {2015}
}
@article{Clamond2006,
abstract = {This paper concerns long time interaction of envelope solitary gravity waves propagating at the surface of a two-dimensional deep fluid in potential flow. Fully nonlinear numerical simulations show how an initially long wave group slowly splits into a number of solitary wave groups. In the example presented, three large wave events are formed during the evolution. They occur during a time scale that is beyond the time range of validity of simplified equations like the nonlinear Schr{\"{o}}dinger (NLS) equation or modifications of this equation. A Fourier analysis shows that these large wave events are caused by significant transfer to side-band modes of the carrier waves. Temporary downshiftings of the dominant wavenumber of the spectrum coincide with the formation large wave events. The wave slope at maximal amplifications is about three times higher than the initial wave slope. The results show how interacting solitary wave groups that emerge from a long wave packet can produce freak wave events. Our reference numerical simulation are performed with the fully nonlinear model of Clamond and Grue [D. Clamond, J. Grue, A fast method for fully nonlinear water wave computations, J. Fluid Mech. 447 (2001) 337–355]. The results of this model are compared with that of two weakly nonlinear models, the NLS equation and its higher-order extension derived by Trulsen et al. [K. Trulsen, I. Kliakhandler, K.B. Dysthe, M.G. Velarde, On weakly nonlinear modulation of waves on deep water, Phys. Fluids 12 (10) (2000) 2432–2437]. They are also compared with the results obtained with a high-order spectral method (HOSM) based on the formulation of West et al. [B.J. West, K.A. Brueckner, R.S. Janda, A method of studying nonlinear random field of surface gravity waves by direct numerical simulation, J. Geophys. Res. 92 (C11) (1987) 11 803–11 824]. An important issue concerning the representation and the treatment of the vertical velocity in the HOSM formulation is highlighted here for the study of long-time evolutions.},
author = {Clamond, D. and Francius, M. and Grue, J. and Kharif, C.},
doi = {10.1016/j.euromechflu.2006.02.007},
journal = {Eur. J. Mech. B/Fluids},
number = {5},
pages = {536--553},
title = {{Long time interaction of envelope solitons and freak wave formations}},
volume = {25},
year = {2006}
}
@article{Clamond2005,
author = {Clamond, D. and Fructus, D. and Grue, J. and Kristiansen, O.},
journal = {J. Comp. Phys.},
month = {may},
pages = {686--705},
title = {{An efficient model for three-dimensional surface wave simulations. Part II: Generation and absorption}},
volume = {205(2)},
year = {2005}
}
@article{Clamond2001,
author = {Clamond, D. and Grue, J.},
journal = {J. Fluid. Mech.},
pages = {337--355},
title = {{A fast method for fully nonlinear water-wave computations}},
volume = {447},
year = {2001}
}
@article{Clauss2011,
author = {Clauss, G. F. and Klein, M. F.},
doi = {10.1016/j.oceaneng.2011.07.022},
journal = {Ocean Engineering},
pages = {1624--1639},
title = {{The New Year Wave in a sea keeping basin: Generation, propagation, kinematics and dynamics}},
volume = {38},
year = {2011}
}
@article{Clement-Rastello2001,
author = {Cl{\'{e}}ment-Rastello, M.},
journal = {Annals of Glaciology},
pages = {259--262},
title = {{A study on the size of snow particles in powder-snow avalanches}},
volume = {32},
year = {2001}
}
@book{Coaz1881,
author = {Coaz, J. W.},
publisher = {Schmid-Franke, Bern},
title = {{Die Lawinen der Schweizer Alpen}},
year = {1881}
}
@article{Cockburn2004,
author = {Cockburn, B. and Li, F. and Shu, C.-W.},
journal = {J. Comp. Phys.},
pages = {588--610},
title = {{Locally divergence-free discontinuous Galerkin methods for the Maxwell equations}},
volume = {194},
year = {2004}
}
@article{Coifman1985,
author = {Coifman, R. R. and Meyer, Y.},
journal = {Pseudodifferential Operators and Applications},
pages = {71--78},
title = {{Nonlinear harmonic analysis and analytic dependence}},
volume = {43},
year = {1985}
}
@phdthesis{Coirier1994,
author = {Coirier, W. J.},
school = {Michigan Univ.},
title = {{An Adaptatively-Refined, Cartesian, Cell-based Scheme for the Euler and Navier-Stokes Equations}},
year = {1994}
}
@article{Colagrossi2003,
author = {Colagrossi, A. and Landrini, M.},
journal = {Comput. Phys. Comm.},
pages = {448--475},
title = {{Numerical simulation of interfacial flows by smoothed particle hydrodynamics}},
volume = {191},
year = {2003}
}
@book{Cole1948,
author = {Cole, R. H.},
publisher = {Princeton University Press},
title = {{Underwater explosions}},
year = {1948}
}
@article{Colin2006,
author = {Colin, M. and Ohta, M.},
journal = {Ann. I. H. Poincar{\'{e}}},
pages = {753--764},
title = {{Stability of solitary waves for derivative nonlinear Schr{\"{o}}dinger equation}},
volume = {23},
year = {2006}
}
@article{Constantin2011,
abstract = {We study the pressure beneath a solitary water wave propagating in an irrotational flow at the free surface of water with a flat bed. The investigation is divided into two parts. The first part concerns a rigorous nonlinear study of the governing equations for water waves. We prove that the pressure in the fluid beneath a solitary wave strictly increases with depth and strictly decreases horizontally away from the vertical line beneath the crest. The second part of the paper describes an experimental study. Excellent agreement is found to exist between the theoretical predictions and the measurements. Our conclusions are also supported by numerical simulations.},
author = {Constantin, A. and Escher, J. and Hsu, H.-C.},
doi = {10.1007/s00205-011-0396-0},
issn = {0003-9527},
journal = {Archive for Rational Mechanics and Analysis},
month = {feb},
number = {1},
pages = {251--269},
title = {{Pressure Beneath a Solitary Water Wave: Mathematical Theory and Experiments}},
url = {http://www.springerlink.com/index/10.1007/s00205-011-0396-0},
volume = {201},
year = {2011}
}
@article{Constantin2008a,
abstract = {The interest in the Camassa-Holm equation inspired the search for various generalizations of this equation with interesting properties and applications. In this Letter we deal with such a two-component integrable system of coupled equations. First we derive the system in the context of shallow water theory. Then we show that while small initial data develop into global solutions, for some initial data wave breaking occurs. We also discuss the solitary wave solutions. Finally, we present an explicit construction for the peakon solutions in the short wave limit of system.},
author = {Constantin, A. and Ivanov, R. I.},
doi = {10.1016/j.physleta.2008.10.050},
issn = {03759601},
journal = {Phys. Lett. A},
month = {dec},
number = {48},
pages = {7129--7132},
title = {{On an integrable two-component Camassa-Holm shallow water system}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960108015351},
volume = {372},
year = {2008}
}
@article{Constantin2008,
author = {Constantin, A. and Johnson, R. S.},
journal = {Fluid Dyn. Res.},
pages = {175--211},
title = {{Propagation of very long water waves, with vorticity, over variable depth, with application to tsunamis}},
volume = {40},
year = {2008}
}
@article{Constantin2006,
author = {Constantin, A. and Sattinger, D. H. and Strauss, W.},
journal = {J. Fluid Mech.},
pages = {151--163},
title = {{Variational formulations for steady water waves with vorticity}},
volume = {548},
year = {2006}
}
@article{Conti2003,
abstract = {Nonlinear optical media that are normally dispersive support a new type of localized (nondiffractive and nondispersive) wave packets that are X shaped in space and time and have slower than exponential decay. High-intensity X waves, unlike linear ones, can be formed spontaneously through a trigger mechanism of conical emission, thus playing an important role in experiments.},
author = {Conti, C. and Trillo, S. and {Di Trapani}, P. and Valiulis, G. and Piskarskas, A. and Jedrkiewicz, O. and Trull, J.},
doi = {10.1103/PhysRevLett.90.170406},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {may},
number = {17},
title = {{Nonlinear Electromagnetic X Waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.90.170406},
volume = {90},
year = {2003}
}
@article{Cooker1995,
author = {Cooker, M. J. and Peregrine, D. H.},
journal = {J. Fluid Mech.},
pages = {193--214},
title = {{Pressure impulse theory for liquid impact problems}},
volume = {297},
year = {1995}
}
@article{Cooker1997,
author = {Cooker, M. J. and Weidman, P. D. and Bale, D. S.},
journal = {J. Fluid Mech.},
pages = {141--158},
title = {{Reflection of a high-amplitude solitary wave at a vertical wall}},
volume = {342},
year = {1997}
}
@article{Cooley1965,
author = {Cooley, J. W. and Tukey, J. W.},
doi = {10.1090/S0025-5718-1965-0178586-1},
issn = {0025-5718},
journal = {Mathematics of Computation},
month = {may},
number = {90},
pages = {297--297},
title = {{An algorithm for the machine calculation of complex Fourier series}},
url = {http://www.ams.org/jourcgi/jour-getitem?pii=S0025-5718-1965-0178586-1},
volume = {19},
year = {1965}
}
@book{copson,
author = {Copson, E. T.},
publisher = {Cambridge University Press},
title = {{Asymptotic expansions}},
year = {1965}
}
@article{Corless1996,
author = {Corless, R. M. and Gonnet, G. H. and Hare, D. E. G. and Jeffrey, D. J. and Knuth, D. E.},
journal = {Adv. Comput. Math.},
pages = {329--359},
title = {{On the Lambert W function}},
volume = {5},
year = {1996}
}
@article{Coron2004,
author = {Coron, J.-M. and Crepeau, E.},
journal = {J. Eur. Math. Soc.},
pages = {367--398},
title = {{Exact boundary controllability of a nonlinear KdV equation with a critical length}},
volume = {6},
year = {2004}
}
@inproceedings{Cortes2000,
author = {Cortes, J. and Ghidaglia, J.-M.},
booktitle = {Trends in Numerical and Physical Modeling for Industrial Multiphase Flows},
title = {{Upwinding at low cost for complex models and flux schemes}},
year = {2000}
}
@article{Costa2014,
author = {Costa, A. and Osborne, A. R. and Resio, D. and Alessio, S. and Chrivi, E. and Saggese, E. and Bellomo, K. and Long, C. E.},
doi = {10.1103/PhysRevLett.113.108501},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {sep},
number = {10},
pages = {108501},
title = {{Soliton Turbulence in Shallow Water Ocean Surface Waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.113.108501},
volume = {113},
year = {2014}
}
@inproceedings{Costes2013,
address = {Alaska, USA},
author = {Costes, J. and Dias, F. and Ghidaglia, J.-M. and Mrabet, A.},
booktitle = {Proceedings of 23rd International Offshore and Polar Engineering Conference (ISOPE)},
title = {{Simulation of Breaking Wave Impacts on a Flat Rigid Wall by a 2D Parallel Finite Volume Solver with Two Compressible Fluids and an Advanced Free Surface Reconstruction}},
year = {2013}
}
@article{Cotter2010,
author = {Cotter, C. and Bokhove, O.},
doi = {10.1007/s10665-009-9346-3},
issn = {0022-0833},
journal = {J. Eng. Math.},
month = {oct},
number = {1-2},
pages = {33--54},
title = {{Variational water-wave model with accurate dispersion and vertical vorticity}},
url = {http://www.springerlink.com/index/10.1007/s10665-009-9346-3},
volume = {67},
year = {2010}
}
@article{Coudiere1999,
author = {Coudiere, Y. and Vila, J. P. and Villedieu, P.},
journal = {M2AN},
pages = {493--516},
title = {{Convergence Rate of a Finite Volume Scheme for a Two Dimensionnal Convection Diffusion Problem}},
volume = {33 (3)},
year = {1999}
}
@article{Courant1928,
author = {Courant, R. and Friedrichs, K. and Lewy, H.},
journal = {Mathematische Annalen},
number = {1},
pages = {32--74},
title = {{{\"{U}}ber die partiellen Differenzengleichungen der mathematischen Physik}},
volume = {100},
year = {1928}
}
@article{Courant1967,
author = {Courant, R. and Friedrichs, K. and Lewy, H.},
journal = {IBM Journal},
pages = {215--234},
title = {{On the partial difference equations of mathematical physics. English translation of the 1928 German original}},
year = {1967}
}
@article{Courant1952,
author = {Courant, R. and Isaacson, E. and Rees, M.},
doi = {10.1002/cpa.3160050303},
issn = {00103640},
journal = {Comm. Pure Appl. Math.},
month = {aug},
number = {3},
pages = {243--255},
title = {{On the solution of nonlinear hyperbolic differential equations by finite differences}},
url = {http://doi.wiley.com/10.1002/cpa.3160050303},
volume = {5},
year = {1952}
}
@article{CourtenayLewis1979,
author = {{Courtenay Lewis}, J. and Tjon, J. A.},
journal = {Phys. Lett.},
pages = {275--279},
title = {{Resonant production of solitons in the RLW equation}},
volume = {73A},
year = {1979}
}
@article{Cox2001,
author = {Cox, E. A. and Kluwick, A.},
journal = {Z. angew. Math. Phys.},
pages = {924--949},
title = {{Waves and nonclassical shocks in a scalar conservation law with nonconvex flux}},
volume = {52},
year = {2001}
}
@article{Cox1986,
abstract = {This paper is concerned with the evolution of small-amplitude, long-wavelength, resonantly forced oscillations of a liquid in a tank of finite length. It is shown that the surface motion is governed by a forced Korteweg-de Vries equation. Numerical integration indicates that the motion does not evolve to a periodic steady state unless there is dissipation in the system. When there is no dissipation there are cycles of growth and decay reminiscent of Fermi-Pasta-Ulam recurrence. The experiments of Chester {\&} Bones (1968) show that for certain frequencies more than one periodic solution is possible. We illustrate the evolution of two such solutions for the fundamental resonance frequency.},
author = {Cox, E. A. and Mortell, M. P.},
doi = {10.1017/S0022112086001945},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {99--116},
title = {{The evolution of resonant water-wave oscillations}},
volume = {162},
year = {1986}
}
@article{Craig1994,
author = {Craig, W. and Groves, M. D.},
journal = {Wave Motion},
pages = {367--389},
title = {{Hamiltonian long-wave approximations to the water-wave problem}},
volume = {19},
year = {1994}
}
@article{CGHHS,
author = {Craig, W. and Guyenne, P. and Hammack, J. and Henderson, D. and Sulem, C.},
doi = {10.1063/1.2205916},
journal = {Phys. Fluids},
pages = {57106},
title = {{Solitary water wave interactions}},
volume = {18(5)},
year = {2006}
}
@article{Craig2005,
author = {Craig, W. and Guyenne, P. and Nicholls, D. P. and Sulem, C.},
journal = {Proc. R. Soc. A},
pages = {839--873},
title = {{Hamiltonian long-wave expansions for water waves over a rough bottom}},
volume = {461},
year = {2005}
}
@article{Craig2002,
author = {Craig, W. and Nicholls, D. P.},
doi = {10.1016/S0997-7546(02)01207-4},
issn = {09977546},
journal = {European Journal of Mechanics - B/Fluids},
month = {nov},
number = {6},
pages = {615--641},
title = {{Traveling gravity water waves in two and three dimensions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754602012074},
volume = {21},
year = {2002}
}
@article{Craig1988,
abstract = {It is shown that all supercritical solitary wave solutions to the equations for water waves are symmetric, and monotone on either side of the crest. The proof is based on the Alexandrov method of moving planes. Further a priori estimates, and asymptotic decay properties of solutions are derived},
author = {Craig, W. and Sternberg, P.},
doi = {10.1080/03605308808820554},
issn = {0360-5302},
journal = {Communications in Partial Differential Equations},
number = {5},
pages = {603--633},
title = {{Symmetry of solitary waves}},
url = {http://www.informaworld.com/openurl?genre=article{\&}doi=10.1080/03605308808820554{\&}magic=crossref||D404A21C5BB053405B1A640AFFD44AE3},
volume = {13},
year = {1988}
}
@article{Craig1993,
author = {Craig, W. and Sulem, C.},
journal = {J. Comput. Phys.},
pages = {73--83},
title = {{Numerical simulation of gravity waves}},
volume = {108},
year = {1993}
}
@article{Craig1992,
author = {Craig, W. and Sulem, C. and Sulem, P.-L.},
journal = {Nonlinearity},
pages = {497--522},
title = {{Nonlinear modulation of gravity waves: a rigorous approach}},
volume = {5(2)},
year = {1992}
}
@article{Craik2004,
abstract = {After early work by Newton, the eighteenth and early nineteenth century French mathematicians Laplace, Lagrange, Poisson, and Cauchy made real theoretical advances in the linear theory of water waves; in Germany, Gerstner considered nonlinear waves, and the brothers Weber performed fine experiments. Later in Britain during 1837-1847, Russell, Green, Kelland, Airy, and Earnshaw all made substantial contributions, setting the scene for subsequent work by Stokes and others.},
author = {Craik, A. D. D.},
doi = {10.1146/annurev.fluid.36.050802.122118},
journal = {Ann. Rev. Fluid Mech.},
pages = {1--28},
title = {{The origins of water wave theory}},
volume = {36},
year = {2004}
}
@book{Craik1988,
abstract = {This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.},
address = {Cambridge},
author = {Craik, A. D. D.},
pages = {336},
publisher = {Cambridge University Press},
title = {{Wave Interactions and Fluid Flows}},
year = {1988}
}
@article{Crandall1983,
author = {Crandall, M. G. and Lions, P.-L.},
doi = {10.2307/1999343},
issn = {00029947},
journal = {Transactions of the American Mathematical Society},
month = {may},
number = {1},
pages = {1--42},
title = {{Viscosity Solutions of Hamilton-Jacobi Equations}},
url = {http://www.jstor.org/stable/1999343?origin=crossref},
volume = {277},
year = {1983}
}
@article{Crooks2003,
author = {Crooks, E. C. M.},
journal = {Adv. Differential Equations},
number = {3},
pages = {257--384},
title = {{Travelling fronts for monostable reaction-diffusion systems with gradient-dependence}},
volume = {8},
year = {2003}
}
@article{Cross1967,
author = {Cross, R. H.},
journal = {J. Waterway, Port, Coastal, and Ocean Eng.},
number = {WW4},
pages = {201--231},
title = {{Tsunami surge forces}},
volume = {93},
year = {1967}
}
@article{Cruz-Atienza2004,
author = {Cruz-Atienza, V. M. and Virieux, J.},
journal = {Geophys. J. Int.},
pages = {939--954},
title = {{Dynamic rupture simulation of non-planar faults with a finite-difference approach}},
volume = {158},
year = {2004}
}
@article{Cummins1999,
abstract = {A new formulation is introduced for enforcing incompressibility in Smoothed Particle Hydrodynamics (SPH). The method uses a fractional step with the velocity field integrated forward in time without enforcing incompressibility. The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation derived from an approximate pressure projection. Unlike earlier approaches used to simulate incompressible flows with SPH, the pressure is not a thermodynamic variable and the Courant condition is based only on fluid velocities and not on the speed of sound. Although larger time-steps can be used, the solution of the resulting elliptic pressure Poisson equation increases the total work per time-step. Efficiency comparisons show that the projection method has a significant potential to reduce the overall computational expense compared to weakly compressible SPH, particularly as the Reynolds number, Re, is increased. Simulations using this SPH projection technique show good agreement with finite-difference solutions for a vortex spin-down and Rayleigh-Taylor instability. The results, however, indicate that the use of an approximate projection to enforce incompressibility leads to error accumulation in the density field.},
author = {Cummins, S. J. and Rudman, M.},
doi = {10.1006/jcph.1999.6246},
isbn = {0021-9991},
issn = {00219991},
journal = {J. Comp. Phys.},
number = {2},
pages = {584--607},
title = {{An SPH Projection Method}},
url = {http://www.sciencedirect.com/science/article/pii/S0021999199962460},
volume = {152},
year = {1999}
}
@article{Curie1880,
author = {Curie, J. and Curie, P.},
journal = {Comptes rendus hebdomadaires des s{\'{e}}ances de l'Acad{\'{e}}mie des sciences},
pages = {294--295},
title = {{D{\'{e}}veloppement par compression de l’{\'{e}}lectricit{\'{e}} polaire dans les cristaux h{\'{e}}mi{\`{e}}dres {\`{a}} faces inclin{\'{e}}es}},
volume = {91},
year = {1880}
}
@article{Cvitanovic1995,
abstract = {Periodic orbit theory methods for evaluation of average values of observables for chaotic dynamical systems are reviewed and illustrated by several examples, such as evaluation of the Lyapunov exponents and the diffusion constants.},
author = {Cvitanovi{\'{c}}, P.},
doi = {10.1016/0167-2789(94)00256-P},
issn = {01672789},
journal = {Phys. D},
month = {may},
number = {1-3},
pages = {109--123},
title = {{Dynamical averaging in terms of periodic orbits}},
volume = {83},
year = {1995}
}
@article{Cvitanovic1991,
abstract = {The authors derive a generalized Selberg-type zeta function for a smooth deterministic flow which relates the spectrum of an evolution operator to the periodic orbits of the flow. This relation is a classical analogue of the quantum trace formulae and Selberg-type zeta functions.},
author = {Cvitanovi{\'{c}}, P. and Eckhardt, B.},
doi = {10.1088/0305-4470/24/5/005},
issn = {0305-4470},
journal = {J. Phys. A: Math. Gen.},
month = {mar},
number = {5},
pages = {L237--L241},
title = {{Periodic orbit expansions for classical smooth flows}},
volume = {24},
year = {1991}
}
@article{D'Ambrosio2006,
author = {D'Ambrosio, D. and Spataro, W. and Iovine, G.},
journal = {Computers {\&} Geosciences},
pages = {861--875},
title = {{Parallel genetic algorithms for optimising cellular automata models of natural complex phenomena: an application to debris-flows}},
volume = {32},
year = {2006}
}
@article{BeiraodaVeiga1983,
author = {da Veiga, H.},
journal = {Ann. Scuola Norm Pisa},
pages = {341--351},
title = {{Diffusion on viscous fluids, Existence ans asymptotic properties of solutions}},
volume = {10},
year = {1983}
}
@article{BeiraodaVeiga1982,
author = {da Veiga, H. and Separioni, H. and Valli, A.},
journal = {J. Math. Anal. Appl.},
pages = {179--191},
title = {{On the motion of nonhomogeneous fluids in the presence of diffusion}},
volume = {85},
year = {1982}
}
@article{Dalitz1997,
abstract = {For two particular collision kernels, we explicitly solve the one-dimensional stationary half-space boundary value problem of the linear Boltzmann equation including a constant external field via an extension of Case's eigenfunction technique. In the first collision model we reproduce a solution recently obtained by Cercignani; in the second model the solution of the stationary boundary value problem is presented for the first time.},
author = {Dalitz, Ch.},
doi = {10.1007/BF02508467},
issn = {0022-4715},
journal = {J. Stat. Phys.},
month = {jul},
number = {1-2},
pages = {129--144},
title = {{Half-space problem of the Boltzmann equation for charged particles}},
url = {http://link.springer.com/10.1007/BF02508467},
volume = {88},
year = {1997}
}
@article{DGK,
author = {Dalrymple, R. A. and Grilli, S. T. and Kirby, J. T.},
journal = {Oceanography},
pages = {142--151},
title = {{Tsunamis and challenges for accurate modeling}},
volume = {19},
year = {2006}
}
@book{Dames&Moore1980,
author = {{Dames {\&} Moore}},
publisher = {Dames {\&} Moore},
title = {{Design and construction standards for residential construction in tsunami-prone areas in Hawaii}},
year = {1980}
}
@article{Tkalich2007,
author = {Dao, M. H. and Tkalich, P.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {741--754},
title = {{Tsunami propagation modelling - a sensitivity study}},
volume = {7},
year = {2007}
}
@article{Das1996,
abstract = {In order to gain insight into how to invert seismograms correctly to estimate the details of the earthquake rupturing process, we perform numerical experiments using artificial data, generated for an idealized faulting model with a very simple rupture and moment release history, and solve the inverse problem using standard widely used inversion methods. We construct synthetic accelerograms in the vicinity of an earthquake for a discrete analog of the Haskell-type rupture model with a prescribed rupture velocity in a layered medium. A constant level of moment is released as the rupture front passes by. We show that using physically based constraints, such as not permitting back slip on the fault, allow us to reproduce many aspects of the solution correctly, whereas the minimum norm solution or the solution with the smallest first differences of moment rates in space and time do not reproduce many aspects for the cases studied here. With the positivity of moment rate constraint, as long as the rupturing area is allowed to be larger than that in the forward problem, it is correctly found for the simple faulting model considered in this paper, provided that the rupture velocity and the Earth structure are known. If, however, the rupture front is constrained either to propagate more slowly or the rupturing area is taken smaller than that in the forward problem, we find that we are unable even to fit the accelerograms well. Use of incorrect crustal structure in the source region also leads to poor fitting of the data. In this case, the proper rupture front is not obtained, but instead a “ghost front” is found behind the correct rupture front and demonstrates how the incorrect crustal structure is transformed into an artifact in the solution. The positions of the centroids of the moment release in time and space are generally correctly obtained.},
author = {Das, S. and Suhadolc, P.},
doi = {10.1029/95JB03533},
issn = {0148-0227},
journal = {Journal of Geophysical Research},
number = {B3},
pages = {5725--5738},
title = {{On the inverse problem for earthquake rupture: The Haskell-type source model}},
url = {http://www.agu.org/pubs/crossref/1996/95JB03533.shtml},
volume = {101},
year = {1996}
}
@article{Dashen1974,
abstract = {This is the first of a series of papers on the use of semiclassical approximations to find particle states in field theory. The meaning of the WKB approximation is examined from a functional-integral approach. Special emphasis is placed on the distinction between a true WKB or semiclassical approach and the weak-coupling approximation to it. Other topics include the center-of-mass motion of particle states and some problems special to field theory such as multiple-particle states, statistics, and infinite-volume systems. Ultraviolet divergences are touched on, but are dealt with more thoroughly in the following paper where specific models are examined. The central result of this series is that certain kinds of nonlinear field theories have extended particle solutions which survive quantization. The most interesting of these objects, which are reminiscent of hadrons, come from theories with spontaneous symmetry breaking.},
author = {Dashen, R. F. and Hasslacher, B. and Neveu, A.},
doi = {10.1103/PhysRevD.10.4114},
issn = {05562821},
journal = {Phys. Rev. D},
number = {12},
pages = {4114--4129},
title = {{Nonperturbative methods and extended-hadron models in field theory. I. Semiclassical functional methods}},
volume = {10},
year = {1974}
}
@article{Davey1974,
author = {Davey, A. and Stewartson, K.},
doi = {10.1098/rspa.1974.0076},
issn = {1364-5021},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
month = {jun},
number = {1613},
pages = {101--110},
title = {{On Three-Dimensional Packets of Surface Waves}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1974.0076},
volume = {338},
year = {1974}
}
@article{Davis1988,
author = {Davis, S. F.},
journal = {SIAM J. Sci. Statist. Comput.},
pages = {445--473},
title = {{Simplified second-order Godunov-type methods}},
volume = {9},
year = {1988}
}
@article{Dawson2005,
author = {Dawson, C. and Aizinger, V.},
journal = {J. Sci. Comput.},
number = {1-3},
pages = {245--267},
title = {{A discontinuous Galerkin method for three-dimensional shallow water equations}},
volume = {22},
year = {2005}
}
@article{Day1999,
abstract = {The CumbreViejavolcano is the youngest component of the island of La Palma. It is a very steep-sided oceanic island volcano, of a type which may undergo large-scale lateral collapse with little precursory deformation. Reconfiguration of the volcanic rift zones and underlying dyke swarms of the volcano is used to determine the present degree of instability of the volcano. For most of its history, from before 125 ka ago to around 20 ka, the CumbreViejavolcano was characterised by a triple (“Mercedes Star”) volcanic rift zone geometry. The three rift zones were unequally developed, with a highly productive south rift zone and weaker NE and NW rift zones: the disparity in activity was probably due to topographic-gravitational stresses associated with the west facing Cumbre Nueva collapse structure underneath the western flank of the CumbreVieja. From 20 ka to about 7 ka, activity on the NW volcanic rift zone diminished and the intersection of the rift zones migrated slightly to the north. More recently, the triple rift geometry has been replaced at the surface by a N–S-trending rift zone which transects the volcano, and by E–W-trending en echelon fissure arrays on the western flank of the volcano. The NE rift zone has become completely inactive. This structural reconfiguration indicates weakening of the western flank of the volcano. The most recent eruption near the summit of the CumbreVieja, that of 1949, was accompanied by development of a west facing normal fault system along the crest of the volcano. The geometry of this fault system and the timing of its formation in relation to episodes of vent opening during the eruption indicate that it is not the surface expression of a dyke. Instead, it is interpreted as being the first surface rupture along a developing zone of deformation and seaward movement within the western flank of the CumbreVieja: the volcano is therefore considered to be at an incipient stage of flank instability. Climatic factors or strain weakening along the Cumbre Nueva collapse structure may account for the recent development of this instability.},
author = {Day, S. J. and Carracedo, J. C. and Guillou, H. and Gravestock, P.},
doi = {10.1016/S0377-0273(99)00101-8},
issn = {03770273},
journal = {Journal of Volcanology and Geothermal Research},
keywords = {CumbreViejavolcano,volcanic rift zones,volcanic vents},
month = {dec},
number = {1-4},
pages = {135--167},
title = {{Recent structural evolution of the Cumbre Vieja volcano, La Palma, Canary Islands: volcanic rift zone reconfiguration as a precursor to volcano flank instability?}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377027399001018},
volume = {94},
year = {1999}
}
@article{Bouard2008,
author = {de Bouard, A. and Craig, W. and Diaz-Espinosa, O. and Guyenne, P. and Sulem, C.},
journal = {Nonlinearity},
pages = {2143--2178},
title = {{Long wave expansions for water waves over random topography}},
volume = {21(9)},
year = {2008}
}
@article{DeBouard2007,
abstract = {We study the asymptotic behavior of the solution of a Korteweg-de Vries equation with an additive noise whose amplitude E tends to zero. The noise is white in time and correlated in space and the initial state of the solution is a soliton solution of the unperturbed Korteweg-de Vries equation. We prove that up to times of the order of 1/epsilon(2), the solution decomposes into the sum of a randomly modulated soliton, and a small remainder, and we derive the equations for the modulation parameters. We prove in addition that the first order part of the remainder converges, as E tends to zero, to a Gaussian process, which satisfies an additively perturbed linear equation. (c) 2006 Elsevier Masson SAS. All rights reserved.},
author = {{De Bouard}, A. and Debussche, A.},
doi = {10.1016/j.anihpc.2006.03.009},
issn = {02941449},
journal = {Ann. Inst. Henri Poincar{\'{e}}},
keywords = {central limit theorem,de vries equation,korteweg,solitary waves,stochastic partial differential equations,white noise},
number = {2},
pages = {251--278},
title = {{Random modulation of solitons for the stochastic Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0294144906000667},
volume = {24},
year = {2007}
}
@article{DeBruijn1981,
author = {de Bruijn, N. G.},
journal = {Nederl. Akad. Wetensch. Indag. Math.},
number = {1},
pages = {39--66},
title = {{Algebraic theory of Penrose's nonperiodic tilings of the plane. I, II}},
volume = {43},
year = {1981}
}
@unpublished{Jong2009,
author = {de Jong, C.},
title = {{Personal communication}},
year = {2009}
}
@article{DelaLlave1997,
author = {de la Llave, R.},
doi = {10.1007/BF02181486},
issn = {0022-4715},
journal = {Journal of Statistical Physics},
month = {apr},
number = {1-2},
pages = {211--249},
title = {{Invariant manifolds associated to nonresonant spectral subspaces}},
volume = {87},
year = {1997}
}
@inproceedings{DeLeffe2009,
address = {Nantes, France},
author = {{De Leffe}, M. and {Le Touz{\'{e}}}, D. and Alessandrini, B.},
booktitle = {4th SPHERIC Workshop Proceedings},
title = {{Normal flux method at the boundary for SPH}},
year = {2009}
}
@inproceedings{DeLuna2008,
abstract = {We present a new model for hyperpycnal plumes or turbidity currents. This model takes into account deposition and erosion effects as well as solid transport of particles at the bed load due to the current. The model is obtained as depth-average equations under the shallow water hypothesis describing the balance of fluid mass, sediment mass and mean flow. The final system is hyperbolic and numerical simulations are carried out using finite volume schemes and path-conservative schemes.},
author = {{De Luna}, T. and Castro-Diaz, M. J. and {Par{\'{e}}s Madro{\~{n}}al}, C.},
booktitle = {Finite Volumes for Complex Applications V},
isbn = {9781848210356},
pages = {593--600},
publisher = {Wiley},
title = {{Modeling and Simulation of Turbidity Currents}},
url = {http://www.iste.co.uk/index.php?p=a{\&}ACTION=View{\&}id=220},
year = {2008}
}
@article{SV1871,
author = {de Saint-Venant, A. J. C.},
journal = {C. R. Acad. Sc. Paris},
pages = {147--154},
title = {{Th{\'{e}}orie du mouvement non-permanent des eaux, avec application aux crues des rivi{\`{e}}res et {\`{a}} l'introduction des mar{\'{e}}es dans leur lit}},
volume = {73},
year = {1871}
}
@article{DeSterck2001,
abstract = {Recently, it has been shown that for strong upstream magnetic field, stationary three-dimensional magnetohydrodynamic (MHD) bow shock flows exhibit a complex double-front shock topology with particular segments of the shock fronts being of the intermediate MHD shock type. The large-scale stability of this new bow shock topology is investigated. Two types of numerical experiments are described in which the upstream flow is perturbed in a time-dependent manner. It is found that large-amplitude noncyclic localized perturbations may cause the disintegration of the intermediate shocks, which are indeed known to be unstable against perturbations with integrated amplitudes above critical values, but that in the driven bow shock problem there are always shock front segments where intermediate shocks are reformed dynamically, resulting in the reappearance of the new double-front topology with intermediate-shock segments after the perturbation has passed. These MHD results indicate a theoretical mechanism for the possible intermittent formation of shock segments of intermediate type in unsteady space physics bow shock flows when upstream magnetic fields are strong, for example, in the terrestrial bow shock during periods of strong interplanetary magnetic field, which are more common under solar maximum conditions, or in leading shock fronts induced by fast coronal mass ejections in the solar corona. It remains to be confirmed if intermediate-shock segments would be formed when kinetic effects and realistic dissipation in real space plasmas are taken into account. The detailed interaction of realistic, wave-like cyclic perturbations with the intermediate-shock segments in bow shock flows may lead to unsteady structures composed of (time-dependent) intermediate shocks, rotational discontinuities, and nonlinear wave trains, as in the scenarios proposed by Markovskii and Skorokhodov [2000]. The possible relevance of the new bow shock topology with intermediate shocks for space weather phenomena is discussed.},
author = {{De Sterck}, H. and Poedts, S.},
doi = {10.1029/2000JA000205},
issn = {0148-0227},
journal = {Journal of Geophysical Research},
number = {A12},
pages = {30023},
title = {{Disintegration and reformation of intermediate-shock segments in three-dimensional MHD bow shock flows}},
url = {http://doi.wiley.com/10.1029/2000JA000205},
volume = {106},
year = {2001}
}
@phdthesis{DeVuyst2002,
author = {{De Vuyst}, F.},
school = {Universit{\'{e}} de Cergy-Pontoise},
title = {{Mod{\'{e}}lisation math{\'{e}}matique et analyse d'{\'{e}}coulements sous l'action de flux au sein de syst{\`{e}}mes complexes en r{\'{e}}gime transitoire et permanent}},
type = {Habilitation {\`{a}} diriger des recherches},
year = {2002}
}
@article{Debussche1999,
abstract = {In this work, we numerically investigate the influence of a homogeneous noise on the evolution of solitons for the Kortewegde Vries equation. Our numerical method is based on finite elements and least-squares. We present numerical experiments for different values of noise amplitude and describe different types of behaviours.},
author = {Debussche, A.},
doi = {10.1016/S0167-2789(99)00072-X},
issn = {01672789},
journal = {Physica D: Nonlinear Phenomena},
number = {2},
pages = {200--226},
title = {{Numerical simulation of the stochastic Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S016727899900072X},
volume = {134},
year = {1999}
}
@article{Deconinck2006,
author = {Deconinck, B. and Kutz, J. N.},
journal = {J. Comp. Phys.},
pages = {296--321},
title = {{Computing spectra of linear operators using the Floquet-Fourier-Hill method}},
volume = {219},
year = {2006}
}
@inbook{Degasperis1999,
author = {Degasperis, A. and Procesi, M.},
booktitle = {Symmetry and Perturbation Theory},
chapter = {Asymptotic},
editor = {Degasperis, A and Gaeta, G},
pages = {23--37},
publisher = {World Scientific},
title = {{Asymptotic integrability}},
year = {1999}
}
@article{DeKa,
author = {Delis, A. I. and Katsaounis, T.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {695--719},
title = {{Relaxation schemes for the shallow water equations}},
volume = {41},
year = {2003}
}
@article{DeKaKa,
author = {Delis, A. I. and Kazolea, M. and Kampanis, N. A.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {419--452},
title = {{A robust high-resolution finite volume scheme for the simulation of long waves over complex domains}},
volume = {56},
year = {2008}
}
@article{Delis2011,
author = {Delis, A. I. and Nikolos, I. K. and Kazolea, M.},
doi = {10.1007/s11831-011-9057-6},
issn = {1134-3060},
journal = {Archives of Computational Methods in Engineering},
month = {feb},
number = {1},
pages = {57--118},
title = {{Performance and Comparison of Cell-Centered and Node-Centered Unstructured Finite Volume Discretizations for Shallow Water Free Surface Flows}},
url = {http://link.springer.com/10.1007/s11831-011-9057-6},
volume = {18},
year = {2011}
}
@article{Dellacherie2005,
author = {Dellacherie, S.},
journal = {ESAIM: M2AN},
pages = {487--514},
title = {{On a diphasic low Mach number system}},
volume = {39},
year = {2005}
}
@article{Dellacherie2007,
author = {Dellacherie, S.},
journal = {J. Comput. Phys.},
pages = {151--187},
title = {{Numerical resolution of a potential diphasic low Mach number system}},
volume = {223},
year = {2007}
}
@article{Dellar2005,
author = {Dellar, P. J. and Salmon, R.},
doi = {10.1063/1.2116747},
issn = {10706631},
journal = {Phys. Fluids},
number = {10},
pages = {106601},
title = {{Shallow water equations with a complete Coriolis force and topography}},
url = {http://scitation.aip.org/content/aip/journal/pof2/17/10/10.1063/1.2116747},
volume = {17},
year = {2005}
}
@book{Demmel1997,
author = {Demmel, J. W.},
publisher = {SIAM, Philadelphia},
title = {{Applied Numerical Linear Algebra}},
year = {1997}
}
@article{Denissenko2007,
author = {Denissenko, P. and Lukaschuk, S. and Nazarenko, S.},
doi = {10.1103/PhysRevLett.99.014501},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {jul},
number = {1},
pages = {014501},
title = {{Gravity Wave Turbulence in a Laboratory Flume}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.99.014501},
volume = {99},
year = {2007}
}
@article{Desveaux2015,
author = {Desveaux, V. and Zenk, M. and Berthon, Ch. and Klingenberg, Ch.},
journal = {Math. Comp.},
title = {{Well-balanced schemes to capture non-explicit steady staets: RIPA model}},
volume = {To appear},
year = {2015}
}
@article{Dewals2006,
abstract = {Successfully modelling flows over a spillway and on strongly vertically curved bottoms is a challenge for any depth-integrated model. This type of computation requires the use of axes properly inclined along the mean flow direction in the vertical plane and a modelling of curvature effects. The proposed generalized model performs such computations by means of suitable curvilinear coordinates in the vertical plane, leading to a fully integrated approach. This means that the flows in the upstream reservoir, on the spillway, in the stilling basin and in the downstream river reach are all handled in a single simulation. The velocity profile is generalized in comparison with the uniform one usually assumed in the classical shallow water equations. The pressure distribution is modified as a function of the bottom curvature and is thus not purely hydrostatic. Representative test cases, as well as the application of the extended model to the design of a large hydraulic structure in Belgium, lead to satisfactory validation results},
author = {Dewals, B. J. and Erpicum, S. and Archambeau, P. and Detrembleur, S. and Pirotton, M.},
doi = {10.1080/00221686.2006.9521729},
issn = {0022-1686},
journal = {Journal of Hydraulic Research},
keywords = {Shallow water,curvilinear coordinates,finite volume,numerical model,reservoir,spillway},
mendeley-tags = {Shallow water,curvilinear coordinates,finite volume,numerical model,reservoir,spillway},
month = {nov},
number = {6},
pages = {785--795},
title = {{Depth-integrated flow modelling taking into account bottom curvature}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00221686.2006.9521729},
volume = {44},
year = {2006}
}
@article{DiGregorio1999,
author = {{Di Gregorio}, S. and Rongo, R. and Siciliano, C. and Sorriso-Valvo, M. and Spataro, W.},
journal = {Physics and Chemistry of the Earth},
pages = {97--100},
title = {{Mount Ontake landslide simulation by the cellular automata model SCIDDICA-3}},
volume = {24},
year = {1999}
}
@article{DiRisio2009,
author = {{Di Risio}, M. and Bellotti, G. and Panizzo, A. and {De Girolamo}, P.},
doi = {10.1016/j.coastaleng.2009.01.009},
issn = {03783839},
journal = {Coastal Engineering},
number = {5-6},
pages = {659--671},
publisher = {Elsevier B.V.},
title = {{Three-dimensional experiments on landslide generated waves at a sloping coast}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378383909000088},
volume = {56},
year = {2009}
}
@article{Dias2006a,
author = {Dias, F. and Bridges, T. J.},
journal = {Fluid Dynamics Research},
pages = {803--830},
title = {{The numerical computation of freely propagating time-dependent irrotational water waves}},
volume = {38},
year = {2006}
}
@incollection{Dias2011,
author = {Dias, F. and Bridges, T. J. and Dudley, J. M.},
booktitle = {Lecture Notes Series. World Scientific Publishing},
title = {{Environmental hazards. The fluid dynamics and geophysics of extreme events}},
year = {2011}
}
@inbook{Dias2006,
abstract = {The life of a tsunami is usually divided into three phases: the generation (tsunami source), the propagation and the inundation. Each phase is complex and often described separately. A brief description of each phase is given. Model problems are identified. Their formulation is given. While some of these problems can be solved analytically, most require numerical techniques. The inundation phase is less documented than the other phases. It is shown that methods based on Smoothed Particle Hydrodynamics (SPH) are particularly well-suited for the inundation phase. Directions for future research are outlined.},
author = {Dias, F. and Dutykh, D.},
booktitle = {Extreme Man-Made and Natural Hazards in Dynamics of Structures},
doi = {10.1007/978-1-4020-5656-7{\_}8},
editor = {Ibrahimbegovic, A. and Kozar, I.},
isbn = {978-1-4020-5654-3},
pages = {35--60},
publisher = {Springer Netherlands},
title = {{Dynamics of tsunami waves}},
url = {http://link.springer.com/chapter/10.1007/978-1-4020-5656-7{\_}8},
year = {2007}
}
@inproceedings{Dias2008a,
author = {Dias, F. and Dutykh, D. and Ghidaglia, J.-M.},
booktitle = {Proceedings of OMAE2008 27th International Conference on Offshore Mechanics and Arctic Engineering, June 15-20, 2008, Estoril, Portugal},
title = {{Simulation of free surface compressible flows via a two fluid model}},
year = {2008}
}
@article{Dias2008,
author = {Dias, F. and Dutykh, D. and Ghidaglia, J.-M.},
journal = {Comput. $\backslash${\&} Fluids},
pages = {283--293},
title = {{A two-fluid model for violent aerated flows}},
volume = {39(2)},
year = {2010}
}
@article{DDG2008,
abstract = {In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained in water in the form of small bubbles, the acoustic properties in the water change dramatically and for example the speed of sound in the mixture is much smaller than in pure water, and even smaller than in pure air. While some work has been done to study small-amplitude disturbances in such mixtures, little work has been done on large disturbances in air-water mixtures. We propose a basic two-fluid model in which both fluids share the same velocities. It is shown that this model can successfully mimic water wave impacts on coastal structures. Even though this is a model without interface, waves can occur. Their dispersion relation is discussed and the formal limit of pure phases (interfacial waves) is considered. The governing equations are discretized by a second-order finite volume method. Numerical results are presented. It is shown that this basic model can be used to study violent aerated flows, especially by providing fast qualitative estimates.},
address = {Cachan, France},
author = {Dias, F. and Dutykh, D. and Ghidaglia, J.-M.},
institution = {Ecole Normale Sup$\backslash$'erieure de Cachan},
journal = {HAL},
pages = {1--38},
title = {{A compressible two-fluid model for the finite volume simulation of violent aerated flows. Analytical properties and numerical results}},
url = {http://hal.archives-ouvertes.fr/hal-00279671/},
year = {2008}
}
@article{Dias2014,
author = {Dias, F. and Dutykh, D. and O'Brien, L. and Renzi, E. and Stefanakis, T.},
doi = {10.1016/j.piutam.2014.01.029},
issn = {22109838},
journal = {Procedia IUTAM},
pages = {338--355},
title = {{On the Modelling of Tsunami Generation and Tsunami Inundation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S2210983814000303},
volume = {10},
year = {2014}
}
@article{Dias2007,
author = {Dias, F. and Dyachenko, A. I. and Zakharov, V. E.},
journal = {Physics Letters A},
pages = {1297--1302},
title = {{Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions}},
volume = {372},
year = {2008}
}
@article{Dias1999,
author = {Dias, F. and Kharif, C.},
journal = {Ann. Rev. Fluid Mech.},
pages = {301--346},
title = {{Nonlinear gravity and capillary-gravity waves}},
volume = {31},
year = {1999}
}
@article{Dias1996,
abstract = {Two types of small-amplitude capillary-gravity solitary waves are known to exist. One type bifurcates from a uniform flow when the Froude number is equal to 1 and the Weber number larger than 1/3. The other type bifurcates from a train of infinitesimal periodic waves at the minimum of the dispersion curve for all values of the Froude number between 0 (infinite depth) and 1. We investigate numerically the behavior of these waves away from their bifurcation point and show that these two types are globally connected. Moreover new families of capillary-gravity solitary waves of finite amplitude are shown to exist.},
author = {Dias, F. and Menasce, D. and Vanden-Broeck, J.-M.},
journal = {Eur. J. Mech. B/Fluids},
number = {1},
pages = {17--36},
title = {{Numerical study of capillary-gravity solitary waves}},
volume = {15},
year = {1996}
}
@article{Dias2010,
author = {Dias, F. and Milewski, P.},
journal = {Phys. Lett. A},
pages = {1049--1053},
title = {{On the fully-nonlinear shallow-water generalized Serre equations}},
volume = {374(8)},
year = {2010}
}
@article{Dias1989,
author = {Dias, F. and Vanden-Broeck, J.-M.},
journal = {J. Fluid Mech.},
pages = {155--170},
title = {{Open channel flows with submerged obstructions}},
volume = {206},
year = {1989}
}
@article{Dias2002,
author = {Dias, F. and Vanden-Broeck, J.-M.},
journal = {Phil. Trans. R. Soc. Lond. A},
pages = {2137--2154},
title = {{Steady two-layer flows over an obstacle}},
volume = {360(1799)},
year = {2002}
}
@article{Didenkulova2010,
author = {Didenkulova, I. and Nikolkina, I. and Pelinovsky, E. N. and Zahibo, N.},
doi = {10.5194/nhess-10-2407-2010},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {2407--2419},
title = {{Tsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth}},
volume = {10},
year = {2010}
}
@article{Didenkulova2008,
author = {Didenkulova, I. and Pelinovsky, E. N.},
journal = {Oceanology},
number = {1},
pages = {1--6},
title = {{Run-up of long waves on a beach: the influence of the incident wave form}},
volume = {48},
year = {2008}
}
@article{Didenkulova2011a,
author = {Didenkulova, I. and Pelinovsky, E. N. and Sergeeva, A.},
journal = {Coastal Engineering},
pages = {94--102},
title = {{Statistical characteristics of long waves nearshore}},
volume = {58},
year = {2011}
}
@inbook{Didenkulova2007,
abstract = {The problem of the long wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. The key and novel moment here is the analysis of the runup of a certain class of asymmetric waves, the face slope steepness of which exceeds the back slope steepness. Shown is that the runup height increases when the relative face slope steepness increases whereas the rundown weakly depends on the steepness. The results partially explain why the tsunami waves with the steep front (as it was for the 2004 tsunami in the Indian Ocean) penetrate deeper into inland compared with symmetric waves of the same height and length.},
author = {Didenkulova, I. and Pelinovsky, E. N. and Soomere, T. and Zahibo, N.},
chapter = {Runup of n},
doi = {10.1007/978-3-540-71256-5},
editor = {Kundu, Anjan},
pages = {175--190},
publisher = {Springer Berlin Heidelberg},
title = {{Tsunami and Nonlinear Waves}},
url = {http://www.springerlink.com/content/vtpm7t8m5n0jm734/},
year = {2007}
}
@article{Didenkulova2006,
author = {Didenkulova, I. and Zahibo, N. and Kurkin, A. and Pelinovsky, E. N. and Soomere, T.},
journal = {Doklady Earth Sciences},
number = {8},
pages = {1241--1243},
title = {{Runup of Nonlinearly Deformed Waves on a Coast}},
volume = {411},
year = {2006}
}
@article{Dietrich1982,
abstract = {Data from 14 previous experimental studies were used to develop an empirical equation that accounts for the effects of size, density, shape, and roundness on the settling velocity of natural sediment. This analysis was done in terms of four nondimensional parameters, namely, the dimensionless nominal diameter D *, the dimensionless settling velocity W *, the Corey shape factor, and the Powers roundness index. For high D * (large or dense particles), changes in roundness and shape factor have similar magnitude effects on settling velocity. Roundness varies much less for naturally occuring grains, however, and hence is a less important control than shape. For a typical coarse sand with a Powers roundness of 3.5 and a Corey shape factor of 0.7, the settling velocity is about 0.68 that of a sphere of the same D *, with shape and roundness effects contributing about equally to the settling velocity reduction. At low D * the reduction in settling velocity due to either shape or roundness is much less. Moreover, at low D *, low roundness causes a greater decrease in settling velocity at low shape factor values than at high shape factor values. This appears to be due to the increased surface drag on the flatter grains.},
author = {Dietrich, W.},
journal = {Water Resour. Res.},
number = {6},
pages = {1615--1626},
title = {{Settling Velocity of Natural Particles}},
volume = {18},
year = {1982}
}
@book{Dingemans1997,
abstract = {The primary objective of this book is to provide a review of techniques available for the problems of wave propagation in regions with uneven beds as they are encountered in coastal areas. The view taken is that the techniques should be useful for application in advisory practice. However, effort is put into a precise definition of the underlying physical principles, so that the validity of the methods used can be evaluated. Both linear and nonlinear wave propagation techniques are discussed. Because of its length, the book comes in two parts: Part 1 covers primarily linear wave propagation, and Part 2 covers nonlinear wave propagation.},
address = {Singapore},
author = {Dingemans, M. W.},
isbn = {978-981-02-0426-6},
pages = {1016},
publisher = {World Scientific},
title = {{Water wave propagation over uneven bottom}},
year = {1997}
}
@article{DiPerna1987,
author = {DiPerna, R. J. and Majda, A. J.},
journal = {Comm. Pure Appl. Math.},
pages = {301--345},
title = {{Concentrations in regularizations for 2-D incompressible flow}},
volume = {40(3)},
year = {1987}
}
@article{DiPerna1987a,
author = {DiPerna, R. J. and Majda, A. J.},
journal = {Comm. Math. Phys.},
pages = {667--689},
title = {{Oscillations and concentrations in weak solutions of the incompressible fluid equations}},
volume = {108(4)},
year = {1987}
}
@article{Dobrokhotov2006,
author = {Dobrokhotov, S. Yu. and Sekerzh-Zenkovich, S. Ya. and Tirozzi, B. and Tudorovskiy, T. Ya.},
journal = {Doklady Mathematics},
number = {1},
pages = {592--596},
title = {{The description of tsunami waves propagation based on the Maslov canonical operator}},
volume = {74},
year = {2006}
}
@article{Dobrokhotov2006a,
author = {Dobrokhotov, S. Yu. and Sekerzh-Zenkovich, S. Ya. and Tirozzi, B. and Volkov, B.},
journal = {Russ. Journ. Earth Sciences},
pages = {1--12},
title = {{Explicit asymptotics for tsunami waves in framework of the piston model}},
volume = {8},
year = {2006}
}
@book{Dodd1984,
author = {Dodd, R. K. and Eilbeck, J. C. and Gibbon, J. D. and Morris, H. C.},
isbn = {978-0122191220},
pages = {630},
publisher = {Academic Press},
title = {{Solitons and Nonlinear Wave Equations}},
year = {1984}
}
@incollection{Domaradzki2001,
author = {Domaradzki, J. A. and Holm, D.},
booktitle = {Modern Simulation Strategies for Turbulent Flow},
editor = {Geurts, B},
pages = {107--122},
title = {{Navier-Stokes-alpha model: LES equations with nonlinear dispersion}},
year = {2001}
}
@article{Domelevo2005,
author = {Domelevo, K. and Omnes, P.},
journal = {ESAIM: M2AN},
number = {6},
pages = {1203--1249},
title = {{A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids}},
volume = {39},
year = {2005}
}
@article{Domelevo2001,
author = {Domelevo, K. and Vignal, M.-H.},
doi = {10.1016/S0764-4442(01)01895-X},
issn = {07644442},
journal = {C. R. Acad. Sci. Paris I},
month = {may},
number = {9},
pages = {863--868},
title = {{Limites visqueuses pour des syst{\`{e}}mes de type Fokker-Planck-Burgers unidimensionnels}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S076444420101895X},
volume = {332},
year = {2001}
}
@article{Domine2007,
author = {Domine, F. and Albert, M. and Huthwelker, T. and Jacobi, H.-W. and Kokhanovsky, A. A. and Lehning, M. and Picard, G. and Simpson, W. R.},
journal = {Atmos. Chem. Phys. Discuss.},
pages = {5941--6036},
title = {{Snow physics as relevant to snow photochemistry}},
volume = {7},
year = {2007}
}
@article{Dommermuth2000,
author = {Dommermuth, D.},
doi = {10.1016/S0165-2125(00)00047-0},
issn = {01652125},
journal = {Wave Motion},
month = {oct},
number = {4},
pages = {307--317},
title = {{The initialization of nonlinear waves using an adjustment scheme}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0165212500000470},
volume = {32},
year = {2000}
}
@article{Dommermuth1987,
abstract = {We develop a robust numerical method for modelling nonlinear gravity waves which is based on the Zakharov equation/mode-coupling idea but is generalized to include interactions up to an arbitrary order M in wave steepness. A large number (N = O(1000)) of free wave modes are typically used whose amplitude evolutions are determined through a pseudospectral treatment of the nonlinear free-surface conditions. The computational effort is directly proportional to N and M, and the convergence with N and M is exponentially fast for waves up to approximately 80{\%} of Stokes limiting steepness (ka [similar] 0.35). The efficiency and accuracy of the method is demonstrated by comparisons to fully nonlinear semi-Lagrangian computations (Vinje {\&} Brevig 1981); calculations of long-time evolution of wavetrains using the modified (fourth-order) Zakharov equations (Stiassnie {\&} Shemer 1987); and experimental measurements of a travelling wave packet (Su 1982). As a final example of the usefulness of the method, we consider the nonlinear interactions between two colliding wave envelopes of different carrier frequencies.},
author = {Dommermuth, D. G. and Yue, D. K. P.},
doi = {10.1017/S002211208700288X},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {267--288},
title = {{A high-order spectral method for the study of nonlinear gravity waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S002211208700288X},
volume = {184},
year = {1987}
}
@article{Dormand1980,
author = {Dormand, J. R. and Prince, P. J.},
journal = {J. Comp. Appl. Math.},
pages = {19--26},
title = {{A family of embedded Runge-Kutta formulae}},
volume = {6},
year = {1980}
}
@article{Dorodnitsyn1994,
abstract = {The present paper is concerned with continuous groups of transformations in a space of discrete variables. The criterion of invariance of difference equations together with difference grid is discussed. One simple method to construct finite-difference equations and grids entirely inheriting admitted Lie groups of transformations of initial differential models is developed.},
author = {Dorodnitsyn, V. A.},
doi = {10.1142/S0129183194000830},
issn = {0129-1831},
journal = {Int. J. Mod. Phys. C},
month = {aug},
number = {04},
pages = {723--734},
title = {{Finite Difference Models Entirely Inheriting Continuous Symmetry of Original Differential Equations}},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0129183194000830},
volume = {05},
year = {1994}
}
@article{Dotsenko1997,
author = {Dotsenko, S. F. and Korobkova, T. Yu.},
journal = {Phys. Oceanogr.},
pages = {143--154},
title = {{The effect of frequency dispersion on plane waves generated as a result of bed motions}},
volume = {8(3)},
year = {1997}
}
@article{DDMM,
author = {Dougalis, V. A. and Dur{\'{a}}n, A. and Lopez-Marcos, M. A. and Mitsotakis, D. E.},
journal = {J. Nonlinear Sci.},
pages = {595--607},
title = {{A numerical study of the stability of solitary waves of Bona-Smith family of Boussinesq systems}},
volume = {17},
year = {2007}
}
@article{Dougalis2012,
abstract = {This paper presents several numerical techniques to generate solitary-wave profiles of the Benjamin equation. The formulation and implementation of the methods focus on some specific points of the problem: on the one hand, the approximation of the nonlocal term is accomplished by Fourier techniques, which determine the spatial discretization used in the experiments. On the other hand, in the numerical continuation procedure suggested by the derivation of the model and already discussed in the literature, several algorithms for solving the nonlinear systems are described and implemented: the Petviashvili method, the Preconditioned Conjugate Gradient Newton method and two Squared-Operator methods. A comparative study of these algorithms is made in the case of the Benjamin equation; Newton's method combined with Preconditioned Conjugate Gradient techniques, emerges as the most efficient. The resulting numerical profiles are shown to have a high accuracy as travelling-wave solutions when they are used as initial conditions in a time-stepping procedure for the Benjamin equation. The paper also explores the generation of multi-pulse solitary waves.},
author = {Dougalis, V. A. and Dur{\'{a}}n, A. and Mitsotakis, D. E.},
doi = {10.1016/j.matcom.2012.07.008},
issn = {03784754},
journal = {Mathematics and Computers in Simulation},
keywords = {Benjamin equation,Numerical computation of solitary waves,Numerical continuation,Spectral methods},
month = {aug},
title = {{Numerical approximation of solitary waves of the Benjamin equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378475412001711},
year = {2012}
}
@inbook{Dougalis2004,
address = {New Jersey},
author = {Dougalis, V. A. and Mitsotakis, D. E.},
booktitle = {Advances in scattering theory and biomedical engineering},
editor = {Fotiadis, D and Massalas, C},
pages = {286--294},
publisher = {World Scientific},
title = {{Solitary waves of the Bona-Smith system}},
year = {2004}
}
@inbook{Dougalis2004,
author = {Dougalis, V. A. and Mitsotakis, D. E.},
chapter = {Solitary w},
editor = {Fotiadis, D and Massalas, C},
pages = {286--294},
publisher = {World Scientific, New Jersey},
title = {{Advances in scattering theory and biomedical engineering}},
year = {2004}
}
@inproceedings{DMII,
author = {Dougalis, V. A. and Mitsotakis, D. E.},
booktitle = {Effective Computational Methods in Wave Propagation},
editor = {Kampanis, N A and Dougalis, V A and Ekaterinaris, J A},
pages = {63--110},
publisher = {CRC Press},
title = {{Theory and numerical analysis of Boussinesq systems: A review}},
year = {2008}
}
@article{DMS2,
author = {Dougalis, V. A. and Mitsotakis, D. E. and Saut, J.-C.},
journal = {Discrete Contin. Dyn. Syst.},
number = {4},
pages = {1191--1204},
title = {{On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain}},
volume = {23},
year = {2009}
}
@article{Dougalis2010,
author = {Dougalis, V. A. and Mitsotakis, D. E. and Saut, J.-C.},
journal = {J. Sci. Comput.},
pages = {109--135},
title = {{Initial-boundary-value problems for Boussinesq systems of Bona-Smith type on a plane domain: theory and numerical analysis}},
volume = {44},
year = {2010}
}
@article{DMS1,
author = {Dougalis, V. A. and Mitsotakis, D. E. and Saut, J.-C.},
journal = {Math. Model. Num. Anal.},
number = {5},
pages = {254--825},
title = {{On some Boussinesq systems in two space dimensions: Theory and numerical analysis}},
volume = {41},
year = {2007}
}
@book{DPP2000,
author = {DPP},
publisher = {Department of Planning and Permitting of Honolulu Hawaii},
title = {{City and County of Honolulu Building Code}},
year = {2000}
}
@book{John,
address = {Cambridge},
author = {Drazin, P. G. and Johnson, R. S.},
editor = {Drazin, P. G. and Johnson, R. S.},
isbn = {0-521-33655-4},
pages = {226},
publisher = {Cambridge University Press},
title = {{Solitons: An introduction}},
year = {1989}
}
@book{Drazin2004,
abstract = {This book begins with a basic introduction to three major areas of hydrodynamic stability: thermal convection, rotating and curved flows, and parallel shear flows. There follows a comprehensive account of the mathematical theory for parallel shear flows. A number of applications of the linear theory are discussed, including the effects of stratification and unsteadiness. The emphasis throughout is on the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, the theory is related to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems, for which hints and references are given, not only provide exercises for students but also provide many additional results in a concise form.},
address = {Cambridge},
author = {Drazin, P. G. and Reid, W. H.},
edition = {2},
isbn = {978-0521525411},
pages = {628},
publisher = {Cambridge University Press},
title = {{Hydrodynamic Stability}},
year = {2004}
}
@article{Dressler1978,
author = {Dressler, R. F.},
journal = {Journal of Hydraulic Research},
pages = {205--222},
title = {{New nonlinear shallow-flow equations with curvature}},
volume = {16(3)},
year = {1978}
}
@article{Drew1979a,
author = {Drew, D. A. and Cheng, I. and Lahey, R. T.},
journal = {Int. J. Multiphase Flow},
pages = {233--242},
title = {{The analysis of virtual mass effects in two-phase flow}},
volume = {5(4)},
year = {1979}
}
@article{Drew1979,
author = {Drew, D. A. and Lahey, R. T.},
journal = {Int. J. Multiphase Flow},
pages = {243--264},
title = {{Application of general constitutive principles to the derivation of multidimensional two-phase flow equations}},
volume = {5},
year = {1979}
}
@inbook{Drew1994,
abstract = {The balance equations (mass, momentum and energy) for each phase in a two-phase flow are derived using ensemble averaging techniques. In order to close the constitutive equations, the results from two different computations were studied, namely a general potential flow around a rigid solid matrix and an irritational flow of an inviscid fluid around a single sphere. The systematic inclusion of all terms arising in the averaged momentum equations yields an appropriate working model for dispersed bubbly flow.},
author = {Drew, D. A. and Wallis, G. B.},
chapter = {Fundamenta},
editor = {Et al., Hewitt},
publisher = {Begell House, Inc., New York},
title = {{Multiphase Science and Technology}},
year = {1994}
}
@incollection{Dubois2001,
author = {Dubois, F.},
booktitle = {Absorbing boundaries and layers, domain decomposition methods: Applications to large scale computations},
editor = {Tourrette, L. and Halpern, L.},
pages = {16--77},
title = {{Partial Riemann problem, boundary conditions, and gas dynamics}},
year = {2001}
}
@article{Dubreil-Jacotin1934,
author = {Dubreil-Jacotin, M.-L.},
journal = {Journal de Math{\{}{\'{e}}{\}}matiques Pures et Appliqu{\{}{\'{e}}{\}}es 9e s{\{}{\'{e}}{\}}rie},
pages = {217--291},
title = {{Sur la d{\{}{\'{e}}{\}}termination rigoureuse des ondes permanentes p{\{}{\'{e}}{\}}riodiques d'ampleur finie}},
volume = {13},
year = {1934}
}
@article{Dubreil-Jacotin1934,
author = {Dubreil-Jacotin, M.-L.},
journal = {Journal de Math{\'{e}}matiques Pures et Appliqu{\'{e}}es 9e s{\'{e}}rie},
pages = {217--291},
title = {{Sur la d{\'{e}}termination rigoureuse des ondes permanentes p{\'{e}}riodiques d'ampleur finie}},
volume = {13},
year = {1934}
}
@article{Ducrozet2012,
abstract = {This paper presents the recent development on the nonlinear directional wave generation process in a 3D Numerical Wave Tank (NWT). The NWT is based on a nonlinear model using the High-Order Spectral (HOS) method, which exhibits high level of accuracy as well as efficiency properties provided by a Fast Fourier Transform (FFT) solution. The wavemaker modeling appears to be a key point in the simulation and it is carefully detailed. Different levels of approximation of the wave generation (up to third-order in nonlinearity) are studied. The properties of the numerical scheme in terms of convergence, stability and accuracy are discussed. This NWT features all the characteristics of the real wave tank (directional wavemaker, absorbing zone, perfectly reflective side walls). Furthermore, several validation results and practical applications where numerical simulations are successfully compared to experiments on 2D and 3D wave fields are presented.},
author = {Ducrozet, G. and Bonnefoy, F. and {Le Touz{\'{e}}}, D. and Ferrant, P.},
doi = {10.1016/j.euromechflu.2012.01.017},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
keywords = {Directional wavemaker,High-Order Spectral,Nonlinear wave generation,Nonlinear waves,Numerical wave tank,Spectral method},
month = {jul},
pages = {19--34},
title = {{A modified High-Order Spectral method for wavemaker modeling in a numerical wave tank}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754612000180},
volume = {34},
year = {2012}
}
@article{Ducrozet2007,
author = {Ducrozet, G. and Bonnefoy, F. and {Le Touz{\'{e}}}, D. and Ferrant, P.},
doi = {10.5194/nhess-7-109-2007},
issn = {1684-9981},
journal = {Natural Hazards and Earth System Science},
month = {jan},
number = {1},
pages = {109--122},
title = {{3-D HOS simulations of extreme waves in open seas}},
url = {http://www.nat-hazards-earth-syst-sci.net/7/109/2007/},
volume = {7},
year = {2007}
}
@article{Dudley2008,
author = {Dudley, J. M. and Genty, G. and Eggleton, B. J.},
journal = {Opt. Express},
pages = {3644--3651},
title = {{Harnessing and control of optical rogue waves in supercontinuum generation}},
volume = {16},
year = {2008}
}
@article{Dufour2001,
author = {Dufour, F. and Gruber, U. and Ammann, W.},
journal = {Les Alpes},
pages = {9--15},
title = {{Avalanches: {\'{e}}tudes effectu{\'{e}}es dans la Vall{\'{e}}e de la Sionne en 1999}},
volume = {2},
year = {2001}
}
@inproceedings{Dufour2000,
author = {Dufour, F. and Gruber, U. and Bartelt, P. and Ammann, W. J.},
booktitle = {Proceedings International Snow Science Workshop, Blue Sky MT, USA, October 1st-6th},
pages = {527--534},
title = {{Overview of the 1999 measurements at the SLF test site Vall{\'{e}}e de la Sionne}},
year = {2000}
}
@article{Duguet2008,
author = {Duguet, Y. and Willis, A. P. and Kerswell, R. R.},
doi = {10.1017/S0022112008003248},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {oct},
pages = {255--274},
title = {{Transition in pipe flow: the saddle structure on the boundary of turbulence}},
volume = {613},
year = {2008}
}
@article{Dullin2004,
author = {Dullin, H. R. and Gottwald, G. A. and Holm, D. D.},
doi = {10.1016/j.physd.2003.11.004},
issn = {01672789},
journal = {Phys. D},
month = {mar},
number = {1-2},
pages = {1--14},
title = {{On asymptotically equivalent shallow water wave equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278903004536},
volume = {190},
year = {2004}
}
@article{Dullin2003,
abstract = {We derive the Camassa-Holm equation (CH) as a shallow water wave equation with surface tension in an asymptotic expansion that extends one order beyond the Korteweg-de Vries equation (KdV). We show that CH is asymptotically equivalent to KdV5 (the fifth-order integrable equation in the KdV hierarchy) by using the non-linear/non-local transformations introduced in Kodama (Phys. Lett. A 107 (1985a) 245; Phys. Lett. A 112 (1985b) 193; Phys. Lett. A 123 (1987) 276). We also classify its travelling wave solutions as a function of Bond number by using phase plane analysis. Finally, we discuss the experimental observability of the CH solutions.},
author = {Dullin, H. R. and Gottwald, G. A. and Holm, D. D.},
journal = {Fluid Dyn. Res.},
number = {1-2},
pages = {73--95},
title = {{Camassa-Holm, Korteweg-de Vries-5 and other asymptotically equivalent equations for shallow water waves}},
volume = {33},
year = {2003}
}
@article{Dullin2001,
author = {Dullin, H. R. and Gottwald, G. and Holm, D.},
doi = {10.1103/PhysRevLett.87.194501},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {oct},
number = {19},
pages = {194501},
title = {{An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.87.194501},
volume = {87},
year = {2001}
}
@article{Duran2013,
author = {Duran, A. and Dutykh, D. and Mitsotakis, D.},
doi = {10.1111/sapm.12015},
issn = {00222526},
journal = {Stud. Appl. Math.},
month = {nov},
number = {4},
pages = {359--388},
title = {{On the Galilean Invariance of Some Nonlinear Dispersive Wave Equations}},
url = {http://doi.wiley.com/10.1111/sapm.12015},
volume = {131},
year = {2013}
}
@article{Duran2011,
author = {Dur{\'{a}}n, A. and Dutykh, D. and Mitsotakis, D.},
journal = {In preparation},
title = {{Peregrine system revisited}},
year = {2011}
}
@thesis{Dutykh2007a,
abstract = {This thesis is devoted to tsunami wave modelling. The life of tsunami waves can be conditionally divided into three parts: generation, propagation and inundation (or run-up). In the first part of the manuscript we consider the generation process of such extreme waves. We examine various existing approaches to its modelling. Then we propose a few alternatives. The main conclusion is that the seismology/hydrodynamics coupling is poorly understood at the present time. The second chapter essentially deals with Boussinesq equations which are often used to model tsunami propagation and sometimes even run-up. More precisely, we discuss the importance, nature and inclusion of dissipative effects in long wave models. In the third chapter we slightly change the subject and turn to two-phase flows. The main purpose of this chapter is to propose an operational and simple set of equations in order to model wave impacts on coastal structures. Another important application includes wave sloshing in liquified natural gas carriers. Then, we discuss the numerical discretization of governing equations in the finite volume framework on unstructured meshes. Finally, this thesis deals with a topic which should be present in any textbook on hydrodynamics but it is not. We mean visco-potential flows. We propose a novel and sufficiently simple approach for weakly viscous flow modelling. We succeeded in keeping the simplicity of the classical potential flow formulation with the addition of viscous effects. In the case of finite depth we derive a correction term due to the presence of the bottom boundary layer. This term is nonlocal in time. Hence, the bottom boundary layer introduces a memory effect to the governing equations.},
author = {Dutykh, D.},
institution = {{\'{E}}cole Normale Sup{\'{e}}rieure de Cachan},
keywords = {Boussinesq equations,tsunami generation,water waves},
month = {dec},
pages = {222},
title = {{Mathematical modelling of tsunami waves}},
type = {PhD thesis},
url = {http://tel.archives-ouvertes.fr/tel-00194763/},
year = {2007}
}
@article{Dutykh2008a,
author = {Dutykh, D.},
journal = {Eur. J. Mech. B/Fluids},
pages = {430--443},
title = {{Visco-potential free-surface flows and long wave modelling}},
volume = {28},
year = {2009}
}
@phdthesis{Dutykh2010f,
author = {Dutykh, D.},
month = {dec},
pages = {378},
school = {Universit{\'{e}} de Savoie},
title = {{Mathematical modeling in the environment: from tsunamis to powder-snow avalanches}},
type = {Habilitation {\`{a}} Diriger des Recherches},
url = {http://tel.archives-ouvertes.fr/tel-00542937/},
year = {2010}
}
@article{Dutykh2014,
author = {Dutykh, D.},
doi = {10.1016/j.piutam.2014.01.046},
issn = {22109838},
journal = {Procedia IUTAM},
pages = {34--43},
title = {{Evolution of Random Wave Fields in the Water of Finite Depth}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S2210983814000479},
volume = {11},
year = {2014}
}
@article{Dutykh2008b,
author = {Dutykh, D.},
journal = {Physics Letters A},
pages = {3212--3216},
title = {{Group and phase velocities in the free-surface visco-potential flow: new kind of boundary layer induced instability}},
volume = {373},
year = {2009}
}
@article{Dutykh2009,
abstract = {Powder-snow avalanches are violent natural disasters which represent a major risk for infrastructures and populations in mountain regions. In this study we present a novel model for the simulation of avalanches in the aerosol regime. The second scope of this study is to get more insight into the interaction process between an avalanche and a rigid obstacle. An incompressible model of two miscible fluids can be successfully employed in this type of problems. We allow for mass diffusion between two phases according to the Fick's law. The governing equations are discretized with a contemporary fully implicit finite volume scheme. The solver is able to deal with arbitrary density ratios. Several numerical results are presented. Volume fraction, velocity, and pressure fields are presented and discussed. Finally, we point out how this methodology can be used for practical problems.},
author = {Dutykh, D. and Acary-Robert, C. and Bresch, D.},
doi = {10.1111/j.1467-9590.2010.00511.x},
journal = {Studies in Applied Mathematics},
number = {1},
pages = {38--66},
title = {{Mathematical modeling of powder-snow avalanche flows}},
url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9590.2010.00511.x/abstract},
volume = {127},
year = {2011}
}
@article{Dutykh2015,
author = {Dutykh, D. and Caputo, J.-G.},
journal = {Submitted},
pages = {1--21},
title = {{Discrete sine-Gordon Dynamics on Networks}},
year = {2015}
}
@article{Dutykh2015,
author = {Dutykh, D. and Chhay, M. and Clamond, D.},
doi = {10.1016/j.physd.2015.04.001},
issn = {01672789},
journal = {Phys. D},
month = {jun},
pages = {23--33},
title = {{Numerical study of the generalised Klein-Gordon equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278915000603},
volume = {304-305},
year = {2015}
}
@article{Dutykh2013a,
author = {Dutykh, D. and Chhay, M. and Fedele, F.},
journal = {Comp. Math. Math. Phys.},
number = {2},
pages = {221--236},
title = {{Geometric numerical schemes for the KdV equation}},
volume = {53},
year = {2013}
}
@article{Dutykh2013,
abstract = {In the present study we propose a modified version of the nonlinear shallow water (Saint-Venant) equations for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive non-hydrostatic extension of the classical Saint-Venant equations. We also propose a finite volume discretization of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modeling are also discussed.},
archivePrefix = {arXiv},
arxivId = {1202.6542},
author = {Dutykh, D. and Clamond, D.},
eprint = {1202.6542},
journal = {Submitted},
month = {feb},
pages = {30},
title = {{Modified 'irrotational' Shallow Water Equations for significantly varying bottoms}},
url = {http://hal.archives-ouvertes.fr/hal-00675209/ http://arxiv.org/abs/1202.6542},
year = {2012}
}
@article{Dutykh2011b,
author = {Dutykh, D. and Clamond, D.},
journal = {J. Phys. A: Math. Theor.},
pages = {332001},
title = {{Shallow water equations for large bathymetry variations}},
volume = {44(33)},
year = {2011}
}
@article{Dutykh2013b,
abstract = {An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and Fenton’s high-order asymptotic expansion. Several important integral quantities are computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.},
author = {Dutykh, D. and Clamond, D.},
doi = {10.1016/j.wavemoti.2013.06.007},
issn = {01652125},
journal = {Wave Motion},
keywords = {Euler equations,Gravity waves,Petviashvili method,Solitary wave,Surface waves},
month = {jan},
number = {1},
pages = {86--99},
title = {{Efficient computation of steady solitary gravity waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0165212513001169},
volume = {51},
year = {2014}
}
@misc{Clamond2015b,
author = {Dutykh, D. and Clamond, D. and Dur{\'{a}}n, A.},
title = {{https://github.com/dutykh/BabenkoCG/}},
url = {https://github.com/dutykh/BabenkoCG/},
year = {2015}
}
@article{Dutykh2011a,
abstract = {After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations in one horizontal dimension. The numerical discretization is validated by comparisons with analytical and experimental data or other numerical solutions obtained by a highly accurate pseudo-spectral method.},
archivePrefix = {arXiv},
arxivId = {1104.4456},
author = {Dutykh, D. and Clamond, D. and Milewski, P. and Mitsotakis, D.},
doi = {10.1017/S0956792513000168},
eprint = {1104.4456},
journal = {Eur. J. Appl. Math.},
number = {05},
pages = {761--787},
title = {{Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations}},
url = {http://hal.archives-ouvertes.fr/hal-00587994/},
volume = {24},
year = {2013}
}
@article{Dutykh2014c,
author = {Dutykh, D. and Clamond, D. and Mitsotakis, D.},
journal = {RIMS K{\^{o}}ky{\^{u}}roku},
number = {4},
pages = {45--65},
title = {{Adaptive modeling of shallow fully nonlinear gravity waves}},
volume = {1947},
year = {2015}
}
@article{Dutykh2007b,
author = {Dutykh, D. and Dias, F.},
journal = {Mathematics and Computers in Simulation},
pages = {837--848},
title = {{Tsunami generation by dynamic displacement of sea bed due to dip-slip faulting}},
volume = {80(4)},
year = {2009}
}
@article{Dutykh2009b,
author = {Dutykh, D. and Dias, F.},
journal = {Proc. R. Soc. A},
pages = {725--744},
title = {{Energy of tsunami waves generated by bottom motion}},
volume = {465},
year = {2009}
}
@article{Dutykh2007,
author = {Dutykh, D. and Dias, F.},
journal = {C. R. Mecanique},
pages = {559--583},
title = {{Dissipative Boussinesq equations}},
volume = {335},
year = {2007}
}
@article{DutykhDias2007,
author = {Dutykh, D. and Dias, F.},
journal = {C. R. Acad. Sci. Paris, Ser. I},
pages = {113--118},
title = {{Viscous potential free-surface flows in a fluid layer of finite depth}},
volume = {345},
year = {2007}
}
@inproceedings{Dutykh2006,
abstract = {Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.},
author = {Dutykh, D. and Dias, F.},
booktitle = {Tsunami and Nonlinear waves},
editor = {Kundu, Anjan},
pages = {65--96},
publisher = {Springer Verlag (Geo Sc.)},
title = {{Water waves generated by a moving bottom}},
year = {2007}
}
@article{Dutykh2008,
author = {Dutykh, D. and Dias, F.},
journal = {Computer Methods in Applied Mechanics and Engineering},
pages = {1268--1275},
title = {{Influence of sedimentary layering on tsunami generation}},
volume = {199(21-22)},
year = {2010}
}
@article{ddk,
author = {Dutykh, D. and Dias, F. and Kervella, Y.},
journal = {C. R. Acad. Sci. Paris, Ser. I},
pages = {499--504},
title = {{Linear theory of wave generation by a moving bottom}},
volume = {343},
year = {2006}
}
@article{Dutykh2011d,
abstract = {Consideration is given to the influence of an underwater landslide on waves at the surface of a shallow body of fluid. The equations of motion which govern the evolution of the barycenter of the landslide mass include various dissipative effects due to bottom friction, internal energy dissipation, and viscous drag. The surface waves are studied in the Boussinesq scaling, with time-dependent bathymetry. A numerical model for the Boussinesq equations is introduced which is able to handle time-dependent bottom topography, and the equations of motion for the landslide and surface waves are solved simultaneously. The numerical solver for the Boussinesq equations can also be restricted to implement a shallow-water solver, and the shallow-water and Boussinesq configurations are compared. A particular bathymetry is chosen to illustrate the general method, and it is found that the Boussinesq system predicts larger wave run-up than the shallow-water theory in the example treated in this paper. It also found that the finite fluid domain has a significant impact on the behaviour of the wave run-up.},
archivePrefix = {arXiv},
arxivId = {1112.5083},
author = {Dutykh, D. and Kalisch, H.},
doi = {10.5194/npg-20-267-2013},
eprint = {1112.5083},
issn = {1607-7946},
journal = {Nonlin. Processes Geophys.},
month = {may},
number = {3},
pages = {267--285},
title = {{Boussinesq modeling of surface waves due to underwater landslides}},
url = {http://hal.archives-ouvertes.fr/hal-00654386/ http://www.nonlin-processes-geophys.net/20/267/2013/},
volume = {20},
year = {2013}
}
@article{Dutykh2011e,
abstract = {Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.},
author = {Dutykh, D. and Katsaounis, T. and Mitsotakis, D.},
doi = {10.1016/j.jcp.2011.01.003},
issn = {00219991},
journal = {J. Comput. Phys.},
keywords = {Dispersive waves,Finite volume method,Runup,Solitary waves,Water waves},
month = {apr},
number = {8},
pages = {3035--3061},
title = {{Finite volume schemes for dispersive wave propagation and runup}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999111000118},
volume = {230},
year = {2011}
}
@conference{Dutykh2011,
address = {Prague},
author = {Dutykh, D. and Katsaounis, T. and Mitsotakis, D.},
booktitle = {Finite Volumes for Complex Applications VI - Problems {\&} Perspectives},
doi = {10.1007/978-3-642-20671-9{\_}41},
editor = {Fort, J.},
pages = {389--397},
publisher = {Springer Berlin Heidelberg},
title = {{Dispersive wave runup on non-uniform shores}},
year = {2011}
}
@article{Dutykh2010e,
author = {Dutykh, D. and Katsaounis, T. and Mitsotakis, D.},
journal = {Int. J. Num. Meth. Fluids},
pages = {717--736},
title = {{Finite volume methods for unidirectional dispersive wave models}},
volume = {71},
year = {2013}
}
@article{Dutykh2011c,
abstract = {The estimation of the maximum wave run-up height is a problem of practical importance. Most of the analytical and numerical studies are limited to a constant slope plain shore and to the classical nonlinear shallow water equations. However, in nature the shore is characterized by some roughness. In order to take into account the effects of the bottom rugosity, various ad hoc friction terms are usually used. In this Letter, we study the effect of the roughness of the bottom on the maximum run-up height. A stochastic model is proposed to describe the bottom irregularity, and its effect is quantified by using Monte Carlo simulations. For the discretization of the nonlinear shallow water equations, we employ modern finite volume schemes. Moreover, the results of the random bottom model are compared with the more conventional approaches.},
author = {Dutykh, D. and Labart, C. and Mitsotakis, D.},
doi = {10.1103/PhysRevLett.107.184504},
journal = {Phys. Rev. Lett},
pages = {184504},
title = {{Long wave run-up on random beaches}},
volume = {107},
year = {2011}
}
@article{Dutykh2010c,
abstract = {The classical dam break problem has become the de factostandard in validating the nonlinear shallow water equations solvers. Moreover, the NSWE are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration. The main purpose of this study is to check the pertinence of the NSWE for flooding processes. From the mathematical point of view, the answer is not obvious since all derivation procedures assumes the total water depth positivity. We performed a comparison between the two-fluid Navier-Stokes simulations and the NSWE solved analytically and numerically. Several conclusions are drawn out and perspectives for future research are outlined.},
author = {Dutykh, D. and Mitsotakis, D.},
journal = {Discrete and Continuous Dynamical Systems - Series B},
keywords = {Free surface flow,dam break problem,finite volume method,shallow water equations,two-phase flow},
pages = {799--818},
title = {{On the relevance of the dam break problem in the context of nonlinear shallow water equations}},
volume = {13(4)},
year = {2010}
}
@inproceedings{Dutykh2012,
abstract = {In this work we study the generation of water waves by an underwater sliding mass. The wave dynamics are assumed to fell into the shallow water regime. However, the characteristic wavelength of the free surface motion is generally smaller than in geophysically generated tsunamis. Thus, dispersive effects need to be taken into account. In the present study the fluid layer is modeled by the Peregrine system modified appropriately and written in conservative variables. The landslide is assumed to be a quasi-deformable body of mass whose trajectory is completely determined by its barycenter motion. A differential equation modeling the landslide motion along a curvilinear bottom is obtained by projecting all the forces acting on the submerged body onto a local moving coordinate system. One of the main novelties of our approach consists in taking into account curvature effects of the sea bed.},
address = {http://hal.archives-ouvertes.fr/hal-00637102/},
author = {Dutykh, D. and Mitsotakis, D. and Beisel, S. A. and Shokina, N. Yu.},
booktitle = {Numerical Methods for Hyperbolic Equations: Theory and Applications},
editor = {Vazquez-Cendon, M E},
pages = {245--250},
title = {{Dispersive waves generated by an underwater landslide}},
url = {http://hal.archives-ouvertes.fr/hal-00637102/},
year = {2012}
}
@article{Dutykh2010d,
abstract = {The main reason for the generation of tsunamis is the deformation of the bottom of the ocean caused by an underwater earthquake. Usually, only the vertical bottom motion is taken into account while the horizontal co-seismic displacements are neglected in the absence of landslides. In the present study we propose a methodology based on the well-known Okada solution to reconstruct in more details all components of the bottom coseismic displacements. Then, the sea-bed motion is coupled with a three-dimensional weakly nonlinear water wave solver which allows us to simulate a tsunami wave generation. We pay special attention to the evolution of kinetic and potential energies of the resulting wave while the contribution of the horizontal displacements into wave energy balance is also quantified. Such contribution of horizontal displacements to the tsunami generation has not been discussed before, and it is different from the existing approaches. The methods proposed in this study are illustrated on the July 17, 2006 Java tsunami and some more recent events.},
author = {Dutykh, D. and Mitsotakis, D. and Chubarov, L. B. and Shokin, Yu. I.},
doi = {10.1016/j.ocemod.2012.07.002},
issn = {14635003},
journal = {Ocean Modelling},
keywords = {Coseismic displacements,Finite fault inversion,Tsunami waves,Water waves,Wave energy},
month = {jul},
pages = {43--56},
title = {{On the contribution of the horizontal sea-bed displacements into the tsunami generation process}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1463500312001011},
volume = {56},
year = {2012}
}
@techreport{Dutykh2010b,
author = {Dutykh, D. and Mitsotakis, D. and Gardeil, X.},
institution = {$\backslash$url{\{}http://www.lama.univ-savoie.fr/{\~{}}dutykh/animations/Java2006{\_}DD-DM-XG.avi{\}}},
title = {{Animation of the free surface elevation during July 17, 2006 Java event}},
year = {2010}
}
@article{Dutykh2010a,
abstract = {The present study is devoted to the problem of tsunami wave generation. The main goal of this work is twofold. First of all, we propose a simple and computationally inexpensive model for the description of the sea bed displacement during an underwater earthquake, based on the finite fault solution for the slip distribution under some assumptions on the dynamics of the rupturing process. Once the bottom motion is reconstructed, we study waves induced on the free surface of the ocean. For this purpose, we consider three different models approximating the Euler equations of the water wave theory. Namely, we use the linearized Euler equations (we are in fact solving the Cauchy–Poisson problem), a Boussinesq system, and a novel weakly nonlinear model. An intercomparison of these approaches is performed. The developments of the present study are illustrated on the July 17, 2006 Java event, where an underwater earthquake of magnitude 7.7 generated a tsunami that inundated the southern coast of Java.},
author = {Dutykh, D. and Mitsotakis, D. and Gardeil, X. and Dias, F.},
doi = {10.1007/s00162-011-0252-8},
issn = {0935-4964},
journal = {Theor. Comput. Fluid Dyn.},
month = {mar},
pages = {177--199},
title = {{On the use of the finite fault solution for tsunami generation problems}},
url = {http://www.springerlink.com/index/10.1007/s00162-011-0252-8},
volume = {27},
year = {2013}
}
@article{Dutykh2014d,
author = {Dutykh, D. and Pelinovsky, E.},
doi = {10.1016/j.physleta.2014.09.008},
issn = {03759601},
journal = {Phys. Lett. A},
month = {aug},
number = {42},
pages = {3102--3110},
title = {{Numerical simulation of a solitonic gas in KdV and KdV-BBM equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960114008895},
volume = {378},
year = {2014}
}
@article{Dutykh2009a,
abstract = {A novel tool for tsunami wave modeling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code VOLNA is able to handle the complete life cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains a detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. The majority of tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps, which are produced with these types of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally, the main conclusions are outlined and the perspectives for future research presented.},
archivePrefix = {arXiv},
arxivId = {1002.4553},
author = {Dutykh, D. and Poncet, R. and Dias, F.},
doi = {10.1016/j.euromechflu.2011.05.005},
eprint = {1002.4553},
journal = {Eur. J. Mech. B/Fluids},
keywords = {Finite volumes,Run-down,Run-up,Shallow water equations,Tsunami generation,Tsunami waves},
number = {6},
pages = {598--615},
title = {{The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation}},
url = {http://hal.archives-ouvertes.fr/hal-00454591/},
volume = {30},
year = {2011}
}
@article{Dutykh2014b,
abstract = {In this letter we demonstrate for the first time the formation of the inverse energy cascade in the focusing modified Korteweg-de Vries (mKdV) equation. We study numerically the properties of this cascade such as the dependence of the spectrum shape on the initial excitation parameter (amplitude), perturbation magnitude and the size of the spectral domain. Most importantly we found that the inverse cascade is always accompanied by the direct one and they both form a very stable quasi-stationary structure in the Fourier space in the spirit of the FPU-like reoccurrence phenomenon. The formation of this structure is intrinsically related to the development of the nonlinear stage of the modulational instability (MI). These results can be used in several fields such as the internal gravity water waves, ion-acoustic waves in plasmas and others.},
author = {Dutykh, D. and Tobisch, E.},
doi = {10.1209/0295-5075/107/14001},
journal = {EPL},
pages = {14001},
title = {{Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation}},
url = {http://hal.archives-ouvertes.fr/hal-00991944/},
volume = {107},
year = {2014}
}
@article{Dutykh2014a,
author = {Dutykh, D. and Tobisch, E.},
journal = {Submitted},
pages = {1--33},
title = {{Direct dynamical energy cascade in the modified KdV equation}},
url = {http://hal.archives-ouvertes.fr/hal-00990724/},
year = {2014}
}
@article{Dyachenko2004,
author = {Dyachenko, A. I. and Korotkevich, A. O. and Zakharov, V. E.},
journal = {Phys. Rev. Lett.},
pages = {134501},
title = {{Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves}},
volume = {92},
year = {2004}
}
@article{Dyachenko2003,
author = {Dyachenko, A. I. and Korotkevich, A. O. and Zakharov, V. E.},
journal = {JETP Lett.},
pages = {546--550},
title = {{Weak turbulence of gravity waves}},
volume = {77},
year = {2003}
}
@article{Dyachenko1996a,
abstract = {Using the combination of the canonical formalism for free-surface hydrodynamics and conformal mapping to the half-plane we obtain a simple system of pseudo-differential equations for the surface shape and hydrodynamic potential. The system is well-adjusted for a numerical simulation. Some typical results of such a simulation are presented.},
author = {Dyachenko, A. I. and Kuznetsov, E. A. and Spector, M. D. and Zakharov, V. E.},
doi = {10.1016/0375-9601(96)00417-3},
issn = {03759601},
journal = {Phys. Lett. A},
keywords = {Conformal mapping,Free surface hydrodynamics,Integrable equation,Potential flow},
month = {sep},
number = {1-2},
pages = {73--79},
title = {{Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping)}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0375960196004173},
volume = {221},
year = {1996}
}
@article{Dyachenko1996b,
abstract = {Using the combination of the canonical formalism and conformal mapping, a theory of the free surface of deep water in the approximation of a high curvature is developed. It is shown that the numerical simulation is in excellent agreement with the analytical description.},
author = {Dyachenko, A. I. and Zakharov, V.},
doi = {10.1016/0375-9601(96)00394-5},
journal = {Physics Letters A},
keywords = {Conformal mapping,Free surface hydrodynamics,Integrable equation,Potential flow},
number = {1-2},
pages = {80--84},
title = {{Toward an integrable model of deep water}},
volume = {221},
year = {1996}
}
@article{Dyachenko1994,
abstract = {A strong argument is found in support of the integrability of free-surfacehydrodynamics in the one-dimensional case. It is shown that the first term in the perturbation series in powers of nonlinearity is identically equal to zero, the consequences of which are discussed as well.},
author = {Dyachenko, A. I. and Zakharov, V.},
doi = {10.1016/0375-9601(94)90067-1},
journal = {Physics Letters A},
number = {2},
pages = {144--148},
title = {{Is free-surfacehydrodynamics an integrable system?}},
volume = {190},
year = {1994}
}
@article{Dyachenko2011,
author = {Dyachenko, A. I. and Zakharov, V. E.},
journal = {JETP Lett.},
number = {12},
pages = {701--705},
title = {{Compact Equation for Gravity Waves on Deep Water}},
volume = {93},
year = {2011}
}
@article{Dyachenko2005,
author = {Dyachenko, A. I. and Zakharov, V. E.},
journal = {JETP Lett.},
number = {6},
pages = {255--259},
title = {{Modulation instability of stokes waves {\$}\backslashto{\$} freak wave}},
volume = {81},
year = {2005}
}
@article{Dyachenko2012,
archivePrefix = {arXiv},
arxivId = {1201.4808},
author = {Dyachenko, A. I. and Zakharov, V. E. and Kachulin, D. I.},
eprint = {1201.4808},
journal = {arXiv:1201.4808},
pages = {15},
title = {{Collision of two breathers at surface of deep water}},
year = {2012}
}
@article{Dyachenko1996,
author = {Dyachenko, A. I. and Zakharov, V. E. and Kuznetsov, E. A.},
journal = {Plasma Physics Reports},
number = {10},
pages = {829--840},
title = {{Nonlinear dynamics of the free surface of an ideal fluid}},
volume = {22},
year = {1996}
}
@article{Dyachenko1989,
author = {Dyachenko, A. I. and Zakharov, V. E. and Pushkarev, A. N. and Shvets, V. F. and Yankov, V. V.},
journal = {JETP Lett.},
pages = {2026--2032},
title = {{Soliton turbulence in nonintegrable wave systems}},
volume = {96},
year = {1989}
}
@article{Dyachenko1992,
author = {Dyachenko, S. and Newell, A. C. and Pushkarev, A. N. and Zakharov, V. E.},
doi = {10.1016/0167-2789(92)90090-A},
issn = {01672789},
journal = {Phys. D},
month = {jun},
number = {1-2},
pages = {96--160},
title = {{Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schr{\"{o}}dinger equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/016727899290090A},
volume = {57},
year = {1992}
}
@article{Dysthe1979,
author = {Dysthe, K. B.},
journal = {Proc. R. Soc. Lond. A},
pages = {105--114},
title = {{Note on a modification to the nonlinear Schr{\"{o}}dinger equation for application to deep water}},
volume = {369},
year = {1979}
}
@article{Dysthe2008,
author = {Dysthe, K. B. and Krogstad, H. E. and Muller, P.},
journal = {Ann. Rev. Fluid Mech.},
number = {40},
pages = {287--310},
title = {{Oceanic rogue waves}},
volume = {40},
year = {2008}
}
@article{Dysthe1999,
author = {Dysthe, K. B. and Trulsen, K.},
journal = {Physica Scripta},
pages = {48--52},
title = {{Note on breather type solutions of the NLS as models for freak-waves}},
volume = {T82},
year = {1999}
}
@article{Dysthe2003,
abstract = {Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schr odinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra relax towards a quasi-stationary state on a timescale (2$\omega$0)1.Inthisstate the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour $\omega$4 on the high-frequency side of the (angularly integrated) spectrum.},
author = {Dysthe, K. B. and Trulsen, K. and Krogstad, H. E. and Socquet-Juglard, H.},
doi = {10.1017/S0022112002002616},
issn = {00221120},
journal = {J. Fluid Mech.},
pages = {1--10},
title = {{Evolution of a narrow-band spectrum of random surface gravity waves}},
volume = {478},
year = {2003}
}
@article{Ebadi2011a,
author = {Ebadi, G. and Biswas, A.},
doi = {10.1016/j.mcm.2010.10.005},
issn = {08957177},
journal = {Mathematical and Computer Modelling},
keywords = {Evolution equation,Integrability,Solitons},
month = {mar},
number = {5-6},
pages = {694--698},
title = {{The G'/G method and 1-soliton solution of the Davey-Stewartson equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S089571771000453X},
volume = {53},
year = {2011}
}
@article{Ebadi2011,
abstract = {This paper studies the Davey-Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.},
author = {Ebadi, G. and Krishnan, E. V. and Labidi, M. and Zerrad, E. and Biswas, A.},
doi = {10.1080/17455030.2011.606853},
issn = {1745-5030},
journal = {Waves in Random and Complex Media},
month = {nov},
number = {4},
pages = {559--590},
title = {{Analytical and numerical solutions to the Davey-Stewartson equation with power-law nonlinearity}},
url = {http://www.tandfonline.com/doi/abs/10.1080/17455030.2011.606853},
volume = {21},
year = {2011}
}
@article{Eckart1960,
author = {Eckart, C.},
journal = {Phys. Fluids},
pages = {421--427},
title = {{Variation principles of hydrodynamics}},
volume = {3},
year = {1960}
}
@article{Eglit1998,
author = {Eglit, M.},
journal = {Annals of Glaciology},
pages = {281--284},
title = {{Mathematical and physical modeling of powder-snow avalanches in Russia}},
volume = {26},
year = {1998}
}
@inproceedings{Eglit1991,
author = {Eglit, M.},
booktitle = {Proceedings of the Steklov Institute of Mathematics},
pages = {187--193},
title = {{The dynamics of snow avalanches}},
volume = {186},
year = {1991}
}
@inbook{Eglit1983,
author = {Eglit, M. E.},
chapter = {Some mathe},
editor = {Shaninpoor, M},
pages = {577--588},
publisher = {Trans Tech Publications, Clausthal-Zellerfeld},
title = {{Advances in the Mechanics and the Flow of Granular Materials}},
year = {1983}
}
@inbook{egorov,
author = {Egorov, Yu. V. and Shubin, M. A.},
chapter = {Elements o},
publisher = {Springer},
series = {Encyclopaedia of Mathematical Sciences},
title = {{Partial Differential Equations}},
volume = {2},
year = {1994}
}
@article{Eilbeck1977,
author = {Eilbeck, J. C. and McGuire, G. R.},
doi = {10.1016/0021-9991(77)90088-2},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {jan},
number = {1},
pages = {63--73},
title = {{Numerical study of the regularized long-wave equation. II: Interaction of solitary waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999177900882},
volume = {23},
year = {1977}
}
@article{Einfeldt1991,
author = {Einfeldt, B. and Munz, C. D. and Roe, P. L. and Sjogreen, B.},
journal = {J. Comput. Phys.},
pages = {273--295},
title = {{On Godunov-type methods near low densities}},
volume = {92},
year = {1991}
}
@article{Einstein1926,
author = {Einstein, A.},
journal = {Die Naturwissenschaften},
number = {11},
pages = {223--224},
title = {{Die Ursache der M{\"{a}}anderbildung der Flu{\ss}l{\"{a}}ufe und des sogenannten Baerschen Gesetzes}},
volume = {14},
year = {1926}
}
@article{Einstein1905,
author = {Einstein, A.},
doi = {10.1002/andp.19053220806},
issn = {00033804},
journal = {Annalen der Physik},
number = {8},
pages = {549--560},
title = {{{\"{U}}ber die von der molekularkinetischen Theorie der W{\"{a}}rme geforderte Bewegung von in ruhenden Fl{\"{u}}ssigkeiten suspendierten Teilchen}},
url = {http://doi.wiley.com/10.1002/andp.19053220806},
volume = {322},
year = {1905}
}
@article{Einstein1952,
author = {Einstein, H. A.},
journal = {American Society of Civil Engineers Transactions},
pages = {561--577},
title = {{Formulas for the transportation of bed load}},
volume = {107},
year = {1952}
}
@article{El2015,
archivePrefix = {arXiv},
arxivId = {1512.02470},
author = {El, G. A.},
eprint = {1512.02470},
journal = {Submitted},
pages = {1--7},
title = {{Critical density of a soliton gas}},
volume = {arXiv:1512},
year = {2015}
}
@article{El2005,
author = {El, G. A.},
doi = {10.1063/1.1947120},
journal = {Chaos},
pages = {37103},
title = {{Resolution of a shock in hyperbolic systems modified by weak dispersion}},
volume = {15},
year = {2005}
}
@article{El2003,
author = {El, G. A.},
doi = {10.1016/S0375-9601(03)00515-2},
issn = {03759601},
journal = {Phys. Lett. A},
month = {may},
number = {4-5},
pages = {374--383},
title = {{The thermodynamic limit of the Whitham equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960103005152},
volume = {311},
year = {2003}
}
@article{El2006,
author = {El, G. A. and Grimshaw, R. H. J. and Smyth, N. F.},
journal = {Phys. Fluids},
pages = {27104},
title = {{Unsteady undular bores in fully nonlinear shallow-water theory}},
volume = {18},
year = {2006}
}
@article{El2008,
author = {El, G. A. and Grimshaw, R. H. J. and Smyth, N. F.},
journal = {Phys. D},
number = {19},
pages = {2423--2435},
title = {{Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory}},
volume = {237},
year = {2008}
}
@article{El2005a,
abstract = {We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, and the evolution reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions. The proposed general procedure of the derivation of the kinetic equation is illustrated by the examples of the Korteweg-de Vries and nonlinear Schr{\"{o}}dinger (NLS) equations. As a simple physical example, we construct an explicit solution for the case of interaction of two cold NLS soliton gases.},
author = {El, G. A. and Kamchatnov, A.},
doi = {10.1103/PhysRevLett.95.204101},
institution = {Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom. G.El@lboro.ac.uk},
issn = {0031-9007},
journal = {Phys. Rev. Lett},
month = {nov},
number = {20},
pages = {204101},
publisher = {APS},
title = {{Kinetic Equation for a Dense Soliton Gas}},
url = {http://arxiv.org/abs/nlin/0507016 http://link.aps.org/doi/10.1103/PhysRevLett.95.204101},
volume = {95},
year = {2005}
}
@article{El2011a,
author = {El, G. A. and Kamchatnov, A. M. and Pavlov, M. V. and Zykov, S. A.},
doi = {10.1007/s00332-010-9080-z},
issn = {0938-8974},
journal = {J. Nonlinear Sci.},
month = {apr},
number = {2},
pages = {151--191},
title = {{Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions}},
url = {http://link.springer.com/10.1007/s00332-010-9080-z},
volume = {21},
year = {2011}
}
@article{El2011,
author = {El, G. A. and Kamchatnov, A. M. and Pavlov, M. V. and Zykov, S. A.},
doi = {10.1007/s00332-010-9080-z},
issn = {0938-8974},
journal = {J. Nonlinear Sci.},
month = {sep},
number = {2},
pages = {151--191},
title = {{Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions}},
url = {http://link.springer.com/10.1007/s00332-010-9080-z},
volume = {21},
year = {2011}
}
@article{El2001,
author = {El, G. A. and Krylov, A. L. and Molchanov, S. A. and Venakides, S.},
doi = {10.1016/S0167-2789(01)00198-1},
issn = {01672789},
journal = {Phys. D},
month = {may},
pages = {653--664},
title = {{Soliton turbulence as a thermodynamic limit of stochastic soliton lattices}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278901001981},
volume = {152-153},
year = {2001}
}
@article{Ellison1959,
abstract = {When a fluid which is lighter than its surroundings is emitted by a source under a sloping roof (or a heavier fluid from a source on a sloping floor), it may flow as a relatively thin turbulent layer. The motion of this layer is governed by the rate at which it entrains the ambient fluid. A theory is presented in which it is assumed that the entrainment is proportional to the velocity of the layer multiplied by an empirical function, E(Ri), of the overall Richardson number for the layer defined by Ri = g($\rho$a - $\rho$) h/$\rho$a V2. This theory predicts that in most practical cases the layer will rapidly attain an equilibrium state in which Ri does not vary with distance downstream, and the gravitational force on the layer is just balanced by the drag due to entrainment together with friction on the floor or roof. Two series of laboratory experiments are described from which E(Ri) can be determined. In the first, the spread of a surface jet of fluid lighter than that over which it is flowing is measured; in the second, a study is made of the flow of a heavy liquid down the sloping floor of a channel. These experiments show that E falls off rapidly as Ri increases and is probably negligible when Ri is more than about 0·8. The theoretical and experimental results allow predictions to be made of flow velocities once the rate of supply of density difference is known. An estimate is also given of the uniform velocity which the ambient fluid must possess in order to cause the motion of the layer to be reversed.},
author = {Ellison, T. H. and Turner, J. S.},
doi = {10.1017/S0022112059000738},
issn = {0022-1120},
journal = {J. Fluid Mech},
month = {mar},
number = {03},
pages = {423--448},
title = {{Turbulent entrainment in stratified flows}},
volume = {6},
year = {1959}
}
@article{Enet2007,
author = {Enet, F. and Grilli, S. T.},
journal = {J. Waterway, Port, Coastal and Ocean Engineering},
number = {6},
pages = {442--454},
title = {{Experimental study of tsunami generation by three-dimensional rigid underwater landslides}},
volume = {133},
year = {2007}
}
@inproceedings{Enet2003,
author = {Enet, F. and Grilli, S. T. and Watts, Ph.},
booktitle = {Proc. of the 13th Offshore and Polar Engrg Conf ISOPE03 Honolulu Hawaii},
keywords = {boundary element method,experiments,numerical wave,submarine landslide,tank,tsunami},
pages = {372--379},
publisher = {Citeseer},
title = {{Laboratory experiments for tsunamis generated by underwater landslides: Comparison with numerical modeling}},
url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.2727{\&}amp;rep=rep1{\&}amp;type=pdf},
volume = {3},
year = {2003}
}
@book{erdelyi,
author = {Erd{\'{e}}lyi, A.},
publisher = {Dover publivations},
title = {{Asymptotic expansions}},
year = {1956}
}
@article{EIK,
author = {Erduran, K. S. and Ilic, S. and Kutija, V.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {1213--1232},
title = {{Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations}},
volume = {49},
year = {2005}
}
@article{Ergun2005,
author = {Ergun, M. and Okay, S. and Sari, C. and Oral, E. Z. and Ash, M. and Hall, J. and Miller, H.},
journal = {Marine Geology},
pages = {349--358},
title = {{Gravity anomalies of the Cyprus Arc and their tectonic implications}},
volume = {221},
year = {2005}
}
@book{Erturk2011,
abstract = {The transformation of vibrations into electric energy through the use of piezoelectric devices is an exciting and rapidly developing area of research with a widening range of applications constantly materialising. With Piezoelectric Energy Harvesting, world-leading researchers provide a timely and comprehensive coverage of the electromechanical modelling and applications of piezoelectric energy harvesters.},
address = {Chichester},
author = {Erturk, A. and Inman, D. J.},
isbn = {9781119991168},
pages = {414},
publisher = {Wiley},
title = {{Piezoelectric energy harvesting}},
year = {2011}
}
@article{Escobedo2014,
author = {Escobedo, R. and Muro, C. and Spector, L. and Coppinger, R. P.},
doi = {10.1098/rsif.2014.0204},
issn = {1742-5689},
journal = {J. R. Soc. Interface},
number = {95},
pages = {20140204--20140204},
title = {{Group size, individual role differentiation and effectiveness of cooperation in a homogeneous group of hunters}},
url = {http://rsif.royalsocietypublishing.org/cgi/doi/10.1098/rsif.2014.0204},
volume = {11},
year = {2014}
}
@article{Eskilsson2005,
author = {Eskilsson, C. and Sherwin, S. J.},
journal = {J. Sci. Comput.},
pages = {269--288},
title = {{Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems}},
volume = {22},
year = {2005}
}
@article{Eskilsson2006,
author = {Eskilsson, C. and Sherwin, S. J.},
journal = {J. Comput. Phys},
number = {2},
pages = {566--589},
title = {{Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations}},
volume = {212},
year = {2006}
}
@article{Eskilsson2006a,
author = {Eskilsson, C. and Sherwin, S. J. and Bergdahl, L.},
journal = {Coastal Engineering},
number = {11},
pages = {947--963},
title = {{An unstructured spectral/hp element model for enhanced Boussinesq-type equations}},
volume = {53},
year = {2006}
}
@article{Esler2011,
author = {Esler, J. G. and Pearce, J. D.},
journal = {J. Fluid Mech.},
pages = {555--585},
title = {{Dispersive dam-break and lock-exchange flows in a two-layer fluid}},
volume = {667},
year = {2011}
}
@phdthesis{Etienne2004a,
author = {Etienne, J.},
school = {Institut National Polytechnique de Grenoble},
title = {{Numerical simulation of high density ratio gravity currents. Application to the avalanches.}},
type = {Ph.D. Thesis},
year = {2004}
}
@article{Etienne2005,
author = {Etienne, J. and Hopfinger, E. J. and Saramito, P.},
doi = {10.1063/1.1849800},
journal = {Phys. Fluids},
pages = {36601},
title = {{Numerical simulations of high density ratio lock-exchange flows}},
volume = {17},
year = {2005}
}
@article{Etienne2004,
author = {Etienne, J. and Saramito, P. and Hopfinger, E. J.},
doi = {10.3189/172756404781815031},
journal = {Annals of Glaciology},
pages = {379--383},
title = {{Numerical simulations of dense clouds on steep slopes: application to powder-snow avalanches}},
volume = {38},
year = {2004}
}
@book{Evans2010,
address = {Providence, Rhode Island},
author = {Evans, L. C.},
doi = {978-0-8218-4974-3},
edition = {2},
pages = {749},
publisher = {American Mathematical Society},
title = {{Partial Differential Equations}},
year = {2010}
}
@article{Eyink2008,
abstract = {We discuss Onsager's conjecture that non-vanishing energy dissipation in high-Reynolds-number turbulence is associated to singular (distributional) solutions of the incompressible Euler equations. We carefully explain the physical and mathematical meaning of the conjecture and also review relevant theoretical, experimental and numerical work, emphasizing some of the dramatic successes of Onsager’s point of view. Finally, we present several new ideas and results on Lagrangian dynamics of circulations and vortex-lines that we believe will be important for future progress.},
author = {Eyink, G. L.},
doi = {10.1016/j.physd.2008.02.005},
issn = {01672789},
journal = {Phys. D},
keywords = {Coarse-graining,Energy dissipation,Euler equations,Turbulence},
month = {aug},
number = {14-17},
pages = {1956--1968},
title = {{Dissipative anomalies in singular Euler flows}},
volume = {237},
year = {2008}
}
@article{Eymard2006,
author = {Eymard, R. and Fuhrmann, J. and G{\"{a}}rtner, K.},
doi = {10.1007/s00211-005-0659-5},
issn = {0029-599X},
journal = {Numerische Mathematik},
month = {jan},
number = {3},
pages = {463--495},
title = {{A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local dirichlet problems}},
url = {http://link.springer.com/10.1007/s00211-005-0659-5},
volume = {102},
year = {2006}
}
@article{Eymard2007,
abstract = {We introduce here a new finite volume scheme which was developed for the discretization of anisotropic diffusion problems; the originality of this scheme lies in the fact that we are able to prove its convergence under very weak assumptions on the discretization mesh.},
author = {Eymard, R. and Gallou{\"{e}}t, T. and Herbin, R.},
journal = {C. R. Acad. Sci. Paris, Ser. I},
pages = {403--406},
title = {{A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis}},
volume = {344},
year = {2007}
}
@article{Ezersky2012,
abstract = {Nonlinear wave run-up on the beach caused by harmonic wave maker located at some distance from the shore line is studied experimentally. It is revealed that under certain wave excitation frequencies a significant increase in run-up amplification is observed. It is found that this amplification is due to the excitation of resonant mode in the region between the shoreline and wave maker. Frequency and magnitude of the maximum amplification are in good correlation with the numerical calculation results represented in the paper (T.S. Stefanakis et al. PRL (2011)). These effects are very important for understanding the nature of rougue waves in the coastle zone.},
archivePrefix = {arXiv},
arxivId = {1207.6508},
author = {Ezersky, A. and Abcha, N. and Pelinovsky, E. N.},
eprint = {1207.6508},
journal = {Nonlin. Processes Geophys.},
month = {jul},
pages = {35--40},
title = {{Physical simulation of resonant wave run-up on a beach}},
url = {http://arxiv.org/abs/1207.6508},
volume = {20},
year = {2013}
}
@book{Faddeev1987,
abstract = {The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schr{\"{o}}dinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions.},
address = {Berlin Heidelberg New York},
author = {Faddeev, L. D. and Takhtajan, L.},
isbn = {978-3-540-69969-9},
pages = {594},
publisher = {Springer},
title = {{Hamiltonian Methods in the Theory of Solitons}},
year = {1987}
}
@article{Falcao2010,
author = {Falc{\~{a}}o, Ant{\'{o}}nio F. de O.},
doi = {10.1016/j.rser.2009.11.003},
issn = {13640321},
journal = {Renewable and Sustainable Energy Reviews},
month = {apr},
number = {3},
pages = {899--918},
title = {{Wave energy utilization: A review of the technologies}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1364032109002652},
volume = {14},
year = {2010}
}
@article{Falnes2007,
author = {Falnes, J.},
doi = {10.1016/j.marstruc.2007.09.001},
issn = {09518339},
journal = {Marine Structures},
month = {oct},
number = {4},
pages = {185--201},
title = {{A review of wave-energy extraction}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0951833907000482},
volume = {20},
year = {2007}
}
@article{Fan1993,
author = {Fan, H. and Hale, J. K.},
doi = {10.1007/BF00383219},
issn = {0003-9527},
journal = {Arch. Rat. Mech. Anal.},
number = {3},
pages = {201--216},
title = {{Large-time behavior in inhomogeneous conservation laws}},
url = {http://link.springer.com/10.1007/BF00383219},
volume = {125},
year = {1993}
}
@article{Faraday1831,
author = {Faraday, M.},
doi = {10.1098/rstl.1831.0018},
journal = {Phil. Trans. R. Soc. Lond},
pages = {299--340},
title = {{On a Peculiar Class of Acoustical Figures; and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces}},
volume = {121},
year = {1831}
}
@article{Farge1992,
author = {Farge, M.},
doi = {10.1146/annurev.fl.24.010192.002143},
issn = {0066-4189},
journal = {Ann. Rev. Fluid Mech.},
month = {jan},
number = {1},
pages = {395--458},
title = {{Wavelet Transforms and their Applications to Turbulence}},
url = {http://www.annualreviews.org/doi/abs/10.1146/annurev.fl.24.010192.002143},
volume = {24},
year = {1992}
}
@article{Farrell1996,
abstract = {Boundary value problems for singularly perturbed semilinear elliptic equations are considered. Special piecewise-uniform meshes are constructed which yield accurate numerical solutions irrespective of the value of the small parameter. Numerical methods composed of standard monotone finite difference operators and these piecewise-uniform meshes are shown theoretically to be uniformly (with respect to the singular perturbation parameter) convergent. Numerical results are also presented, which indicate that in practice the method is first-order accurate.},
author = {Farrell, P. A. and Miller, J. J. H. and O'Riordan, E. and Shishkin, G. I.},
doi = {10.1137/0733056},
issn = {0036-1429},
journal = {SIAM J. Numer. Anal.},
month = {jun},
number = {3},
pages = {1135--1149},
title = {{A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation}},
url = {http://epubs.siam.org/doi/abs/10.1137/0733056},
volume = {33},
year = {1996}
}
@phdthesis{Fawer1937,
author = {Fawer, C.},
doi = {10.5075/epfl-thesis-9},
school = {{\'{E}}cole polytechnique f{\'{e}}d{\'{e}}rale de Lausanne},
title = {{Etude de quelques {\'{e}}coulements permanents {\`{a}} filets courbes}},
type = {Th{\`{e}}se},
year = {1937}
}
@article{Fe2008,
author = {Fe, J. and Cueto-Felgueroso, L. and Navarrina, F. and Puertas, J.},
journal = {Int. J. Num. Meth. Fluids},
pages = {781--802},
title = {{Numerical viscosity reduction in the resolution of the shallow water equations with turbulent term}},
volume = {58},
year = {2008}
}
@article{Fe2009,
author = {Fe, J. and Navarrina, F. and Puertas, J. and Vellando, P. and Ruiz, D.},
journal = {Int. J. Num. Meth. Fluids},
pages = {177--202},
title = {{Experimental validation of two depth-averaged turbulence models}},
volume = {60},
year = {2009}
}
@article{Fedele2012b,
author = {Fedele, F.},
doi = {10.1088/0169-5983/44/4/045509},
issn = {0169-5983},
journal = {Fluid Dynamics Research},
month = {aug},
number = {4},
pages = {45509},
title = {{Travelling waves in axisymmetric pipe flows}},
volume = {44},
year = {2012}
}
@article{Fedele2008a,
author = {Fedele, F.},
journal = {Physica D},
pages = {2127--2131},
title = {{Rogue wave in oceanic turbulence}},
volume = {237},
year = {2008}
}
@article{Fedele2006a,
author = {Fedele, F.},
doi = {10.1016/j.oceaneng.2006.01.001},
issn = {00298018},
journal = {Ocean Engineering},
month = {dec},
number = {17-18},
pages = {2225--2239},
title = {{On wave groups in a Gaussian sea}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0029801806000667},
volume = {33},
year = {2006}
}
@article{Fedele2006,
author = {Fedele, F.},
journal = {Journal of Offshore Mechanics and Arctic Engineering},
pages = {11--16},
title = {{Extreme Events in nonlinear random seas}},
volume = {128},
year = {2006}
}
@article{Fedele2010,
author = {Fedele, F. and Arena, F.},
journal = {J. Phys. Oceanogr.},
pages = {1106--1117},
title = {{Long-term statistics and extreme waves of sea storms}},
volume = {40(5)},
year = {2010}
}
@article{Fedele2011,
abstract = {The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. An accurate Fourier-type spectral scheme is used to solve for the wave dynamics and validate the new conservation laws, which are satisfied up to machine precision. Traveling waves are numerically constructed using the Petviashvili method. It is shown that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.},
archivePrefix = {arXiv},
arxivId = {1110.4083},
author = {Fedele, F. and Dutykh, D.},
doi = {10.1134/S0021364011240039},
eprint = {1110.4083},
journal = {JETP Lett.},
keywords = {Classical Physics,Pattern Formation and Solitons},
month = {oct},
number = {12},
pages = {840--844},
title = {{Hamiltonian form and solitary waves of the spatial Dysthe equations}},
volume = {94},
year = {2011}
}
@article{Fedele2012a,
abstract = {We compute numerical traveling wave solutions to a compact version of the Zakharov equation for unidirectional deep-water waves recently derived by Dyachenko and Zakharov (2011). Furthermore, by means of an accurate Fourier-type spectral scheme we find that solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation.},
author = {Fedele, F. and Dutykh, D.},
doi = {10.1134/S0021364012120041},
issn = {0021-3640},
journal = {JETP Letters},
month = {aug},
number = {12},
pages = {622--625},
title = {{Solitary wave interaction in a compact equation for deep-water gravity waves}},
volume = {95},
year = {2012}
}
@article{Fedele2012,
abstract = {Dyachenko {\&} Zakharov (J. Expl Theor. Phys. Lett., vol. 93, 2011, pp. 701–705) recently derived a compact form of the well-known Zakharov integro-differential equation for the third-order Hamiltonian dynamics of a potential flow of an incompressible, infinitely deep fluid with a free surface. Special travelling wave solutions of this compact equation are numerically constructed using the Petviashvili method. Their stability properties are also investigated. In particular, unstable travelling waves with wedge-type singularities, namely peakons, are numerically discovered. To gain insight into the properties of these singular solutions, we also consider the academic case of a perturbed version of the compact equation, for which analytical peakons with exponential shape are derived. Finally, by means of an accurate Fourier-type spectral scheme it is found that smooth solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation.},
author = {Fedele, F. and Dutykh, D.},
journal = {J. Fluid Mech},
pages = {646--660},
title = {{Special solutions to a compact equation for deep-water gravity waves}},
volume = {712},
year = {2012}
}
@article{Fedele2011a,
abstract = {The spatial version of the fourth-order Dysthe equations describe the evolution of the wave envelope and potential of the wave-induced mean flow in deep waters. The hidden Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new canonical form of the evolution equations. A highly accurate Fourier-type spectral scheme is developed to solve for the equations and validate the new conservation laws, which are satisfied up to machine precision. Further, traveling waves are numerically investigated using the Petviashvili method. It is found that their collision appears inelastic, suggesting the non-integrability of the Dysthe equations.},
archivePrefix = {arXiv},
arxivId = {1110.3605},
author = {Fedele, F. and Dutykh, D.},
eprint = {1110.3605},
journal = {Research report (arxiv: 1110.3605)},
pages = {1--17},
title = {{Hamiltonian description and traveling waves of the spatial Dysthe equations}},
url = {http://hal.archives-ouvertes.fr/hal-00632862/},
year = {2012}
}
@article{Fedele2012c,
abstract = {We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (2012). The KdV dynamics of a perturbation is also investigated by means of an high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (2008). The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.},
author = {Fedele, F. and Dutykh, D.},
doi = {10.1209/0295-5075/101/34003},
issn = {0295-5075},
journal = {EPL},
month = {feb},
number = {3},
pages = {34003},
title = {{Vortexons in axisymmetric Poiseuille pipe flows}},
volume = {101},
year = {2013}
}
@article{Fedele2005,
author = {Fedele, F. and Hitt, D. L. and Prabhu, R. D.},
doi = {10.1016/j.euromechflu.2004.07.005},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
keywords = {Energy growth,Galerkin projection,Non-normality,Orr-Sommerfeld operator,Pulsatile pipe flow,Stability,Vortex tubes},
month = {mar},
number = {2},
pages = {237--254},
title = {{Revisiting the stability of pulsatile pipe flow}},
volume = {24},
year = {2005}
}
@article{Fedele2009,
author = {Fedele, F. and Tayfun, M. A.},
doi = {10.1017/S0022112008004424},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {jan},
pages = {221--239},
title = {{On nonlinear wave groups and crest statistics}},
volume = {620},
year = {2009}
}
@article{Fedele2008,
author = {Fedele, F. and Tayfun, M. A.},
journal = {J. Fluid Mech},
pages = {221--239},
title = {{On nonlinear wave groups and crest statistics}},
volume = {620},
year = {2008}
}
@book{Fedorenko1994,
address = {Moscow},
author = {Fedorenko, R. P.},
isbn = {5-7417-0002-0},
pages = {528},
publisher = {MIPT Press},
title = {{Introduction to Computational Physics}},
year = {1994}
}
@article{Fedorov1995,
abstract = {The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to braking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60{\%}, with respect to a comparable wave in de absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.},
author = {Fedorov, A. V. and Melville, W. K.},
doi = {10.1175/1520-0485(1995)025<2518:PABONK>2.0.CO;2},
issn = {0022-3670},
journal = {J. Phys. Oceanogr.},
month = {nov},
number = {11},
pages = {2518--2531},
title = {{Propagation and Breaking of Nonlinear Kelvin Waves}},
url = {http://journals.ametsoc.org/doi/abs/10.1175/1520-0485(1995)025<2518:PABONK>2.0.CO;2},
volume = {25},
year = {1995}
}
@article{Fedorov2000,
abstract = {Properties of internal wave fronts or Kelvin fronts travelling eastward in the equatorial waveguide are studied, motivated by recent studies on coastal Kelvin waves and jumps and new data on equatorial Kelvin waves. It has been recognized for some time that nonlinear equatorial Kelvin waves can steepen and break, forming a broken wave of depression, or front, propagating eastward. The three-dimensional structure of the wave field associated with such a front is considered. As for linear Kelvin waves, the front is symmetrical with respect to the equator. Sufficiently far away from the front, the wave profile is Gaussian in the meridional direction, with the equatorial Rossby radius of deformation being its decay scale. Due to nonlinearity, the phase speed of the front is greater than that of linear Kelvin waves, resulting in a supercritical flow. This leads to the resonant generation of equatorially trapped gravity-inertial (or Poincar{\'{e}}) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincar{\'{e}} waves are generated, with their wavelength determined by the amplitude of the front. Finally, the propagation of a Kelvin front gives rise to a nonzero poleward mass transport above the thermocline, in consequence of which there is a poleward heat flux.},
author = {Fedorov, A. V. and Melville, W. K.},
doi = {10.1175/1520-0485(2000)030<1692:KFOTET>2.0.CO;2},
issn = {0022-3670},
journal = {J. Phys. Oceanogr.},
month = {jul},
number = {7},
pages = {1692--1705},
title = {{Kelvin Fronts on the Equatorial Thermocline}},
url = {http://journals.ametsoc.org/doi/abs/10.1175/1520-0485(2000)030<1692:KFOTET>2.0.CO;2},
volume = {30},
year = {2000}
}
@article{Fedotova1996,
author = {Fedotova, Z. I. and Karepova, E. D.},
doi = {10.1515/rnam.1996.11.3.183},
issn = {0927-6467},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {3},
pages = {183--204},
title = {{Variational principle for approximate models of wave hydrodynamics}},
url = {http://www.degruyter.com/view/j/rnam.1996.11.issue-3/rnam.1996.11.3.183/rnam.1996.11.3.183.xml},
volume = {11},
year = {1996}
}
@article{Fedotova2009,
author = {Fedotova, Z. I. and Khakimzyanov, G. S.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
pages = {31--42},
title = {{Shallow water equations on a movable bottom}},
volume = {24(1)},
year = {2009}
}
@article{Fedotova2014a,
author = {Fedotova, Z. I. and Khakimzyanov, G. S.},
journal = {J. Appl. Mech. Tech. Phys.},
number = {3},
pages = {404--416},
title = {{Nonlinear dispersive shallow water equations on a rotating sphere and conservation laws}},
volume = {55},
year = {2014}
}
@article{Fedotova2011,
author = {Fedotova, Z. I. and Khakimzyanov, G. S.},
journal = {J. Appl. Mech. Tech. Phys.},
number = {6},
pages = {865--876},
title = {{Fully nonlinear dispersion model for shallow water equations on a rotating sphere}},
volume = {52},
year = {2011}
}
@article{Fedotova2014,
abstract = {A new derivation of completely nonlinear weakly-dispersive shallow water equations is given without assumption of flow potentiality. Boussinesq type equations are derived for weakly nonlinear waves above a moving bottom. It is established that the total energy balance condition holds for all nonlinear dispersion models obtained here.},
author = {Fedotova, Z. I. and Khakimzyanov, G. S. and Dutykh, D.},
doi = {10.1515/rnam-2014-0013},
issn = {1569-3988},
journal = {Russ. J. Numer. Anal. Math. Modelling},
month = {jan},
number = {3},
pages = {167--178},
title = {{Energy equation for certain approximate models of long-wave hydrodynamics}},
url = {http://www.degruyter.com/view/j/rnam.2014.29.issue-3/rnam-2014-0013/rnam-2014-0013.xml},
volume = {29},
year = {2014}
}
@article{Feir1967,
author = {Feir, J. E.},
journal = {Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences},
number = {1456},
pages = {54--58},
title = {{Discussion: Some Results From Wave Pulse Experiments}},
volume = {299},
year = {1967}
}
@article{Feireisl2007,
author = {Feireisl, E. and Vasseur, A.},
journal = {Preprint},
pages = {1--31},
title = {{New perspectives in fluid dynamics: Mathematical analysis of a model proposed by Howard Brenner}},
year = {2007}
}
@book{FEMA2000,
author = {FEMA},
publisher = {Federal Emergency Management Agency},
title = {{FEMA Coastal Construction Manual}},
year = {2000}
}
@article{Fenton1972,
author = {Fenton, J.},
journal = {J. Fluid Mech},
pages = {257--271},
title = {{A ninth-order solution for the solitary wave}},
volume = {53(2)},
year = {1972}
}
@article{Fenton1999,
author = {Fenton, J. D.},
journal = {Adv. Coastal Ocean Engng},
pages = {241--324},
title = {{Numerical methods for nonlinear waves}},
volume = {5},
year = {1999}
}
@article{Fenton1982,
abstract = {A numerical method is developed for solution of the full nonlinear equations governing irrotational flow with a free surface and variable bed topography. It is applied to the unsteady motion of non-breaking water waves of arbitrary magnitude over a horizontal bed. All horizontal variation is approximated by truncated Fourier series. This and finite-difference representation of the time variation are the only necessary approximations. Although the method loses accuracy if the waves become sharp-crested at any stage, when applied to non-breaking waves the method is capable of high accuracy. The interaction of one solitary wave overtaking another was studied using the Fourier method. Results support experimental evidence for the applicability of the Korteweg-de Vries equation to this problem since the waves during interaction are long and low. However, some deviations from the theoretical predictions were observed - the overtaking high wave grew significantly at the expense of the low wave, and the predicted phase shift was found to be only roughly described by theory. A mechanism is suggested for all such solitary-wave interactions during which the high and fast rear wave passes fluid forward to the front wave, exchanging identities while the two waves have only partly coalesced; this explains the observed forward phase shift of the high wave. For solitary waves travelling in opposite directions, the interaction is quite different in that the amplitude of motion during interaction is large. A number of such interactions were studied using the Fourier method, and the waves after interaction were also found to be significantly modified - they were not steady waves of translation. There was a change of wave height and propagation speed, shown by the present results to be proportional to the cube of the initial wave height but not contained in third-order theoretical results. When the interaction is interpreted as a solitary wave being reflected by a wall, third-order theory is shown to provide excellent results for the maximum run-up at the wall, but to be in error in the phase change of the wave after reflection. In fact, it is shown that the spatial phase change depends strongly on the place at which it is measured because the reflected wave travels with a different speed. In view of this, it is suggested that the apparent time phase shift at the wall is the least-ambiguous measure of the change.},
author = {Fenton, J. D. and Rienecker, M. M.},
doi = {10.1017/S0022112082001141},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {411--443},
title = {{A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112082001141},
volume = {118},
year = {1982}
}
@article{Fer2002b,
author = {Fer, I. and Lemmin, U. and Thorpe, S. A.},
journal = {Limnology},
keywords = {limnology,ocean,oceanography},
number = {2},
pages = {576--580},
title = {{Contribution of entrainment and vertical plumes to the winter cascading of cold shelf waters in a deep lake.}},
url = {http://hdl.handle.net/10242/38186},
volume = {47},
year = {2002}
}
@article{Fer2002a,
abstract = {The dissipation rate of turbulent kinetic energy per unit mass, , vertical eddy diffusivity, Kz, and the rate of dissipation of temperature variance, x, are estimated over the sloping sides of Lake Geneva both far from and near the bed, using temperature data from horizontal tracks of a submarine during periods of winter cooling. The estimated values are about one order of magnitude greater near the slope than those distant from it. The mean dissipation rate per unit mass averaged over the epilimnion varies between O(10-10) m2 s-3 in calm weather to O(10-8) m2 s-3 in winds of 8 m s-1, for surface buoyancy fluxes of 6 X 10-9 m2 s-3 and 1.1 X 10-8 m2 s-3, whereas near the slope has an average value of 3 X 10-8 m2 s-3. The relation between Kz and N-2 (where N is the buoyancy frequency) is examined. Values of the mixing efficiency, = N-2Kz-1, of 0.15 0.1 and 0.16 0.1 21 z are obtained in the upper 10-m layer for calm and windy conditions, respectively. Near the slope, is found to be 0.22 0.2, slightly larger than in surface layers under windy conditions. Different mixing mechanisms in different regions, near the slope and in the surface waters of the epilimnion and relatively calm deeper layers, can be identified in the diagram of overturn Froude number versus overturn Reynolds number. Mixing near the slope in the epilimnion appears to be related to the gravitational winter cascading of cold water down the sloping sides of the lake.},
author = {Fer, I. and Lemmin, U. and Thorpe, S. A.},
journal = {Limonology And Oceanography},
keywords = {limnology,ocean,oceanography},
number = {2},
pages = {535--544},
title = {{Observations of mixing near the sides of a deep lake in winter.}},
url = {http://eprints.soton.ac.uk/6054/},
volume = {47},
year = {2002}
}
@article{Fer2002,
author = {Fer, I. and Lemmin, U. and Thorpe, S. A.},
doi = {10.1029/2001JC000828},
issn = {0148-0227},
journal = {Journal of Geophysical Research},
keywords = {cascade,convective processes,dense water,gravity current,lake,shelf},
number = {C6},
pages = {16},
title = {{Winter cascading of cold water in Lake Geneva}},
url = {http://www.agu.org/pubs/crossref/2002/2001JC000828.shtml},
volume = {107},
year = {2002}
}
@article{Fernandes2006,
abstract = {We survey the relationship between symplectic and Poisson geometries, emphasizing the construction of the symplectic groupoid associated with a Poisson manifold.},
author = {Fernandes, R. L.},
journal = {CIM Bulletin},
pages = {15--19},
title = {{Poisson vs. Symplectic Geometry}},
volume = {20},
year = {2006}
}
@article{Fernandez-Nieto2007,
abstract = {In this paper, we present a new two-layer model of Savage-Hutter type to study submarine avalanches. A layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e.g. water). The model is derived in a system of local coordinates following a non-erodible bottom and takes into account its curvature. We prove that the model verifies an entropy inequality, preserves water at rest for a sediment layer and their solutions can be seen as particular solutions of incompressible Euler equations under hydrostatic assumptions. Buoyancy effects and the centripetal acceleration of the grain movement due to the curvature of the bottom are considered in the definition of the Coulomb term. We propose a two-step Roe type solver to discretize the presented model. It exactly preserves water at rest and no movement of the sediment layer, when its angle is smaller than the angle of repose, and up to second order all stationary solutions. Finally, some numerical tests are performed by simulating submarine and sub-aerial avalanches as well as the generated tsunami.},
author = {Fernandez-Nieto, E. D. and Bouchut, F. and Bresch, D. and Castro-Diaz, M. J. and Mangeney, A.},
journal = {J. Comput. Phys.},
number = {16},
pages = {7720--7754},
title = {{A new Savage-Hutter type models for submarine avalanches and generated tsunami}},
volume = {227},
year = {2008}
}
@article{Ferreira1998,
abstract = {This paper deals with the supraconvergence of elliptic finite difference schemes on variable grids for second order elliptic boundary value problems subject to Dirichlet boundary conditions in two-dimensional domains. The assumptions in this paper are less restrictive than those considered so far in the literature allowing also variable coefficients, mixed derivatives and polygonal domains. The nonequidistant grids we consider are more flexible than merely rectangular ones such that, e.g., local grid refinements are covered. The results also develop a close relation between supraconvergent finite difference schemes and piecewise linear finite element methods. It turns out that the finite difference equation is a certain nonstandard finite element scheme on triangular girds combined with a special form of quadrature. In extension to what is known for the standard finite element scheme, here also the gradient is shown to be convergent of second order, and so our result is also a superconvergence result for the underlying finite element method.},
author = {Ferreira, J. A. and Grigorieff, R. D.},
doi = {10.1016/S0168-9274(98)00048-8},
issn = {01689274},
journal = {Appl. Numer. Math.},
keywords = {Finite difference scheme,Nonuniform grids,Stability,Superconvergence,Supraconvergence},
month = {oct},
number = {2-4},
pages = {275--292},
title = {{On the supraconvergence of elliptic finite difference schemes}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0168927498000488},
volume = {28},
year = {1998}
}
@article{FL,
author = {Fetecau, R. and Levy, D.},
journal = {Comm. Math. Sci.},
number = {2},
pages = {159--170},
title = {{Aproximate model equations for water waves}},
volume = {3},
year = {2005}
}
@book{Feynman1998,
abstract = {This classic work presents the main results and calculational procedures of quantum electrodynamics in a simple and straightforward way. Designed for the student of experimental physics who does not intend to take more advanced graduate courses in theoretical physics, the material consists of notes on the third of a three-semester course given at the California Institute of Technology.},
author = {Feynman, R.},
isbn = {978-0201360752},
pages = {208},
publisher = {Westview Press},
title = {{Quantum Electrodynamics}},
year = {1998}
}
@book{Feynman2005,
author = {Feynman, R. and Leighton, R. B. and Sands, M.},
edition = {2},
isbn = {978-0805390469},
pages = {544},
publisher = {Addison Wesley},
title = {{The Feynman Lectures on Physics, Vol. 1: Mainly Mechanics, Radiation, and Heat}},
year = {2005}
}
@article{Fick1855,
author = {Fick, A.},
journal = {Phil. Mag.},
pages = {30},
title = {{No Title}},
volume = {10},
year = {1855}
}
@article{Fick1855a,
author = {Fick, A.},
journal = {Poggendorff's Annel. Physik},
pages = {59},
title = {{No Title}},
volume = {94},
year = {1855}
}
@book{Fickett2001,
abstract = {Comprehensive review of detonation explores the "simple theory" and experimental tests of the theory; flow in a reactive medium; steady detonation; the nonsteady solution; and the structure of the detonation front. Many simple cases are worked out for illustration.},
author = {Fickett, W. and Davis, W. C.},
booktitle = {Materials Research},
file = {:home/dds/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Fickett, Davis - 2001 - Detonation Theory and Experiment(2).pdf:pdf},
isbn = {0486414566},
pages = {386},
publisher = {University of California Press},
title = {{Detonation: Theory and Experiment}},
url = {http://www.librarything.com/work/5606506/book/31887454},
volume = {297},
year = {2001}
}
@article{filon,
author = {Filon, L. N. G.},
journal = {Proceedings of the Royal Society of Edinburgh},
pages = {38--47},
title = {{On a Quadrature Formula for Trigonometric Integrals}},
volume = {49},
year = {1928}
}
@article{Fine2005,
abstract = {On November18, 1929, a M=7.2 earthquake occurred at the southern edge of the GrandBanks, 280 km south of Newfoundland. The earthquake triggered a large submarine slope failure (200 km3), which was transformed into a turbidity current carrying mud and sand eastward up to 1000 km at estimated speeds of about 60-100 km/h, breaking 12 telegraph cables. The tsunamigenerated by this failure killed 28 people, making it the most catastrophic tsunami in Canadian history. Tsunami waves also were observed along other parts of the Atlantic coast of Canada and the United States. Waves crossing the Atlantic were recorded on the coasts of Portugal and the Azores Islands. Tsunami waves had amplitudes of 3-8 m and runup of up to 13 m along the coast of the Burin Peninsula (Newfoundland). To simulate the slide-generatedtsunami from this event, our initial analysis uses a shallow-water model; the slide was assumed to be a viscous, incompressible fluid layer; water was inviscid and incompressible. The preliminary results of the numerical modeling are encouraging, with computed and observed tsunami arrival times in reasonable agreement.},
author = {Fine, I. V. and Rabinovich, A. B. and Bornhold, B. D. and Thomson, R. E. and Kulikov, E. A.},
doi = {10.1016/j.margeo.2004.11.007},
issn = {00253227},
journal = {Marine Geology},
keywords = {1929 Grand Banks earthquake,numerical modeling,submarine landslide,tsunami},
month = {feb},
number = {1-2},
pages = {45--57},
title = {{The Grand Banks landslide-generated tsunami of November 18, 1929: preliminary analysis and numerical modeling}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S002532270400324X},
volume = {215},
year = {2005}
}
@incollection{Fine2003,
abstract = {Recent catastrophic tsunamis at Flores Island, Indonesia (1992), Skagway, Alaska (1994), Papua New Guinea (1998), and Izmit, Turkey (1999) have significantly increased scientific interest in landslides and slide-generated tsunamis. Theoretical investigations and laboratory modeling further indicate that purely submarine landslides are ineffective at tsunami generation compared with subaerial slides. In the present study, we undertook several numerical experiments to examine the influence of the subaerial component of slides on surface wave generation and to compare the tsunami generation efficiency of viscous and rigid-body slide models. We found that a rigid-body slide produces much higher tsunami waves than a viscous (liquid) slide. The maximum wave height and energy of generated surface waves were found to depend on various slide parameters and factors, including slide volume, density, position, and slope angle. For a rigid-body slide, the higher the initial slide above sea level, the higher the generated waves. For a viscous slide, there is an optimal slide position (elevation) which produces the largest waves. An increase in slide volume, density, and slope angle always increases the energy of the generated waves. The added volume associated with a subaerial slide entering the water is one of the reasons that subaerial slides are much more effective tsunami generators than submarine slides. The critical parameter determining the generation of surface waves is the Froude number, Fr (the ratio between slide and wave speeds). The most efficient generation occurs near resonance when Fr = 1.0. For purely submarine slides with 2.0 g cm-3, the Froude number is always less than unity and resonance coupling of slides and surface waves is physically impossible. For subaerial slides there is always a resonant point (in time and space) where Fr = 1.0 for which there is a significant transfer of energy from a slide into surface waves. This resonant effect is the second reason that subaerial slides are much more important for tsunami generation than submarine slides.},
author = {Fine, I. V. and Rabinovich, A. B. and Thomson, R. E. and Kulikov, E. A.},
booktitle = {Submarine Landslides and Tsunamis},
pages = {69--88},
publisher = {Kluwer Academic Publishers},
title = {{Numerical modeling of tsunami generation by submarine and subaerial landslides}},
year = {2003}
}
@article{Flaschka1980,
author = {Flaschka, H. and Forest, M. G. and McLaughlin, D. W.},
doi = {10.1002/cpa.3160330605},
issn = {00103640},
journal = {Comm. Pure Appl. Math.},
month = {nov},
number = {6},
pages = {739--784},
title = {{Multiphase averaging and the inverse spectral solution of the Korteweg-de Vries equation}},
url = {http://doi.wiley.com/10.1002/cpa.3160330605},
volume = {33},
year = {1980}
}
@article{Foche,
author = {Fochesato, C. and Dias, F.},
journal = {Proc. R. Soc. A},
month = {sep},
number = {2073},
pages = {2715--2735},
title = {{A fast method for nonlinear three-dimensional free-surface waves}},
volume = {462},
year = {2006}
}
@article{Fochesato2005a,
abstract = {A variety of problems in nonlinear science can be modelled by a system of two coupled long wave equations. In such systems, a resonance between a solitary wave of one of the two equations and a co-propagating periodic wave of the other equation can occur. The resulting wave is a generalized solitary wave, with non-vanishing oscillatory tails. It is shown that in the case of a ‘table-top’ solitary wave, which is solution to an extended Korteweg-de Vries equation with a cubic nonlinearity, the generalized solitary waves do not behave like standard sech2 generalized solitary waves. In particular, it is shown that the oscillations can vanish in the tails or in the central core, but not in both simultaneously. A simplified model is introduced, which allows a better understanding of these stationary long wave solutions and the occurrence of embedded solitons.},
author = {Fochesato, C. and Dias, F. and Grimshaw, R.},
doi = {10.1016/j.physd.2005.07.010},
issn = {01672789},
journal = {Phys. D},
month = {oct},
number = {1-2},
pages = {96--117},
title = {{Generalized solitary waves and fronts in coupled Korteweg-de Vries systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S016727890500309X},
volume = {210},
year = {2005}
}
@article{Fochesato2005,
author = {Fochesato, C. and Dias, F. and Grimshaw, R.},
journal = {Physica D: Nonlinear Phenomena},
month = {oct},
pages = {96--117},
title = {{Generalized solitary waves and fronts in coupled Korteweg-de Vries systems}},
volume = {210},
year = {2005}
}
@article{Fochesato2007,
author = {Fochesato, C. and Grilli, S. and Dias, F.},
doi = {10.1016/j.wavemoti.2007.01.003},
journal = {Wave Motion},
number = {5},
pages = {395--416},
title = {{Numerical modeling of extreme rogue waves generated by directional energy focusing}},
volume = {44},
year = {2007}
}
@article{Fock1926,
author = {Fock, V.},
doi = {10.1007/BF01321989},
issn = {14346001},
journal = {Z. Phys.},
number = {2-3},
pages = {226--232},
title = {{On the invariant form of the wave equation and the equations of motion for a charged point mass}},
volume = {39},
year = {1926}
}
@article{Foias2002,
author = {Foias, C. and Holm, D. D. and Titi, E. S.},
doi = {10.1023/A:1012984210582},
journal = {J. Dynam. Diff. Eqns.},
number = {1},
pages = {1--35},
title = {{The Three Dimensional Viscous Camassa-Holm Equations, and Their Relation to the Navier-Stokes Equations and Turbulence Theory}},
volume = {14},
year = {2002}
}
@article{Foias2001,
author = {Foias, C. and Holm, D. D. and Titi, E. S.},
doi = {10.1016/S0167-2789(01)00191-9},
issn = {01672789},
journal = {Phys. D},
month = {may},
pages = {505--519},
title = {{The Navier-Stokes-alpha model of fluid turbulence}},
volume = {152-153},
year = {2001}
}
@article{FP,
author = {Fokas, A. S. and Pelloni, B.},
journal = {Math. Phys. Anal. Geom.},
pages = {59--96},
title = {{Boundary value problems for Boussinesq type systems}},
volume = {8},
year = {2005}
}
@book{Folland1995,
address = {Princeton},
author = {Folland, G. B.},
edition = {2},
isbn = {9780691043616},
pages = {336},
publisher = {Princeton University Press},
title = {{Introduction to Partial Differential Equations}},
year = {1995}
}
@book{MATLAB2012,
address = {Tokyo, Japan},
author = {for MATLAB, Multiprecision Computing Toolbox},
editor = {Holodoborodko, P},
publisher = {Advanpix LLC.},
title = {v3.3.8.2611},
year = {2012}
}
@book{MATLAB2012,
address = {Tokyo, Japan},
author = {for MATLAB, Multiprecision Computing Toolbox},
editor = {Holodoborodko, P},
publisher = {Advanpix LLC.},
title = {v3.3.8.2611},
year = {2012}
}
@article{Ford1987,
author = {Ford, W. F. and Sidi, A.},
journal = {SIAM Journal on Numerical Analysis},
pages = {1212--1232},
title = {{An Algorithm for a Generalization of the Richardson Extrapolation Process}},
volume = {24(5)},
year = {1987}
}
@book{Fornberg1996,
address = {Cambridge},
author = {Fornberg, B.},
pages = {242},
publisher = {Cambridge University Press},
title = {{A practical guide to pseudospectral methods}},
year = {1996}
}
@book{FMM,
author = {Forsythe, G. E. and Malcolm, M. A. and Moler, C. B.},
editor = {{Paramus NJ}, U S A},
publisher = {Springer},
title = {{Computer Methods for Mathematical Computations}},
year = {1977}
}
@book{Fourier1822,
author = {Fourier, J.},
publisher = {Didot, Paris},
title = {{Th{\'{e}}orie analytique de la chaleur}},
year = {1822}
}
@article{Fox1968,
author = {Fox, J. A.},
doi = {10.1063/1.1691740},
issn = {00319171},
journal = {Phys. Fluids},
number = {1},
pages = {1},
title = {{Experimental Investigation of the Stability of Hagen-Poiseuille Flow}},
volume = {11},
year = {1968}
}
@article{Fraccarollo2002,
author = {Fraccarollo, L. and Capart, H.},
journal = {J. Fluid Mech.},
pages = {183--228},
title = {{Riemann wave description of erosional dam-break flows}},
volume = {461},
year = {2002}
}
@article{Fraccarollo1995,
author = {Fraccarollo, L. and Toro, E. F.},
journal = {Journal of Hydraulic Research},
pages = {843--864},
title = {{Experimental and numerical assessment of the shallow water model for two-dimensional dam break type problems}},
volume = {33},
year = {1995}
}
@article{Franchi2001,
author = {Franchi, F. and Straughan, B.},
journal = {Adv. in Water Ressources},
pages = {585--594},
title = {{A comparison of the Graffi and Kazhikhov-Smagulov models for heavy pollution instability}},
volume = {24},
year = {2001}
}
@article{Francius2001,
abstract = {Here we present an investigation of the wave dynamics in nonlinear dispersive system, allowing two types of solitary solutions due to the dispersionless behavior of very long and very short waves. This nonintegrable system presents different types of interaction of solitary waves with generation of dispersive tails and other solitary waves. The problem of the evolution of initial impulse and sinusoidal disturbances is herein studied. It is shown that an initial disturbance can create solitons of different types. A case when initially one-signed disturbance produces solitary waves of different polarities is presented.},
author = {Francius, M. and Pelinovsky, E. N. and Slunyaev, A. V.},
journal = {Phys. Lett. A},
keywords = {Nonintegrable systems,Solitons,Wave evolution},
number = {1-2},
pages = {53--57},
title = {{Wave dynamics in nonlinear media with two dispersionless limits for long and short waves}},
volume = {280},
year = {2001}
}
@article{Freeman1970,
abstract = {An equation for waves on the surface of a flow with shear is deduced and shown to reduce by suitable scaling to the classical equation of Korteweg $\backslash${\&} de Vries, which describes such motions on a stationary flow. For steady flows the corresponding theory of cnoidal waves is obtained and the results of Benjamin (1962) for a solitary wave recovered.},
author = {Freeman, N. C. and Johnson, R. S.},
doi = {10.1017/S0022112070001349},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {02},
pages = {401--409},
title = {{Shallow water waves on shear flows}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112070001349},
volume = {42},
year = {1970}
}
@article{Freund1976,
author = {Freund, L. B. and Barnett, D. M.},
journal = {Bull. Seism. Soc. Am.},
pages = {667--675},
title = {{A two-dimensional analysis of surface deformation due to dip-slip faulting}},
volume = {66},
year = {1976}
}
@article{Friedland1998a,
abstract = {Adiabatic passage of weakly coupled nonlinear waves with space-time varying parameters through resonance is investigated. Slow evolution equations describing this wave interaction problem are obtained via Whitham’s averaged variational principle. Autoresonant solutions of these equations are found and, locally, comprise adiabatically varying quasiuniform wave train solutions of the decoupled problem. At the same time, the waves are globally phase locked in an extended region of space-time despite the variation of the system’s parameters. Conditions for entering and sustaining this multidimensional autoresonance are the internal resonant excitation of one of the coupled waves and sufficient adiabaticity and nonlinearity of the problem. These conditions have their origin in a similar adiabatic resonance problem in nonlinear dynamics. The theory is illustrated by an example of the autoresonance in a system of coupled sine-Gordon equations.},
author = {Friedland, L.},
doi = {10.1103/PhysRevE.57.3494},
issn = {1063-651X},
journal = {Physical Review E},
month = {mar},
number = {3},
pages = {3494--3501},
title = {{Autoresonance of coupled nonlinear waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.57.3494},
volume = {57},
year = {1998}
}
@article{Friedland1998,
abstract = {Resonant driving of the nonlinear Schr{\"{o}}dinger (NLS) equation by small-amplitude oscillations or waves with adiabatically varying frequencies and/or wave vectors is proposed as a method of excitation and control of wave-type solutions of the system. The idea is based on the autoresonance phenomenon, i.e., a continuous nonlinear phase locking between the solutions of the NLS equation and the driving oscillations, despite the space-time variation of the parameters of the driver. We illustrate this phenomenon in the examples of excitation of plane and standing waves in the driven NLS system, where one varies the driver parameters in time or space. The relation of autoresonance in these applications to the corresponding problems in nonlinear dynamics is outlined. One of these dynamical problems comprises a different type of multifrequency autoresonance in a Hamiltonian system with two degrees of freedom. The averaged variational principle is used in studying the problem of autoresonant excitation and stabilization of more general cnoidal solutions of the NLS equation.},
author = {Friedland, L.},
doi = {10.1103/PhysRevE.58.3865},
issn = {1063-651X},
journal = {Physical Review E},
month = {sep},
number = {3},
pages = {3865--3875},
title = {{Autoresonant solutions of the nonlinear Schr{\"{o}}dinger equation}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.58.3865},
volume = {58},
year = {1998}
}
@article{Friedland2003,
abstract = {Large amplitude multiphase solutions of the periodic Korteweg-de Vries equation are excited and controlled by a small forcing. The approach uses passage through an ensemble of resonances and subsequent multiphase self-locking of the system with eikonal-type perturbations. The synchronization of each phase in the Korteweg–de Vries wave is robust, provided the corresponding driving amplitude exceeds a threshold.},
author = {Friedland, L. and Shagalov, A.},
doi = {10.1103/PhysRevLett.90.074101},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {feb},
number = {7},
pages = {74101},
title = {{Emergence and Control of Multiphase Nonlinear Waves by Synchronization}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.90.074101},
volume = {90},
year = {2003}
}
@inproceedings{FFTWgen99,
author = {Frigo, M.},
booktitle = {Proc. 1999 ACM SIGPLAN Conf. on Programming Language Design and Implementation},
month = {may},
number = {5},
pages = {169--180},
publisher = {ACM},
title = {{A fast Fourier transform compiler}},
volume = {34},
year = {1999}
}
@article{Frigo2005,
abstract = {FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.},
author = {Frigo, M. and Johnson, S. G.},
doi = {10.1109/JPROC.2004.840301},
file = {:home/dds/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Frigo, Johnson - 2005 - The Design and Implementation of FFTW3(2).pdf:pdf},
issn = {00189219},
journal = {Proceedings of the IEEE},
number = {2},
pages = {216--231},
publisher = {IEEE},
title = {{The Design and Implementation of FFTW3}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=1386650},
volume = {93},
year = {2005}
}
@inproceedings{FFTW98,
author = {Frigo, M. and Johnson, S. G.},
booktitle = {Proc. 1998 IEEE Intl. Conf. Acoustics Speech and Signal Processing},
pages = {1381--1384},
publisher = {IEEE},
title = {{FFTW: An adaptive software architecture for the FFT}},
volume = {3},
year = {1998}
}
@book{Frisch1995,
abstract = {Written five centuries after the first studies of Leonardo da Vinci and half a century after A.N. Kolmogorov's first attempt to predict the properties of flow, this textbook presents a modern account of turbulence, one of the greatest challenges in physics. "Fully developed turbulence" is ubiquitous in both cosmic and natural environments, in engineering applications and in everyday life. Elementary presentations of dynamical systems ideas, probabilistic methods (including the theory of large deviations) and fractal geometry make this a self-contained textbook. This is the first book on turbulence to use modern ideas from chaos and symmetry breaking. The book will appeal to first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, as well as professional scientists and engineers.},
address = {Cambridge},
author = {Frisch, U.},
booktitle = {Journal of Fluid Mechanics},
doi = {10.1017/S0022112096210791},
issn = {0022-1120},
month = {apr},
number = {-1},
pages = {296},
publisher = {Cambridge University Press},
title = {{Turbulence: The Legacy of A. N. Kolmogorov}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112096210791},
volume = {317},
year = {1995}
}
@article{Fritz2007,
abstract = {The 17 July 2006 magnitude Mw 7.8 earthquake off the south coast of western Java, Indonesia, generated a tsunami that effected over 300 km of coastline and killed more than 600 people, with locally focused runup heights exceeding 20 m. This slow earthquake was hardly felt on Java, and wind waves breaking masked any preceding withdrawal of the water from the shoreline, making this tsunami difficult to detect before impact. An International Tsunami Survey Team was deployed within one week and the investigation covered more than 600 km of coastline. Measured tsunami heights and run-up distributions were uniform at 5 to 7 m along 200 km of coast; however there was a pronounced peak on the south coast of Nusa Kambangan, where the tsunami impact carved a sharp trimline in a forest at elevations up to 21 m and 1 km inland. Local flow depth exceeded 8 m along the elevated coastal plain between the beach and the hill slope. We infer that the focused tsunami and runup heights on the island suggest a possible local submarine slump or mass movement.},
author = {Fritz, H. M. and Kongko, W. and Moore, A. and McAdoo, B. and Goff, J. and Harbitz, C. and Uslu, B. and Kalligeris, N. and Suteja, D. and Kalsum, K. and Titov, V. V. and Gusman, A. and Latief, H. and Santoso, E. and Sujoko, S. and Djulkarnaen, D. and Sunendar, H. and Synolakis, C. E.},
journal = {Geophys. Res. Lett.},
pages = {L12602},
title = {{Extreme runup from the 17 July 2006 Java tsunami}},
volume = {34},
year = {2007}
}
@article{Fritz2011,
author = {Fritz, H. M. and Petroff, C. M. and Catal{\'{a}}n, P. A. and Cienfuegos, R. and Winckler, P. and Kalligeris, N. and Weiss, R. and Barrientos, S. E. and Meneses, G. and Valderas-Bermejo, C. and Ebeling, C. and Papadopoulos, A. and Contreras, M. and Almar, R. and Dominguez, J. C. and Synolakis, C. E.},
doi = {10.1007/s00024-011-0283-5},
issn = {0033-4553},
journal = {Pure Appl. Geophys.},
month = {mar},
number = {11},
pages = {1989--2010},
title = {{Field Survey of the 27 February 2010 Chile Tsunami}},
url = {http://www.springerlink.com/index/10.1007/s00024-011-0283-5},
volume = {168},
year = {2011}
}
@article{Frougny2005,
author = {Frougny, C. and Vuillon, L.},
journal = {Journal of Automata, Languages and Combinatorics},
number = {4},
pages = {465--482},
title = {{Coding of Two-Dimensional Constraints of Finite Type by Substitutions}},
volume = {10},
year = {2005}
}
@article{Fructus2005,
author = {Fructus, D. and Clamond, D. and Kristiansen, O. and Grue, J.},
journal = {J. Comput. Phys.},
pages = {665--685},
title = {{An efficient model for threedimensional surface wave simulations. Part I: Free space problems}},
volume = {205},
year = {2005}
}
@article{Fructus2007,
author = {Fructus, D. and Grue, J.},
journal = {J. Comp. Phys.},
pages = {720--739},
title = {{An explicit method for the nonlinear interaction between water waves and variable and moving bottom topography}},
volume = {222},
year = {2007}
}
@article{Fryer2004,
abstract = {The Unimak (eastern Aleutians) earthquake of April1, 1946 is an enigma. The earthquake (MS=7.1) produced a disproportionately large tsunami (Mt=9.3) which killed 167 people. The tsunami was highly directional, and projected its largest waves along a beam perpendicular to the Aleutian arc. Those waves passed just east of the Hawaiian Islands, ran the length of the Pacific, and were still large when they ran ashore in Antarctica. In the near field, the tsunami had very high runup (42 m at Scotch Cap) but rapid lateral decay (6 m at Sanak Village, 120 km to the east). No earthquake source can simultaneously explain the narrow beam of large waves in the far field and the rapid variation in near-source runup. The slow rupture, the tsunami directivity, the rapid variation in near-source wave heights, the period of the waves, and the strong T-phase generation, together suggest an earthquake-triggered landslide rather than a purely tectonic source. From USGS GLORIA imagery we have identified a candidate landslide within the aftershock zone of 1946. The slide bites into the Aleutian shelf at a depth of only 120 m, is 25 km across, 65 km long, and has a volume of 200–300 km3. A slide with these dimensions would produce a tsunami matching the observations while still satisfying the seismic data. Such slope failures appear to be common along the Aleutian forearc, which has serious implications for tsunami warning.},
author = {Fryer, G. J. and Watts, Ph. and Pratson, L. F.},
doi = {10.1016/S0025-3227(03)00305-0},
issn = {00253227},
journal = {Marine Geology},
keywords = {Aleutians,geologic hazards,glacial sediments,submarine landslides,tsunami},
month = {jan},
number = {3-4},
pages = {201--218},
title = {{Source of the great tsunami of 1 April 1946: a landslide in the upper Aleutian forearc}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0025322703003050},
volume = {203},
year = {2004}
}
@article{Fuhrman2009,
author = {Fuhrman, D. R. and Madsen, P. A.},
journal = {Coastal Engineering},
pages = {747--758},
title = {{Tsunami generation, propagation, and run-up with a high-order Boussinesq model}},
volume = {56(7)},
year = {2009}
}
@book{Fuhrmann2014,
address = {Berlin},
author = {Fuhrmann, J. and Ohlberger, M. and Rohde, Ch.},
isbn = {3319055909},
pages = {518},
publisher = {Springer},
title = {{Finite Volumes for Complex Applications VII - Elliptic, Parabolic and Hyperbolic Problems}},
year = {2014}
}
@article{Fujii2006,
abstract = {The source of the West Java tsunami of July 17, 2006, which was generated during a large earthquake near the Sunda trench, is constrained by tsunami waveforms that were recorded on six tide gauges around the Indian Ocean. The tsunami travel times poorly constrain the source area, probably because shallow bathymetry near these gauges is not well known. Inversion of tsunami waveforms, however, reveals that the tsunami source was about 200 km long. The largest slip, about 2.5 m for instantaneous rupture model, was located about 150 km east of the epicenter. Most of the slip occurred on shallow parts of the fault, indicating that this earthquake shares the same characteristics with �tsunami earthquakes� which generate abnormally large tsunamis compared with ground shaking. The slip distribution yields a total seismic moment of 7.0 � 1020 Nm (Mw = 7.8).},
author = {Fujii, Y. and Satake, K.},
doi = {10.1029/2006GL028049},
journal = {Geophys. Res. Lett.},
pages = {L24317},
title = {{Source of the July 2006 West Java tsunami estimated from tide gauge records}},
volume = {33},
year = {2006}
}
@article{Fukao1979,
author = {Fukao, Y.},
journal = {J. Geophys. Res.},
pages = {2303--2314},
title = {{Tsunami Earthquakes and Subduction Processes Near Deep-Sea Trenches}},
volume = {84},
year = {1979}
}
@article{Fukushima1990,
abstract = {Appropriate expressions describing the motion of powder-snow avalanches were derived using a model comprised of four equations--the conservation equations of fluid mass, snow-particle mass, momentum of the cloud, and kinetic energy of the turbulence. Insofar as the density difference between the avalanche and the ambient air becomes rather large compared with the density of the ambient air, the Boussinesq approximation, which is typically used to analyze density currents, was not able to be used. Unlike previous models, the total buoyancy of a powder-snow avalanche was allowed to change freely via erosion from and deposition on to a static snow layer on a slope, the snow-particle entrainment rate from the slope is directly linked to the level of turbulence. A discontinuous, large-scale powder-snow avalanche occurred on 26 January 1986 near Maseguchi , Niigata Prefecture, Japan. The avalanche appears to have had a dense core at its base. The present model was employed to simulate that part of the avalanche above any dense core; the depth of the layer of fresh snow was considered to be an important parameter in the model. The model provided a resonable description of the powder-snow avalanche generated near Maseguchi, and found that the larger the depth of fresh snow, the larger the concentration of snow attained in the avalanche, and the faster its speed. In particular, the model prediction that a powder-snow avalanche strong enough to reach Maseguchi requires a depth of fresh snow of at least 2 meters was found to be in agreement with the observed depth just before the event.},
author = {Fukushima, Y. and Parker, G.},
journal = {Journal of Glaciology},
pages = {229--237},
title = {{Numerical Simulation of Powder-Snow Avalanches}},
volume = {36},
year = {1990}
}
@article{Fuller2006,
author = {Fuller, C. W. and Willett, S. D. and Brandon, M. T.},
journal = {Geology},
pages = {65--68},
title = {{Formation of forearc basins and their influence on subduction zone earthquakes}},
volume = {34},
year = {2006}
}
@article{Funada2002,
author = {Funada, T. and Joseph, D. D.},
journal = {International Journal of Multiphase Flow},
number = {9},
pages = {1459--1478},
title = {{Viscous potential flow analysis of capillary instability}},
volume = {28},
year = {2002}
}
@article{Fuster2009,
author = {Fuster, D. and Agbaglah, G. and Josserand, Ch. and Popinet, S. and Zaleski, S.},
journal = {Fluid Dyn. Res.},
pages = {65001},
title = {{Numerical simulation of droplets, bubbles and waves: state of the art}},
volume = {41},
year = {2009}
}
@article{Galassi2009,
author = {Galassi, M. C. and Coste, P. and More, Ch. and Moretti, F.},
journal = {Science and Technology of Nuclear Installations},
pages = {12},
title = {{Two-Phase Flow Simulations for PTS Investigation by Means of Neptune{\_}CFD Code}},
volume = {2009},
year = {2009}
}
@article{Gallouet2003,
author = {Gallou{\"{e}}t, T. and H{\'{e}}rard, J.-M. and Seguin, N.},
journal = {Comput. {\&} Fluids},
pages = {479--513},
title = {{Some approximate Godunov schemes to compute shallow-water equations with topography}},
volume = {32},
year = {2003}
}
@article{Garcia-Navarro2000,
author = {Garcia-Navarro, P. and Vazquez-Cendon, M. E.},
journal = {Comput. $\backslash${\&} Fluids},
pages = {951--979},
title = {{On numerical treatment of the source terms in the shallow water equations}},
volume = {29},
year = {2000}
}
@article{Garcia-Navarro2000a,
abstract = {Upwind schemes are very well adapted to advection dominated flows and have become popular for applications involving the Euler system of equations. Recently, Riemann solver-based techniques such as Roe’s scheme have become a successful tool for numerical simulation of other conservation laws like the shallow water equations. One of the disadvantages of this technique is related to the treatment of the source terms of the equations. The conservativity of the scheme can be seriously damaged if a careless treatment is applied. Previous papers studied the way to treat the terms arising from bed level changes. This paper deals with the analysis of the main reasons leading to a correct treatment of the geometrical source terms, that is, those representing the changes in cross-section which may be linked to the specific dependence of the flux function on the geometry.},
author = {Garcia-Navarro, P. and Vazquez-Cendon, M. E.},
doi = {10.1016/S0045-7930(99)00038-9},
issn = {00457930},
journal = {Comput. {\&} Fluids},
month = {aug},
number = {8},
pages = {951--979},
title = {{On numerical treatment of the source terms in the shallow water equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0045793099000389},
volume = {29},
year = {2000}
}
@article{Garcia1993a,
abstract = {Laboratory experiments were conducted to observe the behavior of turbidity currents in the vicinity of a slope transition. Both sediment-laden and saline hydraulic jumps were produced. The vertical structure of the currents was found to depend on flow regime. The saline and turbid hydraulic jumps showed similar characteristics. The amount of water entrained by the flows through a jump was small. The change in flow regime caused a marked reduction of the bed shear stress downstream of the jump. In nature, a turbidity current experiencing a hydraulic jump will drop most of its bedload immediately downstream from the jump, while the suspended load will respond more gradually to the change in flow regime and will deposit sediment over a distance far exceeding 1,000 times the jump height.},
author = {Garcia, M. H.},
doi = {10.1061/(ASCE)0733-9429(1993)119:10(1094)},
issn = {07339429},
journal = {J. Hydraul. Eng.},
number = {10},
pages = {1094--1117},
title = {{Hydraulic Jumps in Sediment-Driven Bottom Currents}},
url = {http://link.aip.org/link/JHEND8/v119/i10/p1094/s1{\&}Agg=doi},
volume = {119},
year = {1993}
}
@article{Garcia1993,
abstract = {Experiments on the entrainment of bed sediment into suspension by density underflows are described. The density underflows were created by allowing saline water to move as a steady, continuous current under a body of essentially stagnant fresh water. The bed slope was set at 0.08. Two grades of fine crushed coal, with geometric mean sizes of 100 $\mu$m and 180 $\mu$m, were placed in a trough in the bed with a length of 2 m, over which the density currents passed. Measurements of profiles of flow velocity and concentration of suspended sediment allowed for a back calculation of boundary shear stress and the rate of sediment entrainment from the equations of momentum and mass balance. Two techniques for removing the effect of form drag from the boundary shear stress were explored. The resulting data were used to compare sediment entrainment rates due to density underflows with those observed in open channels. It appears possible to make rather modest adjustments in an existing predictive relation for sediment entrainment in open channels, so as to predict the case pertaining to density underflows as well.},
author = {Garcia, M. and Parker, G.},
doi = {10.1029/92JC02404},
issn = {0148-0227},
journal = {J. Geophys. Res.},
number = {C3},
pages = {4793--4807},
title = {{Experiments on the Entrainment of Sediment Into Suspension by a Dense Bottom Current}},
url = {http://www.agu.org/pubs/crossref/1993/92JC02404.shtml},
volume = {98},
year = {1993}
}
@article{Gardner1974,
author = {Gardner, C. S. and Greene, J. M. and Kruskal, M. D. and Miura, R. M.},
journal = {Comm. Pure Appl. Math.},
pages = {97--133},
title = {{Korteweg-de Vries equation and Generalizations. VI. Methods for Exact Solution}},
volume = {27},
year = {1974}
}
@article{Gardner1967,
author = {Gardner, C. and Greene, J. and Kruskal, M. and Miura, R.},
doi = {10.1103/PhysRevLett.19.1095},
issn = {0031-9007},
journal = {Phys. Rev. Lett},
month = {nov},
number = {19},
pages = {1095--1097},
title = {{Method for Solving the Korteweg-de Vries Equation}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.19.1095},
volume = {19},
year = {1967}
}
@article{Garnier2001,
abstract = {This paper deals with the transmission of a soliton in a random medium described by a randomly perturbed Korteweg-de Vries equation. Different kinds of perturbations are addressed, depending on their specific time or position dependences, with or without damping. We derive effective evolution equations for the soliton parameter by applying a perturbation theory of the inverse scattering transform and limit theorems of stochastic calculus. Original results are derived that are very different compared to a randomly perturbed Nonlinear Schrodinger equation. First the emission of a soliton gas is proved to be a very general feature. Second some perturbations are shown to involve a speeding-up of the soliton, instead of the decay that is usually observed in random media.},
author = {Garnier, J.},
journal = {Journal of Statistical Physics},
keywords = {korteweg de vries equation inverse scattering tran},
number = {5-6},
pages = {789--833},
title = {{Long-time dynamics of Korteweg-de Vries solitons driven by random perturbations}},
volume = {105},
year = {2001}
}
@article{Garnier2007,
author = {Garnier, J. and Mu{\~{n}}oz-Grajales, J. C. and Nachbin, A.},
journal = {SIAM: Multiscale Modeling and Simulation},
pages = {995--1025},
title = {{Effective behavior of solitary waves over random topography}},
volume = {6},
year = {2007}
}
@article{Garnier2013,
author = {Garnier, J. and Xu, G. and Trillo, S. and Picozzi, A.},
doi = {10.1103/PhysRevLett.111.113902},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {sep},
number = {11},
pages = {113902},
title = {{Incoherent Dispersive Shocks in the Spectral Evolution of Random Waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.111.113902},
volume = {111},
year = {2013}
}
@article{Gavrilyuk2015,
author = {Gavrilyuk, S. and Kalisch, H. and Khorsand, Z.},
doi = {10.1088/0951-7715/28/6/1805},
issn = {0951-7715},
journal = {Nonlinearity},
month = {jun},
number = {6},
pages = {1805--1821},
title = {{A kinematic conservation law in free surface flow}},
url = {http://stacks.iop.org/0951-7715/28/i=6/a=1805?key=crossref.a8e4ac47feb2eed0ff08d8c446b0979f},
volume = {28},
year = {2015}
}
@article{Gazi2004,
author = {Gazi, V. and Passino, K. M.},
doi = {10.1080/00207170412331330021},
issn = {0020-7179},
journal = {Int. J. Control},
month = {dec},
number = {18},
pages = {1567--1579},
title = {{A class of attractions/repulsion functions for stable swarm aggregations}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00207170412331330021},
volume = {77},
year = {2004}
}
@article{Ge2011,
abstract = {This paper presents a stochastic approach to model input uncertainty with a general statistical distribution and its propagation through the nonlinear long-wave equations. A Godunov-type scheme mimics breaking waves as bores for accurate description of the energy dissipation in the runup process. The polynomial chaos method expands the flow parameters into series of orthogonal modes, which contain the statistical properties in stochastic space. A spectral projection technique determines the orthogonal modes from ensemble averages of systematically sampled events through the long-wave model. This spectral sampling method generates an output statistical distribution using a much smaller sample of events comparing to the Monte Carlo method. Numerical examples of long-wave transformation over a plane beach and a conical island demonstrate the efficacy of the present approach in describing uncertainty propagation through nonlinear and discontinuous processes for flood-hazard mapping.},
author = {Ge, L. and Cheung, K. F.},
doi = {10.1061/(ASCE)HY.1943-7900.0000301},
journal = {J. Hydraul. Eng.},
keywords = {Floods,Long waves,Monte Carlo method,Polynomials,Sampling,Shallow water,Stochastic models},
number = {3},
pages = {12},
title = {{Spectral Sampling Method for Uncertainty Propagation in Long-Wave Runup Modeling}},
volume = {137},
year = {2011}
}
@article{Gedalin1997,
abstract = {We study solitary wave solutions of the higher order nonlinear Schr{\"{o}}dinger equation for the propagation of short light pulses in an optical fiber. Using a scaling transformation we reduce the equation to a two-parameter canonical form. Solitary wave (1-soliton) solutions always exist provided easily met inequality constraints on the parameters in the equation are satisfied. Conditions for the existence of N-soliton solutions ( N≥2) are determined; when these conditions are met the equation becomes the modified Korteweg–de Vries equation. A proper subset of these conditions meet the Painlev{\'{e}} plausibility conditions for integrability.},
author = {Gedalin, M. and Scott, T. and Band, Y.},
doi = {10.1103/PhysRevLett.78.448},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {jan},
number = {3},
pages = {448--451},
title = {{Optical Solitary Waves in the Higher Order Nonlinear Schr{\"{o}}dinger Equation}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.78.448},
volume = {78},
year = {1997}
}
@article{Geist2002,
author = {Geist, E.},
journal = {J. Geophys. Res.},
pages = {B5},
title = {{Complex earthquake rupture and local tsunamis}},
volume = {107},
year = {2002}
}
@article{Geist2006a,
author = {Geist, E. L. and Bilek, S. L. and Arcas, D. and Titov, V. V.},
journal = {Earth Planets Space},
pages = {185--193},
title = {{Differences in tsunami generation between the December 26, 2004 and March 28, 2005 Sumatra earthquakes}},
volume = {58},
year = {2006}
}
@article{Geist2006,
author = {Geist, E. L. and Titov, V. V. and Synolakis, C. E.},
journal = {Scientific American},
pages = {56--63},
title = {{Tsunami: wave of change}},
volume = {294},
year = {2006}
}
@book{Gelfand1994,
address = {Boston},
author = {Gelfand, I. M. and Kapranov, M. M. and Zelevinsky, A. V.},
pages = {516},
publisher = {Birkh{\"{a}}user},
title = {{Discriminants, resultants and multidimensional determinants}},
year = {1994}
}
@techreport{Geniet2003,
author = {Geniet, F.},
institution = {Preprint LPMT 2003 PM/03-25.},
title = {{Large amplitude surface waves in infinite depth, a variational approach}},
year = {2003}
}
@article{Genty2010,
author = {Genty, G. and de Sterke, C. M. and Bang, O. and Dias, F. and Akhmediev, N. N. and Dudley, J. M.},
journal = {Phys. Lett. A},
pages = {989--996},
title = {{Collisions and turbulence in optical rogue wave formation}},
volume = {374},
year = {2010}
}
@phdthesis{George2006,
author = {George, D. L.},
school = {Department of Applied Mathematics, {\{}U{\}}niversity of {\{}W{\}}ashington, {\{}S{\}}eattle},
title = {{Finite Volume Methods and Adaptive Refinement for Tsunami Propagation and Inundation}},
year = {2006}
}
@article{George2008,
author = {George, D. L.},
journal = {J. Comput. Phys.},
pages = {3089--3113},
title = {{Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation}},
volume = {227},
year = {2008}
}
@article{George2006a,
author = {George, D. L. and Leveque, R. J.},
journal = {Sci. Tsunami Hazards},
pages = {319},
title = {{Finite volume methods and adaptive refinement for global tsunami propagation and local inundation}},
volume = {24(5)},
year = {2006}
}
@article{Gerbeau2001,
author = {Gerbeau, F. and Perthame, B.},
journal = {Discrete Contin. Dynam. Syst. Ser. B},
pages = {89--102},
title = {{Derivation of viscous Saint-Venant system for laminar shallow water}},
volume = {1(1)},
year = {2001}
}
@article{Gerber1949,
author = {Gerber, R.},
journal = {Ann. Inst. Fourier},
pages = {157--162},
title = {{Sur la r{\'{e}}duction {\`{a}} un principe variationnel des {\'{e}}quations du mouvement d'un fluide visqueux incompressible}},
volume = {1},
year = {1949}
}
@phdthesis{Germain1967,
author = {Germain, J.-P.},
school = {Th{\{}{\`{e}}{\}}se de l'Universit{\{}{\'{e}}{\}} de Grenoble, France},
title = {{Contribution {\{}{\`{a}}{\}} l'{\{}{\'{e}}{\}}tude de la houle en eau peu profonde}},
year = {1967}
}
@phdthesis{Germain1967,
author = {Germain, J.-P.},
school = {Th{\`{e}}se de l'Universit{\'{e}} de Grenoble, France},
title = {{Contribution {\`{a}} l'{\'{e}}tude de la houle en eau peu profonde}},
year = {1967}
}
@article{Gerstner1809,
author = {Gerstner, F.},
doi = {10.1002/andp.18090320808},
issn = {1521-3889},
journal = {Annalen der Physik},
number = {8},
pages = {412--445},
title = {{Theorie der Wellen}},
volume = {32},
year = {1809}
}
@incollection{Gesztesy2000,
address = {Singapore},
author = {Gesztesy, F. and Holden, H.},
booktitle = {Mathematical physics and stochastic analysis. Essays in honor of Ludwig Streit},
pages = {198--214},
publisher = {World Scientific},
title = {{The Cole-Hopf and Miura transformations revisited}},
year = {2000}
}
@book{Ghanem2003,
address = {Mineola N.Y.},
author = {Ghanem, R. and Spanos, P.},
isbn = {978-0486428185},
pages = {224},
publisher = {Dover Publications Inc.},
title = {{Stochastic Finite Elements: A Spectral Approach}},
year = {2003}
}
@techreport{Ghidaglia1995,
author = {Ghidaglia, J.-M.},
institution = {D�partement Transferts Thermiques et A�rodynamique, Direction des Etudes et Recherches, Electricit� de France, HT-30/95/015/A},
title = {{Une approche volumes finis pour la r{\{}{\'{e}}{\}}solution des syst{\{}{\`{e}}{\}}mes hyperboliques de lois de conservation, Note}},
year = {1995}
}
@inproceedings{Ghidaglia1998,
address = {Arcachon},
author = {Ghidaglia, J.-M.},
booktitle = {Proceedings of the meeting in honor of P.L. Roe},
editor = {Chattot, J J and Hafez, M},
month = {jul},
title = {{Flux schemes for solving nonlinear systems of conservation laws}},
year = {1998}
}
@inbook{Ghidaglia2001a,
author = {Ghidaglia, J.-M.},
chapter = {Flux schem},
editor = {Chattot, J.-J. and Hafez, M},
publisher = {World Scientific, Singapore},
title = {{Innovative Methods for Numerical Solution of Partial Differential Equations}},
year = {2001}
}
@techreport{Ghidaglia1995,
author = {Ghidaglia, J.-M.},
institution = {D�partement Transferts Thermiques et A�rodynamique, Direction des Etudes et Recherches, Electricit� de France, HT-30/95/015/A},
title = {{Une approche volumes finis pour la r{\'{e}}solution des syst{\`{e}}mes hyperboliques de lois de conservation, Note}},
year = {1995}
}
@book{GhidagliaBook,
author = {Ghidaglia, J.-M.},
publisher = {In preparation},
title = {{Finite volumes methods and complex multi-fluid flows}},
year = {2008}
}
@misc{Ghidaglia2008,
author = {Ghidaglia, J.-M. and Dias, F.},
title = {{Personal communication}},
year = {2008}
}
@article{Ghidaglia2001,
author = {Ghidaglia, J.-M. and Kumbaro, A. and {Le Coq}, G.},
journal = {Eur. J. Mech. B/Fluids},
pages = {841--867},
title = {{On the numerical solution to two fluid models via cell centered finite volume method}},
volume = {20},
year = {2001}
}
@article{Ghidaglia1996,
author = {Ghidaglia, J.-M. and Kumbaro, A. and {Le Coq}, G.},
journal = {C. R. Acad. Sci. I},
pages = {981--988},
title = {{Une m{\'{e}}thode volumes-finis {\`{a}} flux caract{\'{e}}ristiques pour la r{\'{e}}solution num{\'{e}}rique des syst{\`{e}}mes hyperboliques de lois de conservation}},
volume = {322},
year = {1996}
}
@article{Ghidaglia2005,
author = {Ghidaglia, J.-M. and Pascal, F.},
journal = {European Journal of Mechanics B/Fluids},
pages = {1--17},
title = {{The normal flux method at the boundary for multidimensional finite volume approximations in CFD}},
volume = {24},
year = {2005}
}
@inproceedings{Ghidaglia2002,
author = {Ghidaglia, J.-M. and Pascal, F.},
booktitle = {Finite volumes for complex applications III. Problems and perspectives},
editor = {Herbin, R and Kr{\"{o}}ner, D},
pages = {809--816},
title = {{Flux boundary conditions for hyperbolic systems of conservations laws in the finite volume framework}},
year = {2002}
}
@techreport{Ghidaglia2002a,
author = {Ghidaglia, J.-M. and Pascal, F.},
institution = {CMLA, ENS de Cachan},
title = {{On boundary conditions for multidimensional hyperbolic systems of conservation laws in the finite volume framework}},
year = {2002}
}
@article{Ghidaglia1993,
abstract = {Nonelliptic Schr{\"{o}}dinger equations are defined as multidimensional nonlinear dispersive wave equations whose linear part in the space variables is not an elliptic equation. These equations arise in a natural fashion in several contexts in physics and fluid mechanics. The aim of this paper is twofold. First, a brief survey is made of the main nonelliptic Schr{\"{o}}dinger equations known by the authors, with emphasis on water waves. Second, a theory is developed for the Cauchy problem for selected examples. The method is based on linear estimates which are strongly related to the dispersion relation of the problem.},
author = {Ghidaglia, J.-M. and Saut, J.-C.},
doi = {10.1007/BF02429863},
issn = {0938-8974},
journal = {Journal of Nonlinear Science},
month = {dec},
number = {1},
pages = {169--195},
title = {{Nonelliptic Schr{\"{o}}dinger equations}},
url = {http://www.springerlink.com/index/10.1007/BF02429863},
volume = {3},
year = {1993}
}
@article{Ghidaglia1996a,
abstract = {By deriving Pohojaev-type identities we prove that nonelliptic nonlinear Schroedinger equations do not admit localized travelling wave solutions. Similary, we prove that the Davey-Stewartson hyperbolic-elliptic systems do not support travelling wave solutions except for a specific range of the parameters that comprises the DS II focusing case (where the existence of lumps is well known).},
author = {Ghidaglia, J.-M. and Saut, J.-C.},
doi = {10.1007/BF02434051},
issn = {0938-8974},
journal = {Journal of Nonlinear Science},
month = {mar},
number = {2},
pages = {139--145},
title = {{Nonexistence of travelling wave solutions to nonelliptic nonlinear schr{\"{o}}dinger equations}},
url = {http://www.springerlink.com/index/10.1007/BF02434051},
volume = {6},
year = {1996}
}
@article{Ghidaglia1990,
abstract = {In the theory of water waves, the 2D generalisation of the usual cubic 1D Schrodinger equation turns out to be a family of systems: the Davey-Stewartson systems. For special values of the parameters characterising these systems, one obtains systems of the inverse scattering type. The authors' work addresses the very general case and their methods belong to the more standard theory of nonlinear partial differential equations. Well-posedness of the Cauchy problem and also finite-time blow-up are studied.},
author = {Ghidaglia, J.-M. and Saut, J.-C.},
doi = {10.1088/0951-7715/3/2/010},
issn = {0951-7715},
journal = {Nonlinearity},
month = {may},
number = {2},
pages = {475--506},
title = {{On the initial value problem for the Davey-Stewartson systems}},
url = {http://stacks.iop.org/0951-7715/3/i=2/a=010?key=crossref.4bed6038bce2894ef4720aea5e446336},
volume = {3},
year = {1990}
}
@article{Ghidaglia1993,
abstract = {Nonelliptic Schr{\{}{\"{o}}{\}}dinger equations are defined as multidimensional nonlinear dispersive wave equations whose linear part in the space variables is not an elliptic equation. These equations arise in a natural fashion in several contexts in physics and fluid mechanics. The aim of this paper is twofold. First, a brief survey is made of the main nonelliptic Schr{\{}{\"{o}}{\}}dinger equations known by the authors, with emphasis on water waves. Second, a theory is developed for the Cauchy problem for selected examples. The method is based on linear estimates which are strongly related to the dispersion relation of the problem.},
author = {Ghidaglia, J.-M. and Saut, J.-C.},
doi = {10.1007/BF02429863},
issn = {0938-8974},
journal = {Journal of Nonlinear Science},
month = {dec},
number = {1},
pages = {169--195},
title = {{Nonelliptic Schr{\{}{\"{o}}{\}}dinger equations}},
url = {http://www.springerlink.com/index/10.1007/BF02429863},
volume = {3},
year = {1993}
}
@book{Giachetta2009,
address = {Singapore},
author = {Giachetta, G. and Mangiarotti, L. and Sardanashvily, G.},
isbn = {978-9812838957},
pages = {392},
publisher = {World Scientific},
title = {{Advanced Classical Field Theory}},
year = {2009}
}
@article{Gibson2008,
author = {Gibson, J. F. and Halcrow, J. and Cvitanovi{\'{c}}, P.},
doi = {10.1017/S002211200800267X},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {aug},
pages = {107--130},
title = {{Visualizing the geometry of state space in plane Couette flow}},
volume = {611},
year = {2008}
}
@article{Gingold1977,
author = {Gingold, R. A. and Monaghan, J. J.},
journal = {Mon. Not. R. Astron. Soc.},
pages = {375--389},
title = {{Smoothed particle hydrodynamics: theory and application to non-spherical stars}},
volume = {181},
year = {1977}
}
@article{Gisclon1998,
author = {Gisclon, M.},
journal = {Le journal de maths des {\'{e}}l{\`{e}}ves},
number = {4},
pages = {190--197},
title = {{A propos de l'{\'{e}}quation de la chaleur et de l'analyse de Fourier}},
volume = {1},
year = {1998}
}
@article{Gisler2008,
author = {Gisler, G. R.},
journal = {Annu. Rev. Fluid Mech.},
pages = {71--90},
title = {{Tsunami simulations}},
volume = {40},
year = {2008}
}
@article{Gitterman2010,
abstract = {The method of multiple scales is applied to obtain an approximate solution to the nonlinear dynamic equations describing a spring pendulum with the vertical oscillations of the suspension point up to and including the fourth order corrections. The solutions of these equations, where an external force enters the equations multiplicatively, are compared with the solution considered earlier, for the behavior of a spring pendulum subject to an external force, which enters the appropriate equations additively. It turns out that in lower orders in small parameter, the two solutions coincide for the case where the external force and viscous damping force are equally small, but they differ when the damping is much smaller than the external force.},
author = {Gitterman, M.},
doi = {10.1016/j.physa.2010.03.008},
issn = {03784371},
journal = {Physica A},
month = {aug},
number = {16},
pages = {3101--3108},
title = {{Spring pendulum: Parametric excitation vs an external force}},
volume = {389},
year = {2010}
}
@article{Glaister1988,
abstract = {A finite difference scheme based on flux difference splitting was used to solve the one-dimensional shallow water equations of ideal fluid flow. A linearized problem, analagous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. An extension to the one-dimensional equations with source terms, is included. The scheme for the one-dimensional equations was applied to the dam-break problem, and the approximate solution is compared with the exact solution of ideal fluid flow.},
author = {Glaister, P.},
journal = {Journal of Hydraulic Research},
pages = {293--300},
title = {{Approximate Riemann Solutions of the Shallow Water Equations}},
volume = {26},
year = {1988}
}
@article{Glass2010,
author = {Glass, O. and Guerrero, S.},
journal = {Systems and Control Letters},
number = {7},
pages = {390--395},
title = {{Controllability of the Korteweg-de Vries equation from the right Dirichlet boundary condition}},
volume = {59},
year = {2010}
}
@article{Glass2008,
author = {Glass, O. and Guerrero, S.},
journal = {Asymptot. Anal.},
number = {1/2},
pages = {61--100},
title = {{Some exact controllability results for the linear KDV equation and uniform controllability in the zero dispersion limit}},
volume = {60},
year = {2008}
}
@article{Glimm1988,
abstract = {Nonlinearities in wave equations lead to focusing and defocusing of solutions. Focusing causes sharply defined wave fronts. The interaction of such sharply defined wave fronts and more generally of nonlinear hyperbolic waves is of fundamental importance and includes such phenomena as Mach triple point formation, shock wave diffraction patterns and the study of Riemann problems in one and higher dimensions. Recent progress in the study of nonlinear hyperbolic wave interactions has revealed a surprising range of new mathematical phenomena and structures. This mathematical theory should be useful in the design of improved computational algorithms and in part was motivated by such considerations. It is also of considerable interest for its own sake as new mathematical phenomena as well as in terms of the direct insight it provides into physical phenomena. Within the subject matter and point of view adopted here, we have attempted to present a broad and, we hope, a representative account of recent progress.},
author = {Glimm, J.},
doi = {10.1002/cpa.3160410505},
issn = {00103640},
journal = {Comm. Pure Appl. Math.},
month = {jul},
number = {5},
pages = {569--590},
title = {{The interaction of nonlinear hyperbolic waves}},
url = {http://doi.wiley.com/10.1002/cpa.3160410505},
volume = {41},
year = {1988}
}
@article{Glimm2001,
author = {Glimm, J. and Grove, J. W. and Li, X.-L. and Oh, W. and Sharp, D. H.},
journal = {J. Comput. Phys.},
pages = {652--677},
title = {{A critical analysis of Rayleigh-Taylor growth rates}},
volume = {169},
year = {2001}
}
@article{Glimm2000,
author = {Glimm, J. and Grove, J. and Li, X. and Tan, D.},
journal = {SIAM J. Sci. Comput.},
pages = {2240},
title = {{Robust computational algorithms for dynamic interface tracking in three dimensions}},
volume = {21(6)},
year = {2000}
}
@article{Glimm1984,
abstract = {A generalization of the Riemann problem for gas dynamical flows influenced by curved geometry, such as flows in a variable-area duct, is solved. For this generalized Riemann problem the initial data consist of a pair of steady-state solutions separated by a jump discontinuity. The solution of the generalized Riemann problem is used as a basis for a random choice method in which steady-state solutions are used as an Ansatz to approximate the spatial variation of the solution between grid points. For nearly steady flow in a Laval nozzle, where this Ansatz is appropriate, this generalized random choice method gives greatly improved results.},
author = {Glimm, J. and Marshall, G. and Plohr, B.},
doi = {10.1016/0196-8858(84)90002-2},
issn = {01968858},
journal = {Advances in Applied Mathematics},
month = {mar},
number = {1},
pages = {1--30},
title = {{A generalized Riemann problem for quasi-one-dimensional gas flows}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0196885884900022},
volume = {5},
year = {1984}
}
@article{Glimm1986,
abstract = {The basic concepts appropriate for an S matrix theory for classical nonlinear physics are formulated here. These concepts are illustrated by a discussion of shock wave diffraction patterns. Other information concerning solutions of non-linear conservation laws is surveyed, so that a coherent picture of this theory can be seen. Within thisS matrix framework, a number of open problems as well as a few solved ones will be discussed.},
author = {Glimm, J. and Sharp, D. H.},
doi = {10.1007/BF01889377},
issn = {0015-9018},
journal = {Foundations of Physics},
month = {feb},
number = {2},
pages = {125--141},
title = {{An S matrix theory for classical nonlinear physics}},
url = {http://link.springer.com/10.1007/BF01889377},
volume = {16},
year = {1986}
}
@article{Gnutzmann2006,
abstract = {During the last few years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wavefunction statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. In particular, we summarize recent developments on the spectral statistics of generic large quantum graphs based on two approaches: the periodic-orbit approach and the supersymmetry approach. The latter provides a condition and a proof for universal spectral statistics as predicted by random-matrix theory.},
author = {Gnutzmann, S. and Smilansky, U.},
doi = {10.1080/00018730600908042},
issn = {0001-8732},
journal = {Advances in Physics},
month = {jul},
number = {5-6},
pages = {527--625},
title = {{Quantum graphs: Applications to quantum chaos and universal spectral statistics}},
url = {http://www.tandfonline.com/doi/abs/10.1080/00018730600908042},
volume = {55},
year = {2006}
}
@article{Goatin2004,
abstract = {We solve the Riemann problem for a class of resonant hyperbolic systems of balance laws. The systems are not strictly hyperbolic and the solutions take their values in a neighborhood of a state where two characteristic speeds coincide. Our construction generalizes the ones given earlier by Isaacson and Temple for scalar equations and for conservative systems. The class of systems under consideration here includes, in particular, a model from continuum physics that describes the evolution of a fluid flow in a nozzle with discontinuous cross-section.},
author = {Goatin, P. and LeFloch, Ph. G.},
doi = {10.1016/j.anihpc.2004.02.002},
issn = {02941449},
journal = {Annales de l'Institut Henri Poincare (C) Non Linear Analysis},
month = {nov},
number = {6},
pages = {881--902},
title = {{The Riemann problem for a class of resonant hyperbolic systems of balance laws}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0294144904000411},
volume = {21},
year = {2004}
}
@article{Gobbi1999,
abstract = {A Boussinesq model accurate to O($\mu$)4, $\mu$ = k0h0 in dispersion and retaining all nonlinear effects is derived for the case of variable water depth. A numerical implementation of the model in one horizontal direction is described. An algorithm for wave generation using a grid-interior source function is derived. The model is tested in its complete form, in a weakly nonlinear form corresponding to the approximation $\delta$ = O($\mu$2), $\delta$ = a/h0, and in a fully nonlinear form accurate to O($\mu$2) in dispersion [Wei, G., Kirby, J.T., Grilli, S.T., Subramanya R. (1995). A fully nonlinear Boussinesq model for surface waves: Part 1. Highly nonlinear unsteady waves. J. Fluid Mech., 294, 71-92]. Test cases are taken from the experiments described by Dingemans [Dingemans, M.W. (1994). Comparison of computations with Boussinesq-like models and laboratory measurements. Report H-1684.12, Delft Hydraulics, 32 pp.] and Ohyama et al. [Ohyama, T., Kiota, W., Tada, A. (1994). Applicability of numerical models to nonlinear dispersive waves. Coastal Engineering, 24, 297-313.] and consider the shoaling and disintegration of monochromatic wave trains propagating over an elevated bar feature in an otherwise constant depth tank. Results clearly demonstrate the importance of the retention of fully-nonlinear effects in correct prediction of the evolved wave fields.},
author = {Gobbi, M. F. and Kirby, J. T.},
doi = {10.1016/S0378-3839(99)00015-0},
issn = {03783839},
journal = {Coastal Engineering},
keywords = {Boussinesq model,Depth tank,Wave field},
number = {1},
pages = {57--96},
title = {{Wave evolution over submerged sills: Tests of a high-order Boussinesq model}},
volume = {37},
year = {1999}
}
@article{Gobbi2000,
author = {Gobbi, M. F. and Kirby, J. T. and Wei, G.},
doi = {10.1017/S0022112099007247},
issn = {00221120},
journal = {J. Fluid Mech.},
month = {feb},
pages = {181--210},
title = {{A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to O(kh)4}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112099007247},
volume = {405},
year = {2000}
}
@inproceedings{Goda1974,
author = {Goda, Y.},
booktitle = {Proc. 14th Int. Conf. Coastal Eng.},
pages = {1702--1720},
title = {{New wave pressure formulae for composite breakers}},
year = {1974}
}
@book{Goda2010,
author = {Goda, Y.},
publisher = {World Scientific},
series = {Advanced Series on Ocean Engineering},
title = {{Random Seas and Design of Maritime Structures}},
volume = {33},
year = {2010}
}
@book{Godlewski1996,
author = {Godlewski, E. and Raviart, P.-A.},
publisher = {Springer, New York},
title = {{Numerical approximation of hyperbolic systems of conservation laws}},
volume = {118},
year = {1996}
}
@book{Godlewski1990,
address = {Paris},
author = {Godlewski, E. and Raviart, P.-A.},
publisher = {Ellipses},
title = {{Hyperbolic systems of conservation laws}},
year = {1990}
}
@article{Godunov1959,
author = {Godunov, S. K.},
journal = {Mat. Sb.},
pages = {271--290},
title = {{A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics}},
volume = {47},
year = {1959}
}
@article{Godunov1999,
author = {Godunov, S. K.},
journal = {J. Comput. Phys.},
pages = {6--25},
title = {{Reminiscences about Difference Schemes}},
volume = {153},
year = {1999}
}
@book{Godunov1987,
address = {Amsterdam},
author = {Godunov, S. K. and Ryabenkii, V. S.},
isbn = {9780080875408},
pages = {488},
publisher = {North-Holland},
title = {{Difference Schemes}},
year = {1987}
}
@book{Godunov1979,
author = {Godunov, S. K. and Zabrodine, A. and Ivanov, M. and Kraiko, A. and Prokopov, G.},
publisher = {Editions Mir, Moscow},
title = {{R{\'{e}}solution num{\'{e}}rique des probl{\`{e}}mes multidimensionnels de la dynamique des gaz}},
year = {1979}
}
@book{Golub1996,
author = {Golub, G. and {Van Loan}, C.},
edition = {3rd ed.},
publisher = {J. Hopkins University Press},
title = {{Matrix Computations}},
year = {1996}
}
@article{SPH2,
author = {Gomez-Gesteira, M. and Cerqueiro, D. and Crespo, C. and Dalrymple, R. A.},
journal = {Ocean Engineering},
pages = {223--238},
title = {{Green water overtopping analyzed with a SPH model}},
volume = {32},
year = {2005}
}
@article{SPH1,
author = {Gomez-Gesteira, M. and Dalrymple, R. A.},
journal = {Journal of Waterways, Port, Coastal, and Ocean Engineering},
pages = {63--69},
title = {{Using SPH for wave impact on a tall structure}},
volume = {130},
year = {2004}
}
@article{Gong2014,
author = {Gong, Y. and Cai, J. and Wang, Y.},
doi = {10.4208/cicp.090313.041113a},
journal = {Commun. Comput. Phys.},
number = {1},
pages = {35--55},
title = {{Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation}},
volume = {16},
year = {2014}
}
@article{Gonzalez-Vega2002,
abstract = {This paper is devoted to present a new algorithm computing in a very efficient way the topology of a real algebraic plane curve defined implicitly. This algorithm proceeds in a seminumerical way by performing a symbolic preprocessing which allows later to accomplish the numerical computations in a very accurate way.},
author = {Gonzalez-Vega, L. and Necula, I.},
doi = {10.1016/S0167-8396(02)00167-X},
issn = {01678396},
journal = {Computer Aided Geometric Design},
keywords = {Algebraic curves,Seminumerical algorithms,Topology computation},
month = {dec},
number = {9},
pages = {719--743},
title = {{Efficient topology determination of implicitly defined algebraic plane curves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S016783960200167X},
volume = {19},
year = {2002}
}
@article{Gonz,
author = {Gonz{\'{a}}lez, F. I. and Bernard, E. N. and Meinig, C. and Eble, M. C. and Mofjeld, H. O. and Stalin, S.},
journal = {Natural Hazards},
pages = {25--39},
title = {{The NTHMP tsunameter network}},
volume = {35},
year = {2005}
}
@article{Goodman1985,
author = {Goodman, J. D. and LeVeque, R. J.},
journal = {Math. Comp.},
pages = {15--21},
title = {{On the accuracy of stable schemes for 2D conservation laws}},
volume = {45(171)},
year = {1985}
}
@book{Gosse2013,
address = {Milano},
author = {Gosse, L.},
doi = {10.1007/978-88-470-2892-0},
edition = {1},
isbn = {978-88-470-2891-3},
pages = {340},
publisher = {Springer Milan},
series = {SIMAI Springer Series},
title = {{Computing Qualitatively Correct Approximations of Balance Laws: Exponential-Fit, Well-Balanced and Asymptotic-Preserving}},
url = {http://link.springer.com/10.1007/978-88-470-2892-0},
volume = {2},
year = {2013}
}
@article{Gosse2001,
abstract = {This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.},
author = {Gosse, L.},
doi = {10.1090/S0025-5718-01-01354-0},
issn = {0025-5718},
journal = {Math. Comp.},
keywords = {Balance laws,finite difference schemes,nonconservative products,relaxation schemes},
month = {nov},
number = {238},
pages = {553--583},
title = {{Localization effects and measure source terms in numerical schemes for balance laws}},
url = {http://www.ams.org/journal-getitem?pii=S0025-5718-01-01354-0},
volume = {71},
year = {2001}
}
@article{Gosse2008,
author = {Gosse, L. and Runborg, O.},
journal = {SIAM J. Numer. Anal.},
number = {6},
pages = {1618--1640},
title = {{Existence, Uniqueness, and a Constructive Solution Algorithm for a Class of Finite Markov Moment Problems}},
volume = {68},
year = {2008}
}
@article{Gosse2015,
author = {Gosse, L. and Vauchelet, N.},
journal = {Submitted},
title = {{Numerical high-field limits in two-stream kinetic models and 1D aggregation equations}},
year = {2015}
}
@techreport{Goto1997,
author = {Goto, C. and Ogawa, Y. and Shuto, N. and Imamura, F.},
institution = {UNESCO},
title = {{Numerical method of tsunami simulation with the leap-frog scheme}},
year = {1997}
}
@article{Gottardi2004,
author = {Gottardi, G. and Venutelli, M.},
journal = {Advances in Water Resources},
pages = {259--268},
title = {{Central scheme for two-dimensional dam-break flow simulation}},
volume = {27},
year = {2004}
}
@article{Gottlieb2001,
author = {Gottlieb, S. and Shu, C.-W. and Tadmor, E.},
journal = {SIAM Review},
pages = {89--112},
title = {{Strong Stability-Preserving High-Order Time Discretization Methods}},
volume = {43},
year = {2001}
}
@article{Goubet2010,
author = {Goubet, O. and Warnault, G.},
doi = {10.1007/s11401-010-0615-2},
issn = {0252-9599},
journal = {Chinese Annals of Mathematics, Series B},
month = {oct},
number = {6},
pages = {841--854},
title = {{Decay of solutions to a linear viscous asymptotic model for water waves}},
url = {http://link.springer.com/10.1007/s11401-010-0615-2},
volume = {31},
year = {2010}
}
@article{Goudon2014,
author = {Goudon, T. and Jin, S. and Liu, J.-G. and Yan, B.},
doi = {10.1002/fld.3885},
issn = {02712091},
journal = {Int. J. Num. Meth. Fluids},
month = {may},
number = {2},
pages = {81--102},
title = {{Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density}},
url = {http://doi.wiley.com/10.1002/fld.3885},
volume = {75},
year = {2014}
}
@book{Gould2012,
abstract = {This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. Subsequent chapters explore cycles and circuits, planarity, matchings, and independence. The text concludes with considerations of special topics and applications and extremal theory. Exercises appear throughout the text.},
author = {Gould, R.},
edition = {Dover},
isbn = {978-0486498065},
pages = {352},
publisher = {Dover Publications Inc.},
title = {{Graph Theory}},
year = {2012}
}
@article{Gouyon1958,
author = {Gouyon, R.},
journal = {Annales de la facult{\'{e}} des sciences de Toulouse S{\'{e}}r. 4},
pages = {1--55},
title = {{Contributions {\`{a}} la th{\'{e}}orie des houles}},
volume = {22},
year = {1958}
}
@book{gradshteyn,
author = {Gradshteyn, I. S. and Ryzhik, M.},
edition = {6},
editor = {Jeffrey, Alan and Zwillinger, Daniel},
isbn = {0-12-294757-6},
publisher = {Academic Press, Orlando, Florida},
title = {{Tables of Integrals, Series, and Products}},
year = {2000}
}
@article{Graffi1955,
author = {Graffi, D.},
journal = {Rev. Unione Mar Argentina},
pages = {73--77},
title = {{Il teorema di unicit{\'{a}} per i fluidi incompressibili, perferri, eterogenei}},
volume = {17},
year = {1955}
}
@article{Gramstad2007,
author = {Gramstad, O. and Trulsen, K.},
journal = {J. Fluid Mech.},
pages = {463--472},
title = {{Influence of crest and group length on the occurrence of freak waves}},
volume = {582},
year = {2007}
}
@article{Gramstad2011,
author = {Gramstad, O. and Trulsen, K.},
journal = {J. Fluid Mech},
pages = {404--426},
title = {{Hamiltonian form of the modified nonlinear Schr{\"{o}}dinger equation for gravity waves on arbitrary depth}},
volume = {670},
year = {2011}
}
@article{Grant1973,
abstract = {Expansions have been given in the past for steady Stokes waves at or near a largest wave with a 120° corner. It is shown here that the solution is more complicated than has been assumed: that the corner is not a regular singular point, and that waves of less than maximum amplitude have singularities of a different order.},
author = {Grant, M. A.},
doi = {10.1017/S0022112073001552},
issn = {0022-1120},
journal = {J. Fluid Mech},
month = {mar},
pages = {257--262},
title = {{The singularity at the crest of a finite amplitude progressive Stokes wave}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112073001552},
volume = {59},
year = {1973}
}
@techreport{Grass1981,
author = {Grass, A.},
institution = {SERC London Cent. Mar. Technol.},
title = {{Sediment transport by waves and currents}},
year = {1981}
}
@article{Grataloup2003,
author = {Grataloup, G. L. and Mei, C. C.},
doi = {10.1103/PhysRevE.68.026314},
journal = {Phys. Rev. E},
month = {aug},
number = {2},
pages = {26314},
publisher = {American Physical Society},
title = {{Localization of harmonics generated in nonlinear shallow water waves}},
volume = {68},
year = {2003}
}
@article{Grava2008,
author = {Grava, T. and Klein, C.},
doi = {10.1098/rspa.2007.0249},
issn = {1364-5021},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
month = {mar},
number = {2091},
pages = {733--757},
title = {{Numerical study of a multiscale expansion of the Korteweg-de Vries equation and Painlev{\'{e}}-II equation}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2007.0249},
volume = {464},
year = {2008}
}
@article{Grava2007,
author = {Grava, T. and Klein, C.},
doi = {10.1002/cpa.20183},
issn = {00103640},
journal = {Comm. Pure Appl. Math.},
month = {nov},
number = {11},
pages = {1623--1664},
title = {{Numerical solution of the small dispersion limit of Korteweg-de Vries and Whitham equations}},
url = {http://doi.wiley.com/10.1002/cpa.20183},
volume = {60},
year = {2007}
}
@article{Gray1998,
author = {Gray, J.M.N.T. and Wieland, M. and Hutter, K.},
journal = {Proc. R. Soc. Lond. A},
pages = {1841--1874},
title = {{Gravity-driven free surface flow of granular avalanches over complex basal topography}},
volume = {455},
year = {1998}
}
@article{Green1974,
author = {Green, A. E. and Laws, N. and Naghdi, P. M.},
journal = {Proc. R. Soc. Lond. A},
pages = {43--55},
title = {{On the theory of water waves}},
volume = {338},
year = {1974}
}
@article{Green1976,
author = {Green, A. E. and Naghdi, P. M.},
journal = {J. Fluid Mech.},
pages = {237--246},
title = {{A derivation of equations for wave propagation in water of variable depth}},
volume = {78},
year = {1976}
}
@article{Greenberg1996,
author = {Greenberg, J. M. and Leroux, A. Y.},
journal = {SIAM J. Num. Anal.},
number = {1},
pages = {1--16},
title = {{A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations}},
volume = {33},
year = {1996}
}
@article{Greenberg1984,
author = {Greenberg, W. and van der Mee, C. V. M. and Zweifel, P. F.},
doi = {10.1007/BF01204914},
issn = {0378-620X},
journal = {Integral Equations and Operator Theory},
month = {jan},
number = {1},
pages = {60--95},
title = {{Generalized kinetic equations}},
url = {http://link.springer.com/10.1007/BF01204914},
volume = {7},
year = {1984}
}
@article{Greenshields2007,
author = {Greenshields, C. J. and Reese, J. M.},
doi = {10.1017/S0022112007005575},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {may},
pages = {407--429},
title = {{The structure of shock waves as a test of Brenner's modifications to the Navier–Stokes equations}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112007005575},
volume = {580},
year = {2007}
}
@article{Grenier2009,
author = {Grenier, N. and Antuono, M. and Colagrossi, A. and {Le Touz{\'{e}}}, D. and Alessandrini, B.},
doi = {10.1016/j.jcp.2009.08.009},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {dec},
number = {22},
pages = {8380--8393},
title = {{An Hamiltonian interface SPH formulation for multi-fluid and free surface flows}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S002199910900446X},
volume = {228},
year = {2009}
}
@incollection{Griffiths2015,
abstract = {This chapter describes a classical technique for constructing series solutions of linear PDE problems. Classical examples like the heat equation, the wave equation and Laplace’s equations are studied in detail.},
author = {Griffiths, D. F. and Dold, J. W. and Silvester, D. J.},
booktitle = {Essential Partial Differential Equations},
doi = {10.1007/978-3-319-22569-2{\_}8},
pages = {129--159},
publisher = {Springer International Publishing},
title = {{Separation of Variables}},
url = {http://link.springer.com/10.1007/978-3-319-22569-2{\_}8},
year = {2015}
}
@article{Grigorian1967,
annote = {(in Russian)},
author = {Grigorian, S. S. and Eglit, M. E. and Yakimov, Y. L.},
journal = {Trudy Vysokogornogo Geofizicheskogo Instituta},
pages = {104--113},
title = {{A new formulation and solution of the problem of a snow avalanche motion}},
volume = {12},
year = {1967}
}
@article{Grillakis1987,
abstract = {Consider an abstract Hamiltonian system which is invariant under a one-parameter unitary group of operators. By a "solitary wave" we mean a solution the time development of which is given exactly by the one-parameter group. We find sharp conditions for the stability and instability of solitary waves. Applications are given to bound states and traveling waves of nonlinear PDEs such Klein-Gordon and Schr{\"{o}}dinger equations.},
author = {Grillakis, M. and Shatah, J. and Strauss, W.},
doi = {10.1016/0022-1236(87)90044-9},
issn = {00221236},
journal = {Journal of Functional Analysis},
month = {sep},
number = {1},
pages = {160--197},
title = {{Stability theory of solitary waves in the presence of symmetry, I}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0022123687900449},
volume = {74},
year = {1987}
}
@article{Grilli2012,
author = {Grilli, S. T. and Harris, J. C. and {Tajalli Bakhsh}, T. S. and Masterlark, T. L. and Kyriakopoulos, C. and Kirby, J. T. and Shi, F.},
doi = {10.1007/s00024-012-0528-y},
issn = {0033-4553},
journal = {Pure Appl. Geophys.},
month = {jul},
title = {{Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations}},
url = {http://www.springerlink.com/index/10.1007/s00024-012-0528-y},
year = {2012}
}
@article{Grilli1999,
author = {Grilli, S. T. and Watts, P.},
journal = {Engineering Analysis with boundary elements},
pages = {645--656},
title = {{Modeling of waves generated by a moving submerged body. Applications to underwater landslides}},
volume = {23},
year = {1999}
}
@article{Grilli2005,
author = {Grilli, S. T. and Watts, Ph.},
doi = {10.1061/(ASCE)0733-950X(2005)131:6(283)},
issn = {0733950X},
journal = {Journal of Waterway Port Coastal and Ocean Engineering},
number = {6},
pages = {283},
title = {{Tsunami Generation by Submarine Mass Failure. I: Modeling, Experimental Validation, and Sensitivity Analyses}},
url = {http://link.aip.org/link/JWPED5/v131/i6/p283/s1{\&}Agg=doi},
volume = {131},
year = {2005}
}
@article{Grilli,
author = {Grilli, S. and Guyenne, P. and Dias, F.},
doi = {10.1002/1097-0363(20010415)35:7},
journal = {Int. J. Numer. Meth. Fluids},
pages = {829--867},
title = {{A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom}},
volume = {35},
year = {2001}
}
@article{Vogel,
author = {Grilli, S. and Vogelmann, S. and Watts, P.},
journal = {Engng Anal. Bound. Elem.},
pages = {301--313},
title = {{Development of a 3D numerical wave tank for modeling tsunami generation by underwater landslides}},
volume = {26},
year = {2002}
}
@incollection{Grimshaw2002,
abstract = {The basic theory of internal solitary waves is developed, with the main emphasis on environmental situations, such as the many occurrences of such waves in shallow coastal seas and in the atmospheric boundary layer. Commencing with the equations of motion for an inviscid, incompressible density-stratified fluid, we describe asymptotic reductions to model long-wave equations, such as the well-known Korteweg-de Vries equation. We then describe various solitary wave solutions, and propose a variable-coefficient extended Korteweg-de Vries equations as an appropriate evolution equation to describe internal solitary waves in environmental situations, when the effects of a variable background and dissipation need to be taken into account.},
author = {Grimshaw, R.},
booktitle = {Environmental Stratified Flows},
doi = {10.1007/0-306-48024-7{\_}1},
editor = {Grimshaw, R.},
isbn = {978-0-306-48024-9},
pages = {1--27},
publisher = {Springer US},
title = {{Internal Solitary Waves}},
year = {2002}
}
@article{Grimshaw1971,
author = {Grimshaw, R.},
journal = {J. Fluid Mech},
pages = {611--622},
title = {{The solitary wave in water of variable depth. Part 2.}},
volume = {46},
year = {1971}
}
@article{Grimshaw1995,
abstract = {A fifth-order Korteweg-de Vries equation is considered, where the fifth-order derivative term is multiplied by a small parameter. It is known that solitary wave solutions of this model equation are nonlocal in that the central core of the wave is accompanied by copropagating trailing oscillations. Here, using the techniques of exponential asymptotics, these solutions are reexamined and it is established that they form a one-parameter family characterized by the phase shift of the trailing oscillations. Explicit asymptotic formula relating the oscillation amplitude to the phase shift are obtained.},
author = {Grimshaw, R. and Joshi, N.},
doi = {10.1137/S0036139993243825},
issn = {0036-1399},
journal = {SIAM Journal on Applied Mathematics},
month = {feb},
number = {1},
pages = {124--135},
title = {{Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg-De Vries Equation}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0036139993243825},
volume = {55},
year = {1995}
}
@article{Grimshaw2001,
abstract = {The dynamics of wave groups is studied for long waves, using the framework of the extended Korteweg-de Vries equation. It is shown that the dynamics is much richer than the corresponding results obtained just from the Korteweg-de Vries equation. First, a reduction to a nonlinear Schr{\"{o}}dinger equation is obtained for weakly nonlinear wave packets, and it is demonstrated that either the focussing or the defocussing case can be obtained. This is in contrast to the corresponding reduction for the Korteweg-de Vries equation, where only the defocussing case is obtained. Next, the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coefficient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for a high carrier frequency. At the boundary of this parameter space, a modified nonlinear Schr{\"{o}}dinger equation is derived, and its steady-state solutions, including an algebraic soliton, are found. The exact breather solution of the extended Korteweg-de Vries equation is analysed. It is shown that in the limit of weak nonlinearity it transforms to a wave group with an envelope described by soliton solutions of the nonlinear Schr{\"{o}}dinger equation and its modification as described above. Numerical simulations demonstrate the main features of wave group evolution and show some differences in the behaviour of the solutions of the extended Korteweg-de Vries equation, compared with those of the nonlinear Schr{\"{o}}dinger equation.},
author = {Grimshaw, R. and Pelinovsky, D. E. and Pelinovsky, E. N. and Talipova, T.},
doi = {10.1016/S0167-2789(01)00333-5},
issn = {01672789},
journal = {Phys. D},
keywords = {Korteweg-de Vries equation,Nonlinear Schr{\"{o}}dinger equation,Wave group dynamics},
month = {nov},
number = {1-2},
pages = {35--57},
title = {{Wave group dynamics in weakly nonlinear long-wave models}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278901003335},
volume = {159},
year = {2001}
}
@article{Grimshaw2003,
author = {Grimshaw, R. and Pelinovsky, E. N. and Talipova, T.},
journal = {Wave Motion},
pages = {351--364},
title = {{Damping of large-amplitude solitary waves}},
volume = {37},
year = {2003}
}
@article{Grimshaw2004,
author = {Grimshaw, R. and Pelinovsky, E. N. and Talipova, T. and Kurkin, A.},
journal = {J. Phys. Oceanogr.},
pages = {2774--2791},
title = {{Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves}},
volume = {34},
year = {2004}
}
@article{Grimshaw2005,
abstract = {The appearance and disappearance of short-lived large-amplitude pulses in a nonlinear long wave model is studied in the framework of the modified Korteweg-de Vries equation. The major mechanism of such wave generation is modulational instability leading to the generation and interaction of the breathers. The properties of breathers are studied both within the modified Korteweg-de Vries equation, and also within the nonlinear Schr{\"{o}}dinger equations derived by an asymptotic reduction from the modified Korteweg-de Vries for weakly nonlinear wave packets. The associated spectral problems (AKNS or Zakharov-Shabat) of the inverse-scattering transform technique also are utilized. Wave formation due to this modulational instability is investigated for localized and for periodic disturbances. Nonlinear-dispersive focusing is identified as a possible mechanism for the formation of anomalously large pulses.},
author = {Grimshaw, R. and Pelinovsky, E. N. and Talipova, T. and Ruderman, M. S. and Erdelyi, R.},
doi = {10.1111/j.0022-2526.2005.01544.x},
issn = {0022-2526},
journal = {Stud. Appl. Math.},
month = {feb},
number = {2},
pages = {189--210},
title = {{Short-Lived Large-Amplitude Pulses in the Nonlinear Long-Wave Model Described by the Modified Korteweg-De Vries Equation}},
url = {http://doi.wiley.com/10.1111/j.0022-2526.2005.01544.x},
volume = {114},
year = {2005}
}
@article{Grimshaw2010,
abstract = {The initial-value problem for box-like initial disturbances is studied within the framework of an extended Korteweg-de Vries equation with both quadratic and cubic nonlinear terms, also known as the Gardner equation, for the case when the cubic nonlinear coefficient has the same sign as the linear dispersion coefficient. The discrete spectrum of the associated scattering problem is found, which is used to describe the asymptotic solution of the initial-value problem. It is found that while initial disturbances of the same sign as the quadratic nonlinear coefficient result in generation of only solitons, the case of the opposite polarity of the initial disturbance has a variety of possible outcomes. In this case solitons of different polarities as well as breathers may occur. The bifurcation point when two eigenvalues corresponding to solitons merge to the eigenvalues associated with breathers is considered in more detail. Direct numerical simulations show that breathers and soliton pairs of different polarities can appear from a simple box-like initial disturbance.},
author = {Grimshaw, R. and Slunyaev, A. and Pelinovsky, E. N.},
institution = {Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.},
journal = {Chaos},
number = {1},
pages = {13102},
pmid = {20370257},
title = {{Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/20370257},
volume = {20},
year = {2010}
}
@article{Grimshaw1994,
abstract = {The dynamical behaviour of a reduction of the forced (and damped) Korteweg-de Vries equation is studied numerically. Chaos arising from subharmonic instability and homoclinic crossings are observed. Both period-doubling bifurcations and the Melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour, here characterised by a positive Lyapunov exponent. Supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits, and their behaviour under perturbation using Melnikov functions.},
author = {Grimshaw, R. and Tian, X.},
doi = {10.1098/rspa.1994.0045},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {apr},
number = {1923},
pages = {1--21},
title = {{Periodic and Chaotic Behaviour in a Reduction of the Perturbed Korteweg-De Vries Equation}},
volume = {445},
year = {1994}
}
@article{Grinstein2002,
author = {Grinstein, F. F. and Karniadakis, G. E.},
journal = {J. Fluids Eng.},
pages = {821--942},
title = {{Alternative LES and Hybrid RANS/LES}},
volume = {124},
year = {2002}
}
@article{Grue2003,
author = {Grue, J. and Clamond, D. and Huseby, M. and Jensen, A.},
journal = {Applied Ocean Research},
pages = {355--366},
title = {{Kinematics of extreme waves in deep water}},
volume = {25},
year = {2003}
}
@article{Guelfi2007,
author = {Guelfi, A. and Bestion, D. and Boucker, M. and Et al},
journal = {Nuclear Science and Engineering},
pages = {281--324},
title = {{NEPTUNE: a new software platform for advanced nuclear thermal hydraulics}},
volume = {156(3)},
year = {2007}
}
@article{Guerra2004,
author = {Guerra, G.},
doi = {10.1016/j.jde.2004.04.008},
issn = {00220396},
journal = {J. Diff. Eqns.},
month = {nov},
number = {2},
pages = {438--469},
title = {{Well-posedness for a scalar conservation law with singular nonconservative source}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039604001639},
volume = {206},
year = {2004}
}
@article{Mariotti,
author = {Guesmia, M. and Heinrich, P. H. and Mariotti, C.},
journal = {Natural Hazards},
pages = {31--46},
title = {{Numerical simulation of the 1969 Portuguese tsunami by a finite element method}},
volume = {17},
year = {1998}
}
@inproceedings{Guilcher2012,
address = {Rhodes, Greece},
author = {Guilcher, P. M. and Brosset, L. and Couty, N. and {Le Touz{\'{e}}}, D.},
booktitle = {Proceedings of 22nd International Offshore and Polar Engineering Conference (ISOPE)},
title = {{Simulations of breaking wave impacts on a rigid wall at two different scales with a two phase fluid compressible SPH model}},
year = {2012}
}
@inproceedings{Guilcher2010,
address = {Beijing, China},
author = {Guilcher, P. M. and Oger, G. and Brosset, L. and Jacquin, E. and Grenier, N. and {Le Touz{\'{e}}}, D.},
booktitle = {Proceedings of 20th International Offshore and Polar Engineering Conference (ISOPE)},
title = {{Simulation of liquid impacts with a two-phase parallel SPH model}},
year = {2010}
}
@article{Guillard1999,
author = {Guillard, H. and Viozat, C.},
journal = {Comput. {\&} Fluids},
pages = {63--86},
title = {{On the behaviour of upwind schemes in the low Mach number limit}},
volume = {28(1)},
year = {1999}
}
@article{Gulevich2006,
author = {Gulevich, D. and Kusmartsev, F.},
doi = {10.1103/PhysRevLett.97.017004},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {jul},
number = {1},
pages = {017004},
title = {{Flux Cloning in Josephson Transmission Lines}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.97.017004},
volume = {97},
year = {2006}
}
@article{Gulevich2008,
abstract = {We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity.},
author = {Gulevich, D. and Kusmartsev, F. and Savel'ev, S. and Yampol'skii, V. and Nori, F.},
doi = {10.1103/PhysRevLett.101.127002},
issn = {0031-9007},
journal = {Phys. Rev. Lett},
month = {sep},
number = {12},
pages = {127002},
title = {{Shape Waves in 2D Josephson Junctions: Exact Solutions and Time Dilation}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.101.127002},
volume = {101},
year = {2008}
}
@article{Gurevich1974,
author = {Gurevich, A. V. and Pitaevskii, L. P.},
journal = {Sov. Phys. - JETP},
pages = {291--297},
title = {{Nonstationary structure of a collisionless shock wave}},
volume = {38},
year = {1974}
}
@article{Gurevich1974a,
author = {Gurevich, A. V. and Pitaevskii, L. P.},
journal = {Sov. Phys. - JETP},
number = {2},
pages = {291--297},
title = {{Nonstationary structure of a collisionless shock wave}},
volume = {38},
year = {1974}
}
@article{Gurevich1993,
author = {Gurevich, B. and Jeffrey, A. and Pelinovsky, E. N.},
journal = {Wave Motion},
pages = {287--295},
title = {{A Method for obtaining evolution equations for nonlinear waves in random medium}},
volume = {17(5)},
year = {1993}
}
@inproceedings{Gusiakov1978a,
address = {Novosibirsk},
author = {Gusiakov, V. K.},
booktitle = {Conditionally correct problems of mathematical physics in the interpretation of geophysical observations},
pages = {23--51},
publisher = {SO RAN},
title = {{Residual displacements on the surface of elastic half-space}},
year = {1978}
}
@inbook{gusyakov3,
annote = {in Russian},
author = {Gusyakov, V. K.},
chapter = {Estimation},
pages = {46--64},
publisher = {Novosibirsk, VZ SO AN SSSR},
title = {{Ill-posed problems of mathematical physics and problems of interpretation of geophysical observations}},
year = {1976}
}
@inbook{gusyakov,
annote = {in Russian},
author = {Gusyakov, V. K.},
chapter = {Generation},
pages = {250--272},
publisher = {Novosibirsk, VZ SO AN SSSR},
title = {{Mathematical problems of geophysics}},
volume = {3},
year = {1972}
}
@inbook{gusyakov2,
annote = {in Russian},
author = {Gusyakov, V. K.},
chapter = {About conn},
pages = {118--140},
publisher = {Novosibirsk, VZ SO AN SSSR},
title = {{Mathematical problems of geophysics}},
volume = {5},
year = {1974}
}
@article{Gutenberg1939,
author = {Gutenberg, B.},
journal = {Bull. Seism. Soc. Am.},
pages = {517--526},
title = {{Tsunamis and earthquakes}},
volume = {29},
year = {1939}
}
@article{Guyenne2007,
author = {Guyenne, P. and Nicholls, D. P.},
journal = {SIAM J. Sci. Comput.},
pages = {81--101},
title = {{A high-order spectral method for nonlinear water waves over moving bottom topography}},
volume = {30(1)},
year = {2007}
}
@article{Guyenne2012,
author = {Guyenne, Ph. and Parau, E. I.},
doi = {10.1017/jfm.2012.458},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {oct},
pages = {307--329},
title = {{Computations of fully nonlinear hydroelastic solitary waves on deep water}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112012004582},
volume = {713},
year = {2012}
}
@article{Guza2012,
author = {Guza, R. T. and Feddersen, F.},
doi = {10.1029/2012GL051959},
issn = {0094-8276},
journal = {Geophysical Research Letters},
month = {jun},
number = {11},
pages = {L11607},
title = {{Effect of wave frequency and directional spread on shoreline runup}},
url = {http://www.agu.org/pubs/crossref/2012/2012GL051959.shtml},
volume = {39},
year = {2012}
}
@article{Ha2003,
author = {Ha, S.-Y. and Yang, T.},
doi = {10.1137/S0036141001397983},
issn = {0036-1410},
journal = {SIAM Journal on Mathematical Analysis},
month = {jan},
number = {5},
pages = {1226--1251},
title = {{L1 Stability for Systems of Hyperbolic Conservation Laws with a Resonant Moving Source}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0036141001397983},
volume = {34},
year = {2003}
}
@article{Hacker1996,
author = {Hacker, J. and Linden, P. F. and Dalziel, S. B.},
journal = {Dynamics of Atmospheres and Oceans},
pages = {183--195},
title = {{Mixing in lock-release gravity currents}},
volume = {24},
year = {1996}
}
@book{Hadamard1906,
address = {Paris},
author = {Hadamard, J.},
pages = {335},
publisher = {Librairie Armand Colin},
title = {{Le{\c{c}}ons sur la g{\'{e}}om{\'{e}}trie {\'{e}}l{\'{e}}mentaire}},
year = {1906}
}
@article{Haefliger1970,
author = {Haefliger, A.},
doi = {10.1016/0040-9383(70)90040-6},
issn = {00409383},
journal = {Topology},
month = {may},
number = {2},
pages = {183--194},
title = {{Feuilletages sur les vari{\'{e}}t{\'{e}}s ouvertes}},
volume = {9},
year = {1970}
}
@book{Hairer2002,
address = {Berlin, Heidelberg},
author = {Hairer, E. and Lubich, C. and Wanner, G.},
edition = {Second},
issn = {00278424},
pages = {644},
publisher = {Springer-Verlag},
series = {Spring Series in Computational Mathematics},
title = {{Geometric Numerical Integration}},
volume = {31},
year = {2006}
}
@book{Hairer2009,
author = {Hairer, E. and N{\o}rsett, S. P. and Wanner, G.},
pages = {528},
publisher = {Springer},
title = {{Solving ordinary differential equations: Nonstiff problems}},
year = {2009}
}
@book{Hairer1996,
abstract = {The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on one-step and extrapolation methods for stiff problems, another on multistep methods and general linear methods for stiff problems, a third on the treatment of singular perturbation problems, and a last one on differential-algebraic problems with applications to constrained mechanical systems. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g. in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.},
author = {Hairer, E. and Wanner, G.},
isbn = {978-3-642-05221-7},
pages = {614},
publisher = {Springer Series in Computational Mathematics, Vol. 14},
title = {{Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems}},
year = {1996}
}
@techreport{Hall1953,
author = {Hall, J. V. and Watts, J. W.},
institution = {Beach Erosion Board, USACE},
number = {33},
title = {{Laboratory investigation of the vertical rise of solitary waves on impermeable slopes}},
year = {1953}
}
@article{Hamburger1893,
author = {Hamburger, M.},
journal = {J. Reine Ang. Math.},
pages = {205--246},
title = {{Ueber die sigularen losungen der algebraischen differenzialgleichnungen erster ordnung}},
volume = {112},
year = {1893}
}
@incollection{Hamda2002,
address = {Paris},
author = {Hamda, H. and Jouve, F. and Lutton, E. and Schoenauer, M. and Sebag, M.},
booktitle = {Canum 2000: Actes du 32e Congr{\`{e}}s National d'Analyse Num{\'{e}}rique (Port d'Albret)},
pages = {153--179},
publisher = {Soc. Math. Appl. Indust.},
series = {ESAIM Proc.},
title = {{Repr{\'{e}}sentations non structur{\'{e}}es en optimisation topologique de formes par algorithmes {\'{e}}volutionnaires}},
volume = {11},
year = {2002}
}
@article{Hamidou2009,
author = {Hamidou, M. and Molin, B. and Kadri, M. and Kimmoun, O. and Tahakourt, A.},
journal = {Ocean Engineering},
pages = {1377--1385},
title = {{A coupling method between extended Boussinesq equations and the integral equation method with application to a two-dimensional numerical wave-tank}},
volume = {36},
year = {2009}
}
@phdthesis{Hamidouche2001,
abstract = {ON S'INTERESSE AUX PROPRIETES DES SOLUTIONS DES EQUATIONS DE TYPE KADOMTSEV-PETVIASHVILI. CES EQUATIONS PEUVENT ETRE CLASSES EN DEUX CATEGORIES : LES EQUATIONS DE TYPE KPI (DISPERSION TRANSVERSALE NEGATIVE) ET LES EQUATIONS DE TYPE KPII (DISPERSION TRANSVERSALE POSITIVE). CES EQUATIONS FONT INTERVENIR UN EXPOSANT P AU NIVEAU DU TERME NON LINEAIRE. ON COMMENCE PAR ETUDIER L'ANALYSE PAR PERTURBATION TRANSVERSALE D'UNE CLASSE DE SOLUTIONS PARTICULIERES APPELEES LINE-SOLITONS. ON MONTRE NUMERIQUEMENT L'EXISTENCE D'UNE CONDITION GEOMETRIQUE SUR LA LONGUEUR D'ONDE DE LA PERTURBATION POUR AVOIR LA STABILITE DU LINE-SOLITON EN CE QUI CONCERNE L'EQUATION DE KPI DANS LE CAS P = 2. PAR AILLEURS, ON S'INTERESSE A L'EVOLUTION DE DONNEES INITIALES LOCALISEES POUR LES EQUATIONS DE KPI ET KPII. ON MET EN EVIDENCE LES PHENOMENES SUIVANTS : COMPORTEMENT DISPERSIF, COMPORTEMENT DE TYPE SOLITONIQUE ET EXPLOSION EN TEMPS FINI. CES TESTS ONT ETE REFAITS POUR LES EQUATIONS DE KP REGULARISEES. ON RETROUVE LES PROPRIETES DE TYPE DISPERSION ET COMPORTEMENT SOLITONIQUE. ON N'A PAS EN REVANCHE DE COMPORTEMENT DE TYPE EXPLOSION EN TEMPS FINI EN RAISON DES PROPRIETES TRES REGULARISANTES DU TERME DE DISPERSION LONGITUDINALE. ON A CLOTURE AVEC L'ETUDE DE L'INTERACTION SOLITONIQUE POUR KPI ET KPI REGULARISEE LORSQUE P = 1.},
author = {Hamidouche, F.},
school = {Universit{\'{e}} Paris Sud},
title = {{Simulations num{\'{e}}riques des {\'{e}}quations de Kadomtsev-Petviashvili}},
type = {Ph.D.},
url = {http://www.sudoc.fr/071369481},
year = {2001}
}
@article{Hammack,
abstract = {The waves generated in a two-dimensional fluid domain of infinite lateral extent and uniform depth by a deformation of the bounding solid boundary are investigated both theoretically and experimentally. An integral solution is developed for an arbitrary bed displacement (in space and time) on the basis of a linear approximation of the complete (nonlinear) description of wave motion. Experimental and theoretical results are presented for two specific deformations of the bed; the spatial variation of each bed displacement consists of a block section of the bed moving vertically either up or down while the time-displacement history of the block section is varied. The presentation of results is divided into two sections based on two regions of the fluid domain: a generation region in which the bed deformation occurs and a downstream region where the bed position remains stationary for all time. The applicability of the linear approximation in the generation region is investigated both theoretically and experimentally; results are presented which enable certain gross features of the primary wave leaving this region to be determined when the magnitudes of parameters which characterize the bed displacement are known. The results indicate that the primary restriction on the applicability of the linear theory during the bed deformation is that the total amplitude of the bed displacement must remain small compared with the uniform water depth; even this restriction can be relaxed for one type of bed motion. Wave behaviour in the downstream region of the fluid domain is discussed with emphasis on the gradual growth of nonlinear effects relative to frequency dispersion duringpropagationand the subsequent breakdown of the linear theory. A method is presented for finding the wave behaviour in the far field of the downstream region, where the effects of nonlinearities and frequency dispersion have become about equal. This method is based on the use of a model equation in the far field (which includes both linear and nonlinear effects in an approximate manner) first used by Peregrine (1966) and morerecently advocated by Ben jamin, Bona {\&} Mahony (1972) as a preferable model to the more commonly used equation of Korteweg {\&} de Vries (1895). An input-output approach is illustrated for the numerical solution of this equation where the input is computed from the linear theory in its region of applicability. Computations are presented and compared with experiment for the case of a positive bed displacement where the net volume of the generated wave is finite and positive; the results demonstrate the evolution of a train of solitary waves (solitons) ordered by amplitude followed by a dispersive train of oscillatory waves. The case of a negative bed displacement in which the net wave volume is finite and negative (and the initial wave is negative almost everywhere) is also investigated; the results suggest that only a dispersive train of waves evolves (no solitons) for this case.},
annote = {W. M. Keck Laboratory of Hydraulics and Water Resources, California
Institute of Technology, Pasadena},
author = {Hammack, J.},
journal = {J. Fluid Mech.},
pages = {769--799},
title = {{A note on tsunamis: their generation and propagation in an ocean of uniform depth}},
volume = {60},
year = {1973}
}
@phdthesis{Hammack1972,
abstract = {A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered. An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model. Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of nonlinear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation. A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation. An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally. The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.},
author = {Hammack, J. L.},
school = {California Institute of Technology},
title = {{Tsunamis - A Model of Their Generation and Propagation}},
year = {1972}
}
@article{Segur2,
author = {Hammack, J. L. and Segur, H.},
journal = {J. Fluid Mech.},
pages = {289--314},
title = {{The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments}},
volume = {65},
year = {1974}
}
@article{Segur3,
author = {Hammack, J. L. and Segur, H.},
journal = {J. Fluid Mech.},
pages = {337--358},
title = {{The Korteweg-de Vries equation and water waves. Part 3. Oscillatory waves}},
volume = {84},
year = {1978}
}
@inproceedings{Hammack2004,
author = {Hammack, J. and Henderson, D. and Guyenne, P. and Yi, M.},
booktitle = {Proc. 23rd International Conference on Offshore Mechanics and Arctic Engineering},
title = {{Solitary wave collisions}},
year = {2004}
}
@article{Hammani2011,
author = {Hammani, K. and Kibler, B. and Finot, C. and Morin, P. and Fatome, J. and Dudley, J. M. and Millot, G.},
journal = {Optics Letters},
pages = {112--114},
title = {{The Peregrine soliton in a standard telecommunication fiber-based set-up}},
volume = {26},
year = {2011}
}
@article{Hammerton2013,
abstract = {The propagation of long wavelength disturbances on the surface of a fluid layer of finite depth is considered. Attention is focused on the effect of stress applied at the surface. Constant surface tension leads to a normal stress at the surface, but the presence of a surfactant or the application of an electric field can give rise to tangential stresses. In the large Reynolds number limit, the evolution equation for the surface elevation contains contributions from both boundary layers in the flow; one is adjacent to the free surface while the other lies at the base of the fluid layer.Aweakly non-linear analysis is performed leading to an evolution equation similar to the classic Korteweg-de Vries equation, but modified by additional terms due to the viscosity and to the tangential and normal stress at the surface. It is demonstrated that careful treatment of the boundary layer at the free surface is necessary when the tangential stress at the surface is non-zero. Particular cases of flows with tangential surface stress due the presence of a surfactant or due to an electric field are discussed, and a pseudo-spectral scheme is used in order to obtain some typical numerical results.},
author = {Hammerton, P. W. and Bassom, A. P.},
doi = {10.1093/qjmam/hbt012},
issn = {0033-5614},
journal = {Q. J. Mechanics Appl. Math.},
month = {jul},
number = {3},
pages = {395--416},
title = {{The effect of surface stress on interfacial solitary wave propagation}},
url = {http://qjmam.oxfordjournals.org/cgi/doi/10.1093/qjmam/hbt012},
volume = {66},
year = {2013}
}
@article{Hansom2009,
author = {Hansom, J. D. and Hall, A. M.},
journal = {Quaternary International},
pages = {42--52},
title = {{Magnitude and frequency of extra-tropical North Atlantic cyclones: A chronology from cliff-top storm deposits}},
volume = {195},
year = {2009}
}
@book{Happel1983,
abstract = {Low Reynolds number flow theory finds wide application in such diverse fields as sedimentation, fluidization, particle-size classification, dust and mist collection, filtration, centrifugation, polymer and suspension rheology, flow through porous media, colloid science, aerosol and hydrosal technology, lubrication theory, blood flow, Brownian motion, geophysics, meteorology, and a host of other disciplines. This text provides a comprehensive and detailed account of the physical and mathematical principles underlying such phenomena, heretofore available only in the original literature.},
author = {Happel, J. and Brenner, H.},
publisher = {D. Reidel Publishing Co., Hingham, MA},
title = {{Low Reynolds number hydrodynamics}},
year = {1983}
}
@article{Haragus2008,
author = {Haragus, M. and Kapitula, T.},
doi = {10.1016/j.physd.2008.03.050},
issn = {01672789},
journal = {Phys. D},
month = {oct},
number = {20},
pages = {2649--2671},
title = {{On the spectra of periodic waves for infinite-dimensional Hamiltonian systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278908001292},
volume = {237},
year = {2008}
}
@article{Harbitz1992,
author = {Harbitz, C.},
journal = {Marine Geology},
pages = {1--21},
title = {{Model simulations of tsunamis generated by the Storegga Slides}},
volume = {104},
year = {1992}
}
@article{Harbitz2006,
abstract = {The characteristics of a tsunami generated by a submarine landslide are mainly determined by the volume, the initial acceleration, the maximum velocity, and the possible retrogressive behaviour of the landslide. The influence of these features as well as water depth and distance from shore are discussed. Submarine landslides are often clearly sub-critical (Froude number 1), and it is explained that the maximum tsunami elevation generally correlates with the product of the landslide volume and acceleration divided by the wave speed squared. Only a limited part of the potential energy released by the landslide is transferred to wave energy. Examples of numerical simulations with fractions of 0.1-15{\%} are presented. Frequency dispersion is of little importance for waves generated by large and sub-critical submarine landslides. Retrogressive landslide behaviour normally reduces associated tsunami heights, but retrogression might increase the height of the landward propagating wave for unfavourable time lags between release of individual elements of the total landslide mass. Tsunamis generated by submarine landslides often have very large run-up heights close to the source area, but have more limited far-field effects than earthquake tsunamis. It is further shown that the combination of landslides and earthquakes may be necessary to explain observed tsunami behaviour. The various aspects mentioned above are exemplified by simulations of the Holocene Storegga Slide, the 1998 Papua New Guinea, and the 2004 Indian Ocean tsunamis. Comparisons are also made to tsunamis generated by rock slides. Rock slides are most often super-critical and the resulting tsunamis are determined by the frontal area of the rock slide, the impact velocity of the rock slide on the water body, the permeability of the rock slide, and the bathymetry.},
author = {Harbitz, C. B. and Lovholt, F. and Pedersen, G. and Glimsdal, S. and Masson, D. G.},
journal = {Norwegian Journal of Geology},
keywords = {qe geology},
number = {3},
pages = {255--264},
title = {{Mechanisms of tsunami generation by submarine landslides - a short review}},
url = {http://eprints.soton.ac.uk/42982/},
volume = {86},
year = {2006}
}
@article{Harlow1965,
author = {Harlow, F. H. and Welch, J. E.},
journal = {Phys. Fluids},
pages = {2182},
title = {{Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface}},
volume = {8},
year = {1965}
}
@book{Harlow1971,
author = {Harlow, F. and Amsden, A.},
publisher = {LANL Monograph LA-4700},
title = {{Fluid dynamics}},
year = {1971}
}
@article{Harris2013,
abstract = {We study the kinematics of nonlinear resonance broadening of interacting Rossby waves as modelled by the Charney-Hasegawa-Mima equation on a biperiodic domain. We focus on the set of wave modes which can interact quasi-resonantly at a particular level of resonance broadening and aim to characterize how the structure of this set changes as the level of resonance broadening is varied. The commonly held view that resonance broadening can be thought of as a thickening of the resonant manifold is misleading. We show that in fact the set of modes corresponding to a single quasi-resonant triad has a non-trivial structure and that its area in fact diverges for a finite degree of broadening. We also study the connectivity of the network of modes which is generated when quasi-resonant triads share common modes. This network has been argued to form the backbone for energy transfer in Rossby wave turbulence. We show that this network undergoes a percolation transition when the level of resonance broadening exceeds a critical value. Below this critical value, the largest connected component of the quasi-resonant network contains a negligible fraction of the total number of modes in the system whereas above this critical value a finite fraction of the total number of modes in the system are contained in the largest connected component. We argue that this percolation transition should correspond to the transition to turbulence in the system.},
author = {Harris, J. and Connaughton, C. and Bustamante, M. D.},
doi = {10.1088/1367-2630/15/8/083011},
issn = {1367-2630},
journal = {New J. Phys.},
month = {aug},
number = {8},
pages = {083011},
title = {{Percolation transition in the kinematics of nonlinear resonance broadening in Charney-Hasegawa-Mima model of Rossby wave turbulence}},
volume = {15},
year = {2013}
}
@article{Hartel2000,
author = {H{\"{a}}rtel, C. J. and Meiburg, E. and Necker, F.},
journal = {J. Fluid Mech.},
pages = {189--212},
title = {{Analysis and Direct Numerical Simulation of the Flow at a Gravity-current Head. Part 1. Flow topology and front speed for slip and no-slip boundaries}},
volume = {418(9)},
year = {2000}
}
@article{Harten1989,
author = {Harten, A.},
journal = {J. Comput. Phys},
pages = {148--184},
title = {{ENO schemes with subcell resolution}},
volume = {83},
year = {1989}
}
@article{Harten1983,
author = {Harten, A.},
journal = {J. Comp. Phys.},
pages = {357--393},
title = {{High resolution schemes for hyperbolic conservation laws}},
volume = {49},
year = {1983}
}
@article{Harten1983a,
author = {Harten, A. and Lax, P. D. and van Leer, B.},
journal = {SIAM Review},
pages = {35--61},
title = {{On upstream differencing and Godunov-type schemes for hyperbolic conservation laws}},
volume = {25},
year = {1983}
}
@article{HaOs,
author = {Harten, A. and Osher, S.},
journal = {SIAM J. Numer. Anal.},
pages = {279--309},
title = {{Uniformly high-order accurate nonscillatory schemes. I}},
volume = {24},
year = {1987}
}
@incollection{Harterich2005,
address = {Berlin, Heidelberg},
author = {H{\"{a}}rterich, J. and Liebscher, S.},
booktitle = {Analysis and Numerics for Conservation Laws},
doi = {10.1007/3-540-27907-5{\_}12},
editor = {Warnecke, G.},
pages = {281--300},
publisher = {Springer Berlin Heidelberg},
title = {{Travelling Waves in Systems of Hyperbolic Balance Laws}},
url = {http://link.springer.com/10.1007/3-540-27907-5{\_}12},
year = {2005}
}
@book{Hartshorne1977,
abstract = {An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality" "Foundations of Projective Geometry" "Ample Subvarieties of Algebraic Varieties" and numerous research titles.},
address = {New York},
author = {Hartshorne, R.},
edition = {1},
isbn = {978-0387902449},
pages = {496},
publisher = {Springer Verlag},
title = {{Algebraic Geometry}},
year = {1977}
}
@article{Hasimoto1972,
abstract = {Slow modulation of gravity waves on water layer with uniform depth is investigated by using singular perturbation methods. It is found, to the lowest order of perturbation, that the complicated system of equations governing such modulation can be reduced to a simple nonlinear Schrodinger equation. A nonlinear plane wave solution to this equation is found to correspond to the so-called Stokes wave. The linear stability of this plane wave solution is essentially determined by the sign of the product of two coefficients in this equation, yielding Benjamin and Whitham's criterion. The same equation is found to give a weak cnoidal wave derived from the Korteweg-de Vries equation in the shallow-water limit.},
author = {Hasimoto, H. and Ono, H.},
doi = {10.1143/JPSJ.33.805},
issn = {0031-9015},
journal = {Journal of the Physical Society of Japan},
month = {mar},
number = {3},
pages = {805--811},
title = {{Nonlinear Modulation of Gravity Waves}},
url = {http://jpsj.ipap.jp/link?JPSJ/33/805/},
volume = {33},
year = {1972}
}
@article{Haskell1969,
author = {Haskell, N. A.},
journal = {Bull. Seism. Soc. Am.},
pages = {865--908},
title = {{Elastic displacements in the near-field of a propagating fault}},
volume = {59},
year = {1969}
}
@article{Hassani2007,
author = {Hassani, R. and Ionescu, I. R. and Oudet, E.},
doi = {10.1016/j.ijsolstr.2007.02.020},
journal = {Internat. J. Solids Structures},
number = {18-19},
pages = {6187--6200},
title = {{Critical friction for wedged configurations: A genetic algorithm approach}},
url = {http://dx.doi.org/10.1016/j.ijsolstr.2007.02.020},
volume = {44},
year = {2007}
}
@article{Hasselmann1980,
author = {Hasselmann, D. E. and Dunckel, M. and Ewing, J. A.},
journal = {Journal of Physical Oceanography},
number = {8},
pages = {1264--1280},
title = {{Directional Wave Spectra Observed during JONSWAP 1973}},
volume = {10},
year = {1980}
}
@article{Hasselmann1962,
abstract = {The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order analysis yields a fourth-order effect comparable in magnitude to the generating and dissipating processes in wind-generated seas. The energy flux favours equidistribution of energy and vanishes in the limiting case of a white, isotropic spectrum. The influence on the equilibrium structure of fully developed wave spectra and on other phenomena in random seas is discussed briefly.},
author = {Hasselmann, K.},
doi = {10.1017/S0022112062000373},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {04},
pages = {481--500},
title = {{On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory}},
volume = {12},
year = {1962}
}
@article{Hasselmann1976,
author = {Hasselmann, K. and Sell, W. and Ross, D. B. and M{\"{u}}ller, P.},
issn = {0022-3670},
journal = {J. Phys. Oceanogr.},
month = {mar},
number = {2},
pages = {200--228},
title = {{A Parametric Wave Prediction Model}},
volume = {6},
year = {1976}
}
@article{Hayes2000,
abstract = {We consider strictly hyperbolic systems of conservation laws whose characteristic fields are not genuinely nonlinear, and we introduce a framework for the nonclassical shocks generated by diffusive or diffusive-dispersive approximations. A nonclassical shock does not fulfill the Liu entropy criterion and turns out to be undercompressive. We study the Riemann problem in the class of solutions satisfying a single entropy inequality, the only such constraint available for general diffusive-dispersive approximations. Each non-genuinely nonlinear characteristic field admits a two-dimensional wave set, instead of the classical one-dimensional wave curve. In specific applications, these wave sets are narrow and resemble the classical curves. We find that even in strictly hyperbolic systems, nonclassical shocks with arbitrarily small amplitudes occur. The Riemann problem can be solved uniquely using nonclassical shocks, provided an additional constraint is imposed: we stipulate that the entropy dissipation across any nonclassical shock be a given constitutive function. We call this admissibility criterion a kinetic relation, by analogy with similar laws introduced in material science for propagating phase boundaries. In particular, the kinetic relation may be expressed as a function of the propagation speed. It is derived from traveling waves and, typically, depends on the ratioof the diffusion and dispersion parameters.},
author = {Hayes, B. T. and LeFloch, Ph. G.},
doi = {10.1137/S0036141097319826},
issn = {0036-1410},
journal = {SIAM J. Math. Anal.},
month = {jan},
number = {5},
pages = {941--991},
title = {{Nonclassical Shocks and Kinetic Relations: Strictly Hyperbolic Systems}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0036141097319826},
volume = {31},
year = {2000}
}
@techreport{Hayes2011,
author = {Hayes, G.},
institution = {USGS},
title = {{Finite Fault Model Result of the Mar 11, 2011 Mw 9.0 Earthquake Offshore Honshu, Japan}},
url = {$\backslash$url{\{}http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite{\_}fault.php{\}}},
year = {2011}
}
@techreport{Hayes2010,
author = {Hayes, G.},
institution = {USGS},
title = {{Finite Fault Model Result of the Oct 25, 2010 Mw 7.7 Southern Sumatra Earthquake}},
url = {$\backslash$url{\{}http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/usa00043nx/finite{\_}fault.php{\}}},
year = {2010}
}
@article{Hecht2012,
abstract = {This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer.},
author = {Hecht, F.},
doi = {10.1515/jnum-2012-0013},
issn = {1569-3953},
journal = {Journal of Numerical Mathematics},
keywords = {Schwarz domain decomposition,finite element,freefem++,mesh adaptation,parallel computing},
month = {jan},
number = {3-4},
pages = {251--266},
title = {{New development in Freefem++}},
url = {http://www.degruyter.com/view/j/jnma.2012.20.issue-3-4/jnum-2012-0013/jnum-2012-0013.xml},
volume = {20},
year = {2012}
}
@book{Hecht1998,
author = {Hecht, F. and Pironneau, O. and {Le Hyaric}, A. and Ohtsuka, K.},
publisher = {Laboratoire JL Lions, University of Paris VI, France},
title = {{FreeFem++}}
}
@article{Heemink1990,
abstract = {A random walk model to describe the dispersion of pollutants in shallow water is developed. By deriving the Fokker-Planck equation, the model is shown to be consistent with the two-dimensional advection-diffusion equation with space-varying dispersion coefficient and water depth. To improve the behaviour of the model shortly after the deployment of the pollutant, a random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection-diffusion equation. The various numerical aspects of the implementation of the stochastic models are discussed and finally a realistic application to predict the dispersion of a pollutant in the Eastern Scheldt estuary is described.},
author = {Heemink, A. W.},
doi = {10.1007/BF01543289},
issn = {0931-1955},
journal = {Stochastic Hydrology and Hydraulics},
month = {jun},
number = {2},
pages = {161--174},
title = {{Stochastic modelling of dispersion in shallow water}},
url = {http://link.springer.com/10.1007/BF01543289},
volume = {4},
year = {1990}
}
@article{Heitner1970,
author = {Heitner, K. L. and Housner, G. W.},
journal = {J. Waterway, Port, Coastal and Ocean Engineering},
pages = {701--719},
title = {{Numerical model for tsunami runup}},
volume = {96},
year = {1970}
}
@article{Helal2001,
abstract = {It is well known that many hydrodynamical problems appearing in the study of shallow water theory or the theory of rotating fluids, can be reduced to Korteweg-de Vries equation subject to certain initial and boundary conditions. In this work, a Chebyshev spectral method for obtaining a semi-analytical solution to such equation is presented. One numerical application is considered to show how we can apply the presented proposed method. A comparison between our results and the numerical results obtained by the Hopscotch method are made.},
author = {Helal, M. A.},
doi = {10.1016/S0960-0779(00)00131-4},
journal = {Chaos, Solitons {\&} Fractals},
number = {5},
pages = {943--950},
title = {{A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application}},
volume = {12},
year = {2001}
}
@article{Golay2005,
abstract = {This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.},
author = {Helluy, Ph. and Golay, F. and Caltagirone, J.-P. and Lubin, P. and Vincent, S. and Drevard, D. and Marcer, R. and Fraunie, Ph. and Seguin, N. and Grilli, S. and Lesage, A.-C. and Dervieux, A. and Allain, O.},
journal = {Mathematical Modelling and Numerical Analysis},
number = {3},
pages = {591--607},
title = {{Numerical simulation of wave breaking}},
url = {http://hal.archives-ouvertes.fr/hal-00139601/en/},
volume = {39},
year = {2005}
}
@article{Helmholtz1868,
author = {Helmholtz, H.},
journal = {Monthly Reports of the Royal Prussian Academy of Philosophy in Berlin},
pages = {215},
title = {{On the discontinuous movements of fluids}},
volume = {23},
year = {1868}
}
@article{Helmholtz1858,
author = {Helmholtz, H.},
journal = {Journal f{\"{u}}r die reine und angewandte Mathematik},
pages = {25--55},
title = {{{\"{U}}ber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen}},
volume = {55},
year = {1858}
}
@article{Henderson2010,
abstract = {Recent predictions from competing theoretical models have disagreed about the stability/instability of bi-periodic patterns of surface waves on deep water. We present laboratory experiments to address this controversy. Growth rates of modulational perturbations are compared to predictions from: (i) inviscid coupled nonlinear Schr{\"{o}}dinger (NLS) equations, according to which the patterns are unstable and (ii) dissipative coupled NLS equations, according to which they are linearly stable. For bi-periodic wave patterns of small amplitude and nearly permanent form, we find that the dissipative model predicts the experimental observations more accurately. Hence, our experiments support the claim that these bi-periodic wave patterns are linearly stable in the presence of damping. For bi-periodic wave patterns of large enough amplitude or subject to large enough perturbations, both models fail to predict accurately the observed behaviour, which includes frequency downshifting.},
author = {Henderson, D. and Segur, H. and Carter, J. D.},
doi = {10.1017/S0022112010001643},
issn = {0022-1120},
journal = {J. Fluid Mech},
keywords = {stability,surface gravity waves},
month = {aug},
pages = {247--278},
title = {{Experimental evidence of stable wave patterns on deep water}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112010001643},
volume = {658},
year = {2010}
}
@article{Henderson1999,
author = {Henderson, K. L. and Peregrine, D. H. and Dold, J. W.},
journal = {Wave Motion},
pages = {341--361},
title = {{Unsteady water wave modulation: fully nonlinear solutions and comparison with the nonlinear Schr{\"{o}}dinger equation}},
volume = {29},
year = {1999}
}
@inproceedings{HermannF.andIsslerD.andKeller1993,
address = {Grenoble},
author = {Hermann, F. and Issler, D. and Keller, S.},
booktitle = {Comptes Rendus International Workshop on Gravitational Mass Movements},
editor = {Buisson, L},
pages = {137--144},
title = {{Numerical simulations of powder-snow avalanches and laboratory experiments in turbidity currents}},
year = {1993}
}
@book{Hermite1891,
address = {Paris},
author = {Hermite, Ch.},
edition = {Quatri{\`{e}}me},
pages = {383},
publisher = {Librairie Scientifique A. Hermannn},
title = {{Cours d'analyse}},
year = {1891}
}
@book{Herrera1984,
author = {Herrera, I.},
publisher = {Pitman},
title = {{Boundary Methods: An Algebraic Theory}},
year = {1984}
}
@inproceedings{Herrera1982,
address = {Tokyo},
author = {Herrera, I.},
booktitle = {Finite Elements Flow Analysis},
editor = {Kawai, T.},
pages = {897--906},
publisher = {University of Tokyo Press},
title = {{Boundary methods: development of complete systems of solutions}},
year = {1982}
}
@article{Herterich1980,
author = {Herterich, K. and Hasselmann, K.},
doi = {10.1017/S0022112080002522},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
number = {01},
pages = {215--224},
title = {{A similarity relation for the nonlinear energy transfer in a finite-depth gravity-wave spectrum}},
volume = {97},
year = {1980}
}
@article{Herty2013,
author = {Herty, M. and Sea{\"{\i}}d, M.},
doi = {10.1002/fld.3719},
issn = {02712091},
journal = {Int. J. Num. Meth. Fluids},
month = {apr},
number = {11},
pages = {1438--1460},
title = {{Assessment of coupling conditions in water way intersections}},
url = {http://doi.wiley.com/10.1002/fld.3719},
volume = {71},
year = {2013}
}
@article{Hervouet2000,
author = {Hervouet, J.-M.},
journal = {Hydrol. Process.},
pages = {2211--2230},
title = {{A high resolution 2-D dam-break model using parallelization}},
volume = {14},
year = {2000}
}
@article{Hibberd1979,
author = {Hibberd, S. and Peregrine, D. H.},
journal = {J. Fluid Mech.},
pages = {323--345},
title = {{Surf and run-up on a beach: a uniform bore}},
volume = {95},
year = {1979}
}
@article{Higham2001,
abstract = {A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler's method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable; however, no knowledge of advanced probability theory or stochastic processes is assumed. The article is built around 10 MATLAB programs, and the topics covered include stochastic integration, the Euler-Maruyama method, Milstein's method, strong and weak convergence, linear stability, and the stochastic chain rule.},
author = {Higham, D. J.},
doi = {10.1137/S0036144500378302},
issn = {0036-1445},
journal = {SIAM Review},
month = {jan},
number = {3},
pages = {525--546},
title = {{An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0036144500378302},
volume = {43},
year = {2001}
}
@article{Higham1993,
author = {Higham, D. J. and Trefethen, L. N.},
doi = {10.1007/BF01989751},
journal = {BIT Numerical Mathematics},
number = {2},
pages = {285--303},
title = {{Stiffness of ODEs}},
volume = {33},
year = {1993}
}
@book{Higham2002,
author = {Higham, N. J.},
edition = {2nd ed.},
publisher = {SIAM Philadelphia},
title = {{Accuracy and Stability of Numerical Algorithms}},
year = {2002}
}
@article{Hilbert1915,
author = {Hilbert, D.},
journal = {Konigl. Gesell. d. Wiss. G{\"{o}}ttingen, Nachr. Math.-Phys. Kl.},
pages = {395--407},
title = {{Die Grundlagen der Physik}},
year = {1915}
}
@article{Hillairet2007,
author = {Hillairet, M.},
doi = {10.1007/s00021-005-0202-6},
journal = {J. Math. Fluid. Mech.},
month = {aug},
number = {3},
pages = {343--376},
title = {{Propagation of density-oscillations in solutions to barotropic compressible Navier-Stokes system}},
volume = {9},
year = {2007}
}
@article{Hirt1981,
author = {Hirt, C. W. and Nichols, B. D.},
journal = {J. Comput. Phys.},
pages = {201--225},
title = {{Volume of fluid (VOF) method for the dynamics of free boundaries}},
volume = {39},
year = {1981}
}
@article{Hochbruck2010,
author = {Hochbruck, M. and Ostermann, A.},
doi = {10.1017/S0962492910000048},
journal = {Acta Numerica},
pages = {209--286},
title = {{Exponential integrators}},
year = {2010}
}
@article{Hoefer2007,
abstract = {Collisions and interactions of dispersive shock waves in defocusing (repulsive) nonlinear Schr{\"{o}}dinger type systems are investigated analytically and numerically. Two canonical cases are considered. In one case, two counterpropagating dispersive shock waves experience a head-on collision, interact and eventually exit the interaction region with larger amplitudes and altered speeds. In the other case, a fast dispersive shock overtakes a slower one, giving rise to an interaction. Eventually the two merge into a single dispersive shock wave. In both cases, the interaction region is described by a modulated, quasi-periodic two-phase solution of the nonlinear Schr{\"{o}}dinger equation. The boundaries between the background density, dispersive shock waves and their interaction region are calculated by solving the Whitham modulation equations. These asymptotic results are in excellent agreement with full numerical simulations. It is further shown that the interactions of two dispersive shock waves have some qualitative similarities to the interactions of two classical shock waves.},
author = {Hoefer, M. A. and Ablowitz, M. J.},
doi = {10.1016/j.physd.2007.07.017},
issn = {01672789},
journal = {Phys. D},
keywords = {Bose-Einstein condensates,Dispersive shock wave interactions,Dispersive shock waves,Nonlinear Schrodinger equation,Nonlinear optics,Shock wave interactions,Shock waves},
month = {dec},
number = {1},
pages = {44--64},
title = {{Interactions of dispersive shock waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278907002412},
volume = {236},
year = {2007}
}
@article{Hof2003,
author = {Hof, B. and Juel, A. and Mullin, T.},
doi = {10.1103/PhysRevLett.91.244502},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {dec},
number = {24},
pages = {244502},
title = {{Scaling of the Turbulence Transition Threshold in a Pipe}},
volume = {91},
year = {2003}
}
@article{Hof2004,
abstract = {Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable traveling waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these traveling waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.},
author = {Hof, B. and van Doorne, C. W. H. and Westerweel, J. and Nieuwstadt, F. T. M. and Faisst, H. and Eckhardt, B. and Wedin, H. and Kerswell, R. R. and Waleffe, F.},
doi = {10.1126/science.1100393},
issn = {1095-9203},
journal = {Science},
month = {sep},
number = {5690},
pages = {1594--1598},
pmid = {15361619},
title = {{Experimental observation of nonlinear traveling waves in turbulent pipe flow.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15361619},
volume = {305},
year = {2004}
}
@article{Hofmeister2011,
author = {Hofmeister, R. and Beckers, J.-M. and Burchard, H.},
journal = {Ocean Modelling},
pages = {233--247},
title = {{Realistic modelling of the major inflows into the central Baltic Sea in 2003 using terrain-following coordinates}},
volume = {39},
year = {2011}
}
@article{Hofmeister2010,
author = {Hofmeister, R. and Burchard, H. and Beckers, J.-M.},
journal = {Ocean Modelling},
pages = {70--86},
title = {{Non-uniform adaptive vertical grids for 3D numerical ocean models}},
volume = {33},
year = {2010}
}
@article{Hogan1985,
abstract = {The stability of a train of nonlinear gravity-capillary waves on the surface of an ideal fluid of infinite depth is considered. An evolution equation is derived for the wave envelope, which is correct to fourth order in the wave steepness. The derivation is made from the Zakharov equation under the assumption of a narrow band of waves, and including the full form of the interaction coefficient for gravity-capillary waves. It is assumed that conditions are away from subharmonic resonant wavelengths. Just as was found by K. B. Dysthe (Proc. R. Soc. Lond. A 369 (1979)) for pure gravity waves, the main difference from the third-order evolution equation is, as far as stability is concerned, the introduction of a mean flow response. There is a band of waves that remains stable to fourth order. In general the mean flow effects for pure capillary waves are of opposite sign to those of pure gravity waves. The second-order corrections to first-order stability properties are shown to depend on the interaction between the mean flow and the envelope frequency-dispersion term in the governing equation. The results are shown to be in agreement with some recent computations of the full problem for sufficiently small values of the wave steepness.},
author = {Hogan, S. J.},
journal = {Proc. R. Soc. A},
number = {1823},
pages = {359--372},
title = {{The fourth-order evolution equation for deep-water gravity-capillary waves}},
volume = {402},
year = {1985}
}
@article{Hogan1986,
author = {Hogan, S. J.},
journal = {Physics of Fluids},
number = {10},
pages = {3479--3480},
title = {{The potential form of the 4th-order evolution equation for deep-water gravity capillary waves}},
volume = {29},
year = {1986}
}
@article{Holm1988,
author = {Holm, D.},
journal = {Phys. Fluids},
number = {8},
pages = {2371--2373},
title = {{Hamiltonian structure for two-dimensional hydrodynamics with nonlinear dispersion}},
volume = {31},
year = {1988}
}
@article{Holman1986,
author = {Holman, R. A.},
doi = {10.1016/0378-3839(86)90002-5},
issn = {03783839},
journal = {Coastal Engineering},
month = {mar},
number = {6},
pages = {527--544},
title = {{Extreme value statistics for wave run-up on a natural beach}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0378383986900025},
volume = {9},
year = {1986}
}
@inproceedings{Holmes1989,
author = {Holmes, D. G. and Connel, S. D.},
booktitle = {AIAA 9th Computational Fluid Dynamics Conference},
month = {jun},
title = {{Solution of the 2D Navier-Stokes equations on unstructured adaptive grids}},
volume = {89-1932-CP},
year = {1989}
}
@article{Holzer2012,
abstract = {We study invasion speeds in the Lotka-Volterra competition model when the rate of diffusion of one species is small. Our main result is the construction of the selected front and a rigorous asymptotic approximation of its propagation speed, valid to second order. We use techniques from geometric singular perturbation theory and geometric desingularization. The main challenge arises from the slow passage through a saddle-node bifurcation. From a perspective of linear versus nonlinear speed selection, this front provides an interesting example as the propagation speed is slower than the linear spreading speed. However, our front shares many characteristics with pushed fronts that arise when the influence of nonlinearity leads to faster than linear speeds of propagation. We show that this is a result of the linear spreading speed arising as a simple pole of the resolvent instead of as a branch pole. Using the pointwise Green's function, we show that this pole poses no a priori obstacle to marginal stability of the nonlinear travelling front, thus explaining how nonlinear systems can exhibit slower spreading that their linearization in a robust fashion.},
author = {Holzer, M. and Scheel, A.},
doi = {10.1088/0951-7715/25/7/2151},
issn = {0951-7715},
journal = {Nonlinearity},
month = {jul},
number = {7},
pages = {2151--2179},
title = {{A slow pushed front in a Lotka–Volterra competition model}},
url = {http://stacks.iop.org/0951-7715/25/i=7/a=2151?key=crossref.012b4f0ee92682c66d4c82165356a5ed},
volume = {25},
year = {2012}
}
@article{Hong2006,
author = {Hong, J. M.},
doi = {10.1016/j.jde.2005.06.016},
issn = {00220396},
journal = {J. Diff. Eqns.},
month = {mar},
number = {2},
pages = {515--549},
title = {{An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by “weaker than weak” solutions of the Riemann problem}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039605002202},
volume = {222},
year = {2006}
}
@article{Hong2003,
abstract = {We describe the generic solution of the Riemann problem near a point of resonance in a general 2x2 system of balance laws coupled to a stationary source. The source is treated as a conserved quantity in an augmented 3x3 system, and Resonance is between a nonlinear wave family and the stationary source. Transonic compressible Euler flow in a variable area duct, as well as spherically symmetric flow, are shown to be special cases of the general class of equations studied here.},
author = {Hong, J. and Temple, B.},
journal = {Methods Appl. Anal.},
number = {2},
pages = {279--294},
title = {{The Generic Solution of the Riemann Problem in a Neighborhood of a Point of Reaonance for Systems of Nonlinear Balance Laws}},
volume = {10},
year = {2003}
}
@article{Hoogakker2004,
author = {Hoogakker, B. A. A. and Rothwell, R. G. and Rohling, E. J. and Paterne, M. and Stow, D. A. V. and Herrle, J. O. and Clayton, T.},
journal = {Marine Geology},
pages = {21--43},
title = {{Variations in terrigenous dilution in western Mediterranean Sea pelagic sediments in response to climate change during the last glacial cycle}},
volume = {211},
year = {2004}
}
@article{Hopfinger1983,
author = {Hopfinger, E. J.},
journal = {Ann. Rev. Fluid Mech.},
pages = {47--76},
title = {{Snow avalanche motion and related phenomena}},
volume = {15},
year = {1983}
}
@article{Hopfinger1977,
author = {Hopfinger, E. J. and Tochon-Danguy, J.-C.},
journal = {Journal of Glaciology},
pages = {343--356},
title = {{A model study of powder-snow avalanches}},
volume = {81},
year = {1977}
}
@article{Hosono2003,
author = {Hosono, Y.},
journal = {Discrete Contin. Dynam. Syst. Ser. B},
number = {1},
pages = {79--95},
title = {{Traveling waves for a diffusive Lotka-Volterra competition model I: singular perturbations}},
volume = {3},
year = {2003}
}
@article{Hou2007,
abstract = {In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations. We consider two different ways of removing the aliasing errors in a pseudo-spectral method. The first one is the traditional 2/3 dealiasing rule. The second one is a high (36th) order Fourier smoothing which keeps a significant portion of the Fourier modes beyond the 2/3 cut-off point in the Fourier spectrum for the 2/3 dealiasing method. Both the 1D Burgers equation and the 3D incompressible Euler equations are considered. We demonstrate that the pseudo-spectral method with the high order Fourier smoothing gives a much better performance than the pseudo-spectral method with the 2/3 dealiasing rule. Moreover, we show that the high order Fourier smoothing method captures about 12–15{\%} more effective Fourier modes in each dimension than the 2/3 dealiasing method. For the 3D Euler equations, the gain in the effective Fourier codes for the high order Fourier smoothing method can be as large as 20{\%} over the 2/3 dealiasing method. Another interesting observation is that the error produced by the high order Fourier smoothing method is highly localized near the region where the solution is most singular, while the 2/3 dealiasing method tends to produce oscillations in the entire domain. The high order Fourier smoothing method is also found be very stable dynamically. No high frequency instability has been observed. In the case of the 3D Euler equations, the energy is conserved up to at least six digits of accuracy throughout the computations.},
author = {Hou, T. Y. and Li, R.},
doi = {10.1016/j.jcp.2007.04.014},
issn = {00219991},
journal = {J. Comp. Phys.},
keywords = {Dealiasing,Incompressible flow,Pseudo spectral methods,Singular solutions},
month = {sep},
number = {1},
pages = {379--397},
title = {{Computing nearly singular solutions using pseudo-spectral methods}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999107001623},
volume = {226},
year = {2007}
}
@techreport{Houston,
author = {Houston, J. R. and Garcia, A. W.},
institution = {USACE WES Report No. H-74-3},
number = {Report No. H-74-3},
title = {{Type 16 flood insurance study}},
year = {1974}
}
@article{Houston2001,
abstract = {We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first-order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our {\{}a posteriori{\}} error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments.},
author = {Houston, P. and S{\"{u}}li, E.},
doi = {10.1137/S1064827500378799},
issn = {1064-8275},
journal = {SIAM J. Sci. Comput.},
month = {jan},
number = {4},
pages = {1226--1252},
title = {{hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems}},
url = {http://epubs.siam.org/doi/abs/10.1137/S1064827500378799},
volume = {23},
year = {2001}
}
@article{Hu2006,
author = {Hu, X. Y. and Adams, N. A.},
journal = {J. Comp. Phys.},
pages = {844--861},
title = {{A multi-phase SPH method for macroscopic and mesoscopic flows}},
volume = {213},
year = {2006}
}
@article{Hua2008,
author = {Hua, J.},
doi = {10.1016/j.jde.2008.04.009},
issn = {00220396},
journal = {Journal of Differential Equations},
month = {jul},
number = {2},
pages = {337--358},
title = {{Systems of hyperbolic conservation laws with a resonant moving source}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039608001824},
volume = {245},
year = {2008}
}
@article{Huang1999,
author = {Huang, N. E. and Shen, Z. and Long, S. R.},
journal = {Ann. Rev. Fluid Mech.},
pages = {417--457},
title = {{A new view of nonlinear water waves: the Hilbert spectrum}},
volume = {31},
year = {1999}
}
@article{Huang2011,
author = {Huang, W. and Han, M.},
doi = {10.1016/j.jde.2011.05.012},
issn = {00220396},
journal = {Journal of Differential Equations},
keywords = {Minimum wave speed,Non-linear determinacy,Traveling wave,competition model},
month = {sep},
number = {6},
pages = {1549--1561},
title = {{Non-linear determinacy of minimum wave speed for a Lotka-Volterra competition model}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039611001872},
volume = {251},
year = {2011}
}
@article{Huang2001,
abstract = {A class of moving mesh algorithms based upon a so-called moving mesh partial differential equation (MMPDE) is reviewed. Various forms for the MMPDE are presented for both the simple one- and the higher-dimensional cases. Additional practical features such as mesh movement on the boundary, selection of the monitor function, and smoothing of the monitor function are addressed. The overall discretization and solution procedure, including for unstructured meshes, are briefly covered. Finally, we discuss some physical applications suitable for MMPDE techniques and some challenges facing MMPDE methods in the future.},
author = {Huang, W. and Russell, R. D.},
doi = {10.1016/S0377-0427(00)00520-3},
issn = {03770427},
journal = {J. Comp. Appl. Math.},
month = {mar},
number = {1-2},
pages = {383--398},
title = {{Adaptive mesh movement - the MMPDE approach and its applications}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377042700005203},
volume = {128},
year = {2001}
}
@inproceedings{Hubert1996,
author = {Hubert, E.},
booktitle = {Proceedings of the 1996 international symposium on Symbolic and algebraic computation},
doi = {10.1145/236869.237073},
isbn = {0897917960},
pages = {189--195},
title = {{The general solution of an ordinary differential equation}},
url = {http://portal.acm.org/citation.cfm?id=237073},
year = {1996}
}
@article{Hugoniot1887,
author = {Hugoniot, H.},
journal = {Journal de l'Ecole Polytechnique},
pages = {3--97},
title = {{M{\'{e}}moire sur la propagation des mouvements dans les corps et sp{\'{e}}cialement dans les gaz parfaits (premi{\`{e}}re partie)}},
volume = {57},
year = {1887}
}
@article{Hunt1982,
author = {Hunt, B.},
journal = {J. Hydraul. Div. ASCE},
pages = {115--126},
title = {{Asymptotic solution for dam break problem}},
volume = {108},
year = {1982}
}
@article{Hunt05,
author = {Hunt, J. and Burgers, J. M.},
journal = {Mathematics TODAY},
month = {oct},
pages = {144--146},
title = {{Tsunami waves and coastal flooding}},
year = {2005}
}
@phdthesis{Hunt2013,
author = {Hunt, M.},
pages = {157},
school = {University College London},
title = {{Linear and Nonlinear Free Surface Flows in Electrohydrodynamics}},
type = {PhD},
year = {2013}
}
@article{Hunter1983a,
author = {Hunter, J. K. and Vanden-Broeck, J.-M.},
doi = {10.1017/S0022112083003316},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {205--219},
title = {{Solitary and periodic gravity-capillary waves of finite amplitude}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112083003316},
volume = {134},
year = {1983}
}
@article{Hunter1983,
author = {Hunter, J. K. and Vanden-Broeck, J.-M.},
doi = {10.1017/S0022112083002050},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {63--71},
title = {{Accurate computations for steep solitary waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112083002050},
volume = {136},
year = {1983}
}
@article{Hunter1995,
author = {Hunter, J. K. and Zheng, Y.},
doi = {10.1007/BF00379260},
issn = {0003-9527},
journal = {Arch. Rat. Mech. Anal.},
number = {4},
pages = {355--383},
title = {{On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits}},
url = {http://link.springer.com/10.1007/BF00379260},
volume = {129},
year = {1995}
}
@article{Hutter1991,
author = {Hutter, K.},
journal = {Acta Mechanica},
pages = {167--181},
title = {{Two- and three dimensional evolution of granular avalanche flow - Theory and experiments revisited}},
volume = {1},
year = {1991}
}
@inbook{Hutter1996,
author = {Hutter, K.},
chapter = {Avalanche},
editor = {Singh, V P},
pages = {317--394},
publisher = {Kluwer Academic Publishers},
title = {{Hydrology of disasters}},
year = {1996}
}
@article{Hutter1993,
author = {Hutter, K. and Greve, R.},
journal = {Journal of Glaciology},
pages = {357--372},
title = {{Two-dimensional similarity solutions for finite-mass granular avalanches with Coulomb and viscous-type frictional resistance}},
volume = {39},
year = {1993}
}
@article{Hutter2005,
author = {Hutter, K. and Wang, Y. and Pudasaini, S. P.},
journal = {Phil. Trans. R. Soc. Lond. A},
pages = {1507--1528},
title = {{The Savage-Hutter avalanche model. How far can it be pushed?}},
volume = {363},
year = {2005}
}
@article{Hydon2005,
author = {Hydon, P. E.},
journal = {Proc. R. Soc. A},
pages = {1627--1637},
title = {{Multisymplectic conservation laws for differential and differential-difference equations}},
volume = {461},
year = {2005}
}
@article{Ichinose2000,
author = {Ichinose, G. A. and Satake, K. and Anderson, J. G. and Lahren, M. M.},
journal = {Geophys. Res. Lett.},
pages = {1203--1206},
title = {{The potential hazard from tsunami and seiche waves generated by large earthquakes within Lake Tahoe, California-Nevada}},
volume = {27},
year = {2000}
}
@article{Ichinose2007,
author = {Ichinose, G. and Somerville, P. and Thio, H.-K. and Graves, R. and O'Connell, D.},
doi = {10.1029/2006JB004728},
issn = {0148-0227},
journal = {Journal of Geophysical Research},
month = {jul},
number = {B7},
pages = {B07306},
title = {{Rupture process of the 1964 Prince William Sound, Alaska, earthquake from the combined inversion of seismic, tsunami, and geodetic data}},
url = {http://www.agu.org/pubs/crossref/2007/2006JB004728.shtml},
volume = {112},
year = {2007}
}
@article{Iguchi2007,
author = {Iguchi, T.},
journal = {Bull. Inst. Math. Acad. Sin.},
pages = {179--220},
title = {{A long wave approximation for capillary-gravity waves and the Kawahara equation}},
volume = {2},
year = {2007}
}
@article{Ilin1969,
abstract = {A differencing scheme is introduced for a differential equation with a small parameter affecting the highest derivatives. In the case of an ordinary differential equation, the solution of the difference equation is shown to converge uniformly with respect to the small parameter.},
author = {Il'in, A. M.},
doi = {10.1007/BF01093706},
issn = {0001-4346},
journal = {Mathematical Notes of the Academy of Sciences of the USSR},
month = {aug},
number = {2},
pages = {596--602},
title = {{Differencing scheme for a differential equation with a small parameter affecting the highest derivative}},
url = {http://link.springer.com/10.1007/BF01093706},
volume = {6},
year = {1969}
}
@inbook{Imamura1996,
author = {Imamura, F.},
chapter = {Simulation},
editor = {Yeh, H. and Liu, P. and Synolakis, C. E.},
pages = {231--241},
publisher = {World Scientific},
title = {{Long-wave runup models}},
year = {1996}
}
@article{Imamura1995,
abstract = {Numerical analysis of the 1992 Flores Island, Indonesia earthquake tsunami is carried out with the composite fault model consisting of two different slip values. Computed results show good agreement with the measured runup heights in the northeastern part of Flores Island, except for those in the southern shore of Hading Bay and at Riangkroko. The landslides in the southern part of Hading Bay could generate local tsunamis of more than 10 m. The circular-arc slip model proposed in this study for wave generation due to landslides shows better results than the subsidence model, It is, however, difficult to reproduce the tsunami runup height of 26.2 m at Riangkroko, which was extraordinarily high compared to other places. The wave propagation process on a sea bottom with a steep slope, as well as landslides, may be the cause of the amplification of tsunami at Riangkroko. The simulation model demonstrates that the reflected wave along the northeastern shore of Flores Island, accompanying a high hydraulic pressure, could be the main cause of severe damage in the southern coast of Babi Island.},
author = {Imamura, F. and Gica, E. and Takahashi, T. and Shuto, N.},
doi = {10.1007/BF00874383},
issn = {0033-4553},
journal = {Pure Appl. Geophys.},
keywords = {The 1992 Flores earthquake tsunami,hydraulic pressure,landslide,numerical simulation,tsunami damage},
number = {3-4},
pages = {555--568},
title = {{Numerical simulation of the 1992 Flores tsunami: Interpretation of tsunami phenomena in northeastern Flores Island and damage at Babi Island}},
url = {http://www.springerlink.com/index/10.1007/BF00874383},
volume = {144},
year = {1995}
}
@manual{Imamura2006,
author = {Imamura, F. and Yalciner, A. C. and Ozyurt, G.},
month = {apr},
title = {{Tsunami modelling manual}},
year = {2006}
}
@article{Inard1996,
author = {Inard, C. and Bouia, H. and Dalicieux, P.},
journal = {Energy and Buildings},
pages = {125--132},
title = {{Prediction of air temperature distribution in buildings with a zonal model}},
volume = {24(2)},
year = {1996}
}
@book{Incropera2001,
author = {Incropera, F. P. and DeWitt, D. P.},
pages = {944},
publisher = {Wiley; 5 edition},
title = {{Fundamentals of Heat and Mass Transfer}},
year = {2001}
}
@book{Infeld2000,
address = {Cambridge},
author = {Infeld, E. and Rowlands, G.},
pages = {412},
publisher = {Cambridge University Press},
title = {{Nonlinear Waves, Solitons and Chaos}},
year = {2000}
}
@book{InstantSport2012,
author = {{Instant Sport}, S. L.},
title = {http://www.wavegarden.com/},
year = {2012}
}
@article{Ionescu-Kruse2013a,
author = {Ionescu-Kruse, D.},
journal = {Appl. Anal.},
pages = {1241--1253},
title = {{Variational derivation of two-component Camassa-Holm shallow water system}},
volume = {92},
year = {2013}
}
@article{Ionescu-Kruse2012,
abstract = {We consider the two-dimensional irrotational water-wave problem with a free surface and a flat bottom. In the shallow-water regime and without smallness assumption on the wave amplitude we derive, by a variational approach in the Lagrangian formalism, the Green-Naghdi equations (1.1). The second equation in (1.1) is a transport equation, the free surface is advected by the fluid flow. We show that the first equation of the system (1.1) yields the critical points of an action functional in the space of paths with fixed endpoints, within the Lagrangian formalism.},
author = {Ionescu-Kruse, D.},
doi = {10.1142/S1402925112400013},
issn = {1402-9251},
journal = {J. Nonlinear Math. Phys.},
month = {jan},
pages = {1240001},
title = {{Variational derivation of the Green-Naghdi shallow-water equations}},
volume = {19},
year = {2012}
}
@article{Ionescu-Kruse2013,
abstract = {For propagation of surface shallow-water waves on irrotational flows, we derive a new two-component system. The system is obtained by a variational approach in the Lagrangian formalism. The system has a non-canonical Hamiltonian formulation. We also find its exact solitary-wave solutions.},
author = {Ionescu-Kruse, D.},
journal = {Quar. Appl. Math.},
pages = {1--16},
title = {{A new two-component system modelling shallow-water waves}},
volume = {In Press},
year = {2013}
}
@article{Iooss2005,
author = {Iooss, G. and Plotnikov, P. I. and Toland, J. F.},
journal = {Arch. Rat. Mech. Anal.},
pages = {367--478},
title = {{Standing waves on an infinitely deep perfect fluid under gravity}},
volume = {177(3)},
year = {2005}
}
@article{Ioualalen2007,
author = {Ioualalen, M. and Asavanant, J. and Kaewbanjak, N. and Grilli, S. T. and Kirby, J. T. and Watts, P.},
journal = {Journal of Geophysical Research},
pages = {C07024},
title = {{Modeling the 26 December 2004 Indian Ocean tsunami: Case study of impact in Thailand}},
volume = {112},
year = {2007}
}
@book{Isaacson1966,
author = {Isaacson, E. and Keller, H. B.},
booktitle = {New York},
editor = {Isaacson, E. and Keller, H. B.},
isbn = {0486680290},
pages = {541},
publisher = {Dover Publications},
title = {{Analysis of Numerical Methods}},
url = {http://www.amazon.com/dp/0486680290},
year = {1966}
}
@article{Isaacson1995,
author = {Isaacson, E. and Temple, B.},
journal = {SIAM J. Appl. Math},
number = {3},
pages = {625--640},
title = {{Convergence of the 2x2 Godunov method for a general resonant nonlinear balance law,}},
volume = {55},
year = {1995}
}
@book{Ishii1975,
author = {Ishii, M.},
publisher = {Eyrolles, Paris},
title = {{Thermo-Fluid Dynamic Theory of Two-Phase Flow}},
year = {1975}
}
@book{Ishii2006,
author = {Ishii, M. and Hibiki, T.},
publisher = {Birkh{\"{a}}user},
title = {{Thermo-fluid dynamics of two-phase flow}},
year = {2006}
}
@article{Islas2005,
abstract = {Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and provides insight into the preservation properties of the scheme. In this paper we initiate a backward error analysis for PDE discretizations, in particular of multisymplectic box schemes for the nonlinear Schr{\"{o}}dinger equation. We show that the associated modified differential equations are also multisymplectic and derive the modified conservation laws which are satisfied to higher order by the numerical solution. Higher order preservation of the modified local conservation laws is verified numerically.},
author = {Islas, A. L. and Schober, C. M.},
doi = {10.1016/j.matcom.2005.01.006},
journal = {Math. Comp. Simul.},
keywords = {Backward error analysis,Hamiltonian PDEs,Multisymplectic schemes},
number = {3-4},
pages = {290--303},
title = {{Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs}},
volume = {69},
year = {2005}
}
@article{Ismail2000,
abstract = {The Korteweg-de Vries (KdV) equation has been generalized by Rosenau and Hyman 3 to a class of partial differential equations (PDEs) which has solitary wave solution with compact support. These solitary wave solutions are called compactons. Compactons are solitary waves with the remarkable soliton property, that after colliding with other compactons, they reemerge with the same coherent shape. These particle like waves exhibit elastic collision that are similar to the soliton interaction associated with completely integrable systems. The point where two compactons collide are marked by a creation of low amplitude compacton-anticompacton pair. These equations have only a finite number of local consevation laws. In this paper, an implicit numerical method has been developed to solve the K(2, 3) equation. Accuracy and stability of the method have been studied. The analytical solution and the conserved quantities are used to assess the accuracy of the suggested method. The numerical results have shown that this compacton exhibits true soliton behavior.},
author = {Ismail, M. S.},
journal = {International Journal of Computer Mathematics},
keywords = {compacton,finite difference method,newton,soliton},
number = {2},
pages = {185--193},
title = {{A finite difference method for Korteweg-de Vries like equation with nonlinear dispersion}},
volume = {74},
year = {2000}
}
@article{Israwi2011,
author = {Israwi, S.},
doi = {10.1016/j.na.2010.08.019},
issn = {0362546X},
journal = {Nonlinear Analysis: Theory, Methods $\backslash${\&} Applications},
month = {jan},
number = {1},
pages = {81--93},
title = {{Large time existence for 1D Green-Naghdi equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0362546X10005730},
volume = {74},
year = {2011}
}
@incollection{Issler2003,
author = {Issler, D.},
booktitle = {Dynamic Response of Granular and Porous Materials Under Large and Catastrophic Deformations},
editor = {Hutter, K. and Kirchner, N.},
publisher = {Springer, Berlin},
title = {{Experimental information on the dynamics of dry-snow avalanches}},
volume = {11},
year = {2003}
}
@article{Itoh1977,
author = {Itoh, N.},
doi = {10.1017/S0022112077000780},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
number = {03},
pages = {469--479},
title = {{Nonlinear stability of parallel flows with subcritical Reynolds numbers. Part 2. Stability of pipe Poiseuille flow to finite axisymmetric disturbances}},
volume = {82},
year = {1977}
}
@article{iwa79,
author = {Iwasaki, T. and Sato, R.},
journal = {J. Phys. Earth},
pages = {285--314},
title = {{Strain field in a semi-infinite medium due to an inclined rectangular fault}},
volume = {27},
year = {1979}
}
@article{Jacovkis1991,
abstract = {The one-dimensional hydrodynamic flow in complex networks that include many branches, junction points, and open boundary points is studied. The shallow-water equations are linearized, and the compatibility conditions at junction points and the boundary conditions at some or all of the open boundary points are analysed. Existence and uniqueness of smooth solutions is discussed and, under certain assumptions, proved. The necessary compatibility conditions depend on whether the flow is subcritical or supercritical. The results are extended to linear hyperbolic systems of more than two equations in networks. In particular, the flow over a network of channels with mobile (erodible) beds, modelled by means of a system of three equations, is analysed.},
author = {Jacovkis, P. M.},
journal = {SIAM J. Appl. Math},
number = {4},
pages = {948--966},
title = {{One-Dimensional Hydrodynamic Flow in Complex Networks and Some Generalizations}},
volume = {51},
year = {1991}
}
@article{Jafari2012,
author = {Jafari, H. and Sooraki, A. and Talebi, Y. and Biswas, A.},
journal = {Nonlinear Analysis: Modelling and Control},
number = {2},
pages = {182--193},
title = {{The first integral method and traveling wave solutions to Davey-Stewartson equation}},
volume = {17},
year = {2012}
}
@article{James2001,
author = {James, G.},
journal = {Arch. Rational Mech. Anal.},
pages = {41--90},
title = {{Internal travelling waves in the limit of a discontinuously stratified fluid}},
volume = {160},
year = {2001}
}
@article{Jamois2006,
author = {Jamois, E. and Fuhrman, D. R. and Bingham, H. B. and Molin, B.},
journal = {Coastal Engineering},
pages = {929--945},
title = {{A numerical study of nonlinear wave run-up on a vertical plate}},
volume = {53},
year = {2006}
}
@article{Janssen1983,
author = {Janssen, P. A. E. M.},
journal = {J. Fluid Mech},
pages = {1--11},
title = {{On a fourth-order envelope equation for deep-water waves}},
volume = {126},
year = {1983}
}
@article{Janssen2003,
author = {Janssen, P. A. E. M.},
journal = {Phys. Oceanogr.},
pages = {863--884},
title = {{Nonlinear four-wave interactions and freak waves}},
volume = {33},
year = {2003}
}
@phdthesis{Jasak1996,
author = {Jasak, H.},
school = {University of London and Imperial College},
title = {{Error analysis and estimation for the finite volume method with applications to fluid flows}},
year = {1996}
}
@book{Jaynes2003,
abstract = {Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.},
address = {Cambridge},
author = {Jaynes, E. T.},
isbn = {9780521592710},
pages = {753},
publisher = {Cambridge University Press},
title = {{Probability Theory}},
year = {2003}
}
@article{Jeffrey1982,
author = {Jeffrey, A. and Mvungi, J.},
doi = {10.1016/0165-2125(82)90006-3},
issn = {01652125},
journal = {Wave Motion},
month = {oct},
number = {4},
pages = {381--389},
title = {{The random choice method and the free-surface water profile after the collapse of a dam wall}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0165212582900063},
volume = {4},
year = {1982}
}
@article{Jensen2007,
author = {Jensen, A. and Clamond, D. and Huseby, M. and Grue, J.},
journal = {Ocean Engineering},
pages = {426--435},
title = {{On local and convective accelerations in steep wave events}},
volume = {34},
year = {2007}
}
@article{Jezequel2014,
author = {J{\'{e}}z{\'{e}}quel, T. and Bernard, P. and Lombardi, E.},
journal = {Arxiv:1401.1509},
pages = {1--79},
title = {{Homoclinic orbits with many loops near a {\$}0{\^{}}2i\backslashomega{\$} resonant fixed point of Hamiltonian systems}},
year = {2014}
}
@techreport{Ji2006,
author = {Ji, C.},
institution = {USGS},
title = {{Preliminary Result of the 2006 July 17 Magnitude 7.7 - South of Java, Indonesia Earthquake}},
url = {$\backslash$url{\{}http://neic.usgs.gov/neis/eq{\_}depot/2006/eq{\_}060717{\_}qgaf/neic{\_}qgaf{\_}ff.html{\}}},
year = {2006}
}
@article{Ji2002,
author = {Ji, C. and Wald, D. J. and Helmberger, D. V.},
journal = {Bull. Seism. Soc. Am.},
pages = {1192--1207},
title = {{Source description of the 1999 Hector Mine, California earthquake; Part I: Wavelet domain inversion theory and resolution analysis}},
volume = {92(4)},
year = {2002}
}
@article{Jiang1996,
author = {Jiang, L. and Ting, C.-L. and Perlin, M. and Schultz, W. W.},
journal = {J. Fluid Mech.},
pages = {275--307},
title = {{Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries}},
volume = {329},
year = {1996}
}
@techreport{Johannesson2009,
author = {Johannesson, T. and Gauer, P. and Issler, P. and Lied, K.},
institution = {European Commission},
title = {{The design of avalanche protection dams}},
year = {2009}
}
@article{Johnson1993,
author = {Johnson, J. M. and Satake, K.},
journal = {Geophysical Research Letters},
pages = {1487--1490},
title = {{Source parameters of the 1957 Aleutian earthquake from tsunami waveforms}},
volume = {20},
year = {1993}
}
@article{Johnson2013,
abstract = {We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDEs of KdV type, including generalized KdV and Benjamin--Ono equations. In this investigation, we consider the spectral stability of such solutions that arise as small perturbations of an equilibrium state. A key feature of our analysis is the development of a nonlocal Floquet-like theory that is suitable to analyze the {\$}L{\^{}}2(\backslashmathbb{\{}R{\}}){\$} spectrum of the associated linearized operators. Using spectral perturbation theory then, we derive a relationship between the power of the nonlinearity and the symbol of the fractional dispersive operator that determines the spectral stability and instability to arbitrary small localized perturbations.},
author = {Johnson, M. A.},
doi = {10.1137/120894397},
issn = {0036-1410},
journal = {SIAM J. Math. Anal.},
month = {oct},
number = {5},
pages = {3168--3193},
title = {{Stability of Small Periodic Waves in Fractional KdV-Type Equations}},
url = {http://epubs.siam.org/doi/abs/10.1137/120894397},
volume = {45},
year = {2013}
}
@article{Johnson2010a,
abstract = {In this paper, we consider the spectral stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long-wavelength perturbations. Specifically, we extend the work of Bronski and Johnson by demonstrating that the homogenized system describing the mean behavior of a slow modulation (WKB) approximation of the solution correctly describes the linearized dispersion relation near zero frequency of the linearized equations about the background periodic wave. The latter has been shown by rigorous Evans function techniques to control the spectral stability near the origin, that is, stability to slow modulations of the underlying solution. In particular, through our derivation of the WKB approximation we generalize the modulation expansion of Whitham for the KdV to a more general class of equations which admit periodic waves with nonzero mean. As a consequence, we will show that, assuming a particular nondegeneracy condition, spectral stability near the origin is equivalent with the local well-posedness of the Whitham system.},
author = {Johnson, M. A. and Zumbrun, K.},
doi = {10.1111/j.1467-9590.2010.00482.x},
issn = {00222526},
journal = {Stud. Appl. Math.},
month = {mar},
number = {1},
pages = {69--89},
title = {{Rigorous Justification of the Whitham Modulation Equations for the Generalized Korteweg-de Vries Equation}},
url = {http://doi.wiley.com/10.1111/j.1467-9590.2010.00482.x},
volume = {125},
year = {2010}
}
@article{Johnson2010,
abstract = {In this paper, we consider the relation between Evans-function-based approaches to the stability of periodic travelling waves and other theories based on long-wavelength asymptotics together with Bloch wave expansions. In previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the linearized Whitham averaged system accurately describes the spectral stability to long-wavelength perturbations. To clarify the connection between Bloch-wave-based expansions and Evans-function-based approaches, we reproduce this result without reference to the Evans function by using direct Bloch expansion methods and spectral perturbation analysis. One of the novelties of this approach is that we are able to calculate the relevant Bloch waves explicitly for arbitrary finite-amplitude solutions. Furthermore, this approach has the advantage of being applicable in the more general multi-periodic setting where no conveniently computable Evans function has yet been devised.},
author = {Johnson, M. A. and Zumbrun, K. and Bronski, J. C.},
doi = {10.1016/j.physd.2010.07.012},
issn = {01672789},
journal = {Phys. D},
month = {nov},
number = {23-24},
pages = {2057--2065},
title = {{On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278910002228},
volume = {239},
year = {2010}
}
@book{Johnson1997,
author = {Johnson, R. S.},
editor = {Johnson, R. S.},
publisher = {Cambridge University Press, Cambridge},
title = {{A modern introduction to the mathematical theory of water waves}},
year = {1997}
}
@article{Johnson1977,
author = {Johnson, R. S.},
journal = {Proc. R. Soc. Lond. A},
pages = {131--141},
title = {{On the modulation of water waves in the neighbourhood of kh $\backslash$backslashapprox 1.363}},
volume = {357},
year = {1977}
}
@article{Johnson2002,
author = {Johnson, R. S.},
journal = {J. Fluid Mech.},
pages = {63--82},
title = {{Camassa-Holm, Korteweg-de Vries and related models for water waves}},
volume = {455},
year = {2002}
}
@article{Johnson1977,
author = {Johnson, R. S.},
journal = {Proc. R. Soc. Lond. A},
pages = {131--141},
title = {{On the modulation of water waves in the neighbourhood of kh $\backslash$approx 1.363}},
volume = {357},
year = {1977}
}
@book{Johnson2004,
author = {Johnson, R. S.},
editor = {Johnson, R. S.},
publisher = {Cambridge University Press},
title = {{A Modern Introduction to the Mathematical Theory of Water Waves}},
year = {2004}
}
@article{Johnson1982,
author = {Johnson, R. and Moser, J.},
doi = {10.1007/BF01208484},
issn = {0010-3616},
journal = {Comm. Math. Phys.},
month = {sep},
number = {3},
pages = {403--438},
title = {{The rotation number for almost periodic potentials}},
url = {http://link.springer.com/10.1007/BF01208484},
volume = {84},
year = {1982}
}
@article{Joseph2006,
author = {Joseph, D. D.},
journal = {Int. J. Multiphase Flow},
pages = {285--310},
title = {{Potential Flow of Viscous Fluids: Historical Notes}},
volume = {32},
year = {2006}
}
@book{Joseph2007,
abstract = {The goal of this book is to show how potential flows enter into the general theory of motions of viscous and viscoelastic fluids. Traditionally, the theory of potential flows is thought to apply to idealized fluids without viscosity. Here we show how to apply this theory to real fluids that are viscous. The theory is applied to problems of the motion of bubbles; to the decay of waves on interfaces between fluids; to capillary, Rayleigh-Taylor, and Kelvin-Hemholtz instabilities; to viscous effects in acoustics; to boundary layers on solids at finite Reynolds numbers; to problems of stress-induced cavitation; and to the creation of microstructures in the flow of viscous and viscoelastic liquids.},
address = {Cambridge},
author = {Joseph, D. D. and Funada, T. and Wang, J.},
edition = {1},
isbn = {978-0521873376},
pages = {516},
publisher = {Cambridge University Press},
title = {{Potential Flows of Viscous and Viscoelastic Liquids}},
year = {2007}
}
@article{Joseph1994,
author = {Joseph, D. D. and Liao, T. Y.},
journal = {J. Fluid Mech.},
pages = {1--23},
title = {{Potential flows of viscous and viscoelastic fluids}},
volume = {265},
year = {1994}
}
@book{Joseph1993,
author = {Joseph, D. D. and Renardy, Y. Y.},
publisher = {Interdisciplinary Applied Mathematics. Springer Verlag, New-York},
title = {{Fundamentals of two-fluid dynamics}},
year = {1993}
}
@article{Joseph2004,
author = {Joseph, D. D. and Wang, J.},
journal = {J. Fluid Mech.},
pages = {365--377},
title = {{The dissipation approximation and viscous potential flow}},
volume = {505},
year = {2004}
}
@book{Journee2001,
abstract = {This text book is an attempt to provide a comprehensive treatment of hydromechanics for offshore engineers. The treatment of the selected topics includes both the background theory and its applications to realistic problems.},
address = {Delft},
author = {Journ{\'{e}}e, J. M. J. and Massie, W. W.},
pages = {570},
publisher = {Delft University of Technology},
title = {{Offshore Hydromechanics}},
year = {2001}
}
@article{Julien2009,
author = {Julien, K. and Watson, M.},
journal = {J. Comp. Phys.},
pages = {1480--1503},
title = {{Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods}},
volume = {228},
year = {2009}
}
@article{Kachanov1993,
abstract = {This work brings together experimental and theoretical studies of nonlinear stages aimed at the K-regime in boundary-layer transition, and some combined theoretical and experimental results are discussed. It is shown that the initial stages in the formation of so-called spikes, observed in many experiments, may be described very well by the asymptotic theory. These flashes-spikes are shown to be (in certain regimes) possible solitons of the boundary layer and governed by the integral-differential Benjamin-Ono equation. Properties of the spike-solitons, obtained both theoretically and experimentally in the quasi-planar stages of their development, are presented. Features of the disturbance behaviour connected with the subsequent development of three-dimensionality are also discussed, as are the effects of viscosity and shorter lengthscales. The main conclusion of the work concerns the hypothesis of the possible soliton nature of the flashes-spikes (within limits), which seems reliably corroborated by the good agreement found between the theory and the experimental data.},
author = {Kachanov, Y. S. and Ryzhov, O. S. and Smith, F. T.},
doi = {10.1017/S0022112093003416},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {273--297},
title = {{Formation of solitons in transitional boundary layers: theory and experiment}},
volume = {251},
year = {1993}
}
@techreport{Kahan2006,
author = {Kahan, W.},
pages = {56},
title = {{How futile are mindless assessments of roundoff in floating-point computation?}},
year = {2006}
}
@article{Kahan1979,
author = {Kahan, W. and Palmer, J.},
doi = {10.1145/1057520.1057522},
issn = {01635778},
journal = {ACM SIGNUM Newsletter},
month = {oct},
number = {si-2},
pages = {13--21},
title = {{On a proposed floating-point standard}},
url = {http://portal.acm.org/citation.cfm?doid=1057520.1057522},
volume = {14},
year = {1979}
}
@article{Kajiura1970,
author = {Kajiura, K.},
journal = {Bull. Earthquake Research Institute},
pages = {835--869},
title = {{Tsunami source, energy and the directivity of wave radiation}},
volume = {48},
year = {1970}
}
@article{kajiura,
author = {Kajiura, K.},
journal = {Bull. Earthquake Res. Inst., Tokyo Univ.},
pages = {535--571},
title = {{The leading wave of tsunami}},
volume = {41},
year = {1963}
}
@incollection{Kajiura1977,
author = {Kajiura, K.},
booktitle = {Waves on Water of Variable Depth},
editor = {Provis, D and Radok, R},
pages = {72--79},
publisher = {Springer Berlin / Heidelberg},
series = {Lecture Notes in Physics},
title = {{Local behaviour of tsunamis}},
volume = {64},
year = {1977}
}
@article{KM,
author = {Kakutani, T. and Matsuuchi, K.},
journal = {J. Phys. Soc. Japan},
pages = {237--246},
title = {{Effect of viscosity on long gravity waves}},
volume = {39},
year = {1975}
}
@article{Kalinichenko2007,
abstract = {It is shown that in the two-dimensional Faraday surface waves excited in a vertically oscillating rectangular water-filled vessel there is a system of secondary circulatory flows that occupies the entire fluid volume between the vessel bottom and the free surface. In parallel with the oscillations at the wave frequency, the fluid particles are slowly displaced in accordance with these circulatory flows. The secondary flow velocity field is measured and the trajectories of individual fluid particles in the standing wave are determined. The experimental data are compared with the Longuet-Higgins model. It is shown that the initial stage of formation of regular structures on the surface of a sediment layer on the vessel bottom may be related with the presence of secondary circulatory flows.},
author = {Kalinichenko, V. A. and Sekerzh-Zenkovich, S. Ya.},
doi = {10.1134/S0015462808010146},
journal = {Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza},
pages = {103--110},
title = {{Experimental Investigation of Secondary Steady Flows in Faraday Surface Waves}},
volume = {42(6)},
year = {2007}
}
@article{Kalisch2004,
author = {Kalisch, H.},
journal = {Discrete and Continuous Dynamical Systems},
pages = {709--717},
title = {{Stability of solitary waves for a nonlinearly dispersive equation}},
volume = {10},
year = {2004}
}
@article{Kalisch2004a,
author = {Kalisch, H.},
journal = {Nonlinear Analysis},
pages = {779--785},
title = {{A uniqueness result for periodic traveling waves in water of finite depth}},
volume = {58},
year = {2004}
}
@article{Kalisch2004b,
author = {Kalisch, H.},
journal = {J. Nonlinear Math. Phys.},
pages = {461--471},
title = {{Periodic traveling water waves with isobaric streamlines}},
volume = {11},
year = {2004}
}
@article{Kalisch2013,
abstract = {The regularized long-wave equation admits families of positive and negative solitary waves. Interactions of these waves are studied, and it is found that interactions of pairs of positive and pairs of negative solitary waves feature the same phase shift asymptotically as the wave velocities grow large as long as the same amplitude ratio is maintained. The collision of a positive with a negative wave leads to a host of phenomena, including resonance, annihilation and creation of secondary waves. A sharp criterion on the resonance for positive-negative interactions is found.},
author = {Kalisch, H. and Nguyen, H. Y. and Nguyen, N. T.},
journal = {Electron. J. Diff. Equ.},
number = {19},
pages = {1--13},
title = {{Solitary wave collisions in the regularized long wave equation}},
volume = {2013},
year = {2013}
}
@article{Kamalakis2006,
abstract = {Waveguide-cavity interactions may find important applications in future nanophotonic devices. This paper provides a detailed derivation of the evolution equation of the amplitude of a cavity mode coupled to a waveguide, starting from Maxwell's equations and using the reciprocity relations. The analysis applies to both constant cross-section and periodic waveguides as well. Unlike previous studies, the analysis enables the estimation of the frequency dependence of the coupling coefficients. It is also confirmed that the waveguide-cavity coupling causes a detuning of the resonant frequency of the cavity mode. The detuning is estimated in the case of a photonic crystal waveguide-cavity system and it is shown that it can be significant especially if the structure is intended for filtering applications. The analysis is generalized to the case of a multimode or multiple cavities and provides a useful tool in the analysis of devices based on coupled cavities.},
author = {Kamalakis, T. and Sphicopoulos, T.},
doi = {10.1109/JQE.2006.877298},
issn = {0018-9197},
journal = {IEEE Journal of Quantum Electronics},
month = {aug},
number = {8},
pages = {827--837},
title = {{Frequency Dependence of the Coupling Coefficients and Resonant Frequency Detuning in a Nanophotonic Waveguide-Cavity System}},
volume = {42},
year = {2006}
}
@article{Kameyama2005,
author = {Kameyama, M. and Kageyama, A. and Sato, T.},
journal = {J. Comput. Phys},
pages = {162--181},
title = {{Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity}},
volume = {206},
year = {2005}
}
@article{Kan-on1997a,
author = {Kan-on, Y.},
doi = {10.1016/0362-546X(95)00142-I},
issn = {0362546X},
journal = {Nonlinear Analysis: Theory, Methods {\&} Applications},
month = {jan},
number = {1},
pages = {145--164},
title = {{Fisher wave fronts for the Lotka-Volterra competition model with diffusion}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0362546X9500142I},
volume = {28},
year = {1997}
}
@article{Kan-on1997,
author = {Kan-on, Y.},
doi = {10.1006/jmaa.1997.5309},
issn = {0022247X},
journal = {Journal of Mathematical Analysis and Applications},
month = {apr},
number = {1},
pages = {158--170},
title = {{Instability of Stationary Solutions for a Lotka-Volterra Competition Model with Diffusion}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022247X97953099},
volume = {208},
year = {1997}
}
@article{Kanamori1972,
author = {Kanamori, H.},
doi = {10.1016/0031-9201(72)90058-1},
issn = {00319201},
journal = {Physics of the Earth and Planetary Interiors},
month = {jan},
number = {5},
pages = {346--359},
title = {{Mechanism of tsunami earthquakes}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0031920172900581},
volume = {6},
year = {1972}
}
@article{Kanamori1970,
author = {Kanamori, H.},
journal = {Journal of Geophysical Research},
pages = {5029--5040},
title = {{The Alaska earthquake of 1964: Radiation of Long-Period Surface Waves and Source Mechanism}},
volume = {75(26)},
year = {1970}
}
@article{Kanamori2006,
author = {Kanamori, H. and Rivera, L.},
journal = {Geophysical Monograph Series},
pages = {3--13},
title = {{Energy partitioning during an earthquake}},
volume = {170},
year = {2006}
}
@article{Kanoglu2004,
author = {Kanoglu, U.},
journal = {J. Fluid Mech.},
pages = {363--372},
title = {{Nonlinear evolution and runup-rundown of long waves over a sloping beach}},
volume = {513},
year = {2004}
}
@inbook{Kanoglu1995,
author = {Kanoglu, U. and Synolakis, C. E.},
chapter = {Analytic s},
editor = {Yeh, H and Liu, P and Synolakis, C E},
publisher = {Singapore: World Scientific},
title = {{Long wave runup models}},
year = {1995}
}
@article{Kanoglu2006,
author = {Kanoglu, U. and Synolakis, C. E.},
journal = {Phys. Rev. Lett.},
pages = {148501},
title = {{Initial Value Problem Solution of Nonlinear Shallow Water-Wave Equations}},
volume = {97},
year = {2006}
}
@article{Kanoglu1998,
author = {Kanoglu, U. and Synolakis, C. E.},
journal = {J. Fluid Mech.},
pages = {1--28},
title = {{Long wave runup on piecewise linear topographies}},
volume = {374},
year = {1998}
}
@article{Kanoglu2013,
author = {Kanoglu, U. and Titov, V. V. and Aydin, B. and Moore, C. and Stefanakis, T. and Zhou, H. and Spillane, M. and Synolakis, C. E.},
doi = {10.1098/rspa.2013.0015},
issn = {1364-5021},
journal = {Proc. R. Soc. A},
month = {feb},
number = {2153},
pages = {20130015--20130015},
title = {{Focusing of long waves with finite crest over constant depth}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2013.0015},
volume = {469},
year = {2013}
}
@book{Kaper1982,
author = {Kaper, H. G. and Lekkerkerker, C. G. and Hejtmanek, J.},
pages = {345},
publisher = {Birkh{\"{a}}user Verlag},
title = {{Spectral Methods in Linear Transport Theory}},
year = {1982}
}
@article{Kapitula1998,
abstract = {The propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear Schr{\"{o}}dinger equation (NLS). When considering realistic fibers one must examine perturbed NLS equations, with the particular perturbation depending on the physical situation that is being modeled. A common example is the complex Ginzburg-Landau equation (CGL), which is a dissipative perturbation. It is known that some of the stable bright solitons of the NLS survive a dissipative perturbation such as the CGL. Given that a wave persists, it is then important to determine its stability with respect to the perturbed NLS. A major difficulty in analyzing the stability of solitary waves upon adding dissipative terms is that eigenvalues may bifurcate out of the essential spectrum. Since the essential spectrum of the NLS is located on the imaginary axis, such eigenvalues may lead to an unstable wave. In fact, eigenvalues can pop out of the essential spectrum even if the unperturbed problem has no eigenvalue embedded in the essential spectrum. Here we present a technique which can be used to track these bifurcating eigenvalues. As a consequence, we are able to locate the spectrum for bright solitary-wave solutions to various perturbed nonlinear Schr{\"{o}}dinger equations, and determine precise conditions on parameters for which the waves are stable. In addition, we show that a particular perturbation, the parametrically forced NLS equation, supports stable multi-bump solitary waves. The technique for tracking eigenvalues which bifurcate from the essential spectrum is very general and should therefore be applicable to a larger class of problems than those presented here.},
author = {Kapitula, T. and Sandstede, B.},
doi = {10.1016/S0167-2789(98)00172-9},
issn = {01672789},
journal = {Phys. D},
month = {dec},
number = {1-3},
pages = {58--103},
title = {{Stability of bright solitary-wave solutions to perturbed nonlinear Schr{\"{o}}dinger equations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278998001729},
volume = {124},
year = {1998}
}
@article{Karlsen2004,
author = {Karlsen, K. H. and Risebro, N. H. and Towers, J. D.},
doi = {10.1142/S0219891604000068},
issn = {0219-8916},
journal = {J. Hyp. Diff. Eqs.},
month = {mar},
number = {1},
pages = {115--148},
title = {{Front tracking for scalar balance equations}},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0219891604000068},
volume = {1},
year = {2004}
}
@article{Kartashova2012,
author = {Kartashova, E.},
doi = {10.1209/0295-5075/97/30004},
issn = {0295-5075},
journal = {EPL},
month = {feb},
number = {3},
pages = {30004},
title = {{Energy spectra of 2D gravity and capillary waves with narrow frequency band excitation}},
url = {http://stacks.iop.org/0295-5075/97/i=3/a=30004?key=crossref.739c2075b09e79bc5b377690b24ba0ad},
volume = {97},
year = {2012}
}
@book{Kartashova2010,
abstract = {Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory.},
address = {Cambridge},
author = {Kartashova, E.},
doi = {10.1017/CBO9780511779046},
isbn = {9780511779046},
pages = {223},
publisher = {Cambridge University Press},
title = {{Nonlinear Resonance Analysis}},
year = {2010}
}
@article{Kartashova2013,
abstract = {Presently two models for computing energy spectra in weakly nonlinear dispersive media are known: kinetic wave turbulence theory, using a statistical description of an energy cascade over a continuous spectrum (K-cascade), and the D-model, describing resonant clusters and energy cascades (D-cascade) in a deterministic way as interaction of distinct modes. In this letter we give an overview of these structures and their properties and a list of criteria about which model of energy cascade should be used in the analysis of a given experiment, using water waves as an example. Applying the time scale analysis to weakly nonlinear wave systems modeled by the focusing nonlinear Sch{\"{o}}dinger equation, we demonstrate that K-cascade and D-cascade are not competing processes but rather two processes taking place at different time scales, at different characteristic levels of nonlinearity and based on different physical mechanisms. Applying those criteria to data known from experiments with surface water waves we find that the energy cascades observed occur at short characteristic times compatible only with a D-cascade. The only pre-requisite for a D-cascade being a focusing nonlinear Sch{\"{o}}dinger equation, the same analysis may be applied to existing experiments with wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.},
author = {Kartashova, E.},
doi = {10.1209/0295-5075/102/44005},
issn = {0295-5075},
journal = {EPL},
month = {may},
number = {4},
pages = {44005},
title = {{Time scales and structures of wave interaction exemplified with water waves}},
url = {http://stacks.iop.org/0295-5075/102/i=4/a=44005?key=crossref.d68519fa5a1041e3cf5447a9f5d00b13},
volume = {102},
year = {2013}
}
@article{Kartashova2006,
abstract = {A model of laminated wave turbulence is presented. This model consists of two coexisting layers - one with continuous wave spectra, covered by KAM theory and Kolmogorov-like power spectra, and one with discrete wave spectra, covered by discrete classes of waves and the Clipping method. Some known laboratory experiments and numerical simulations are explained in the frame of this model.},
author = {Kartashova, E.},
doi = {10.1134/S0021364006070058},
issn = {0021-3640},
journal = {JETP Lett.},
month = {jun},
number = {7},
pages = {283--287},
title = {{Model of laminated wave turbulence}},
url = {http://link.springer.com/10.1134/S0021364006070058},
volume = {83},
year = {2006}
}
@article{Kartashova2012a,
author = {Kartashova, E.},
doi = {10.1103/PhysRevE.86.041129},
issn = {1539-3755},
journal = {Phys. Rev. E},
month = {oct},
number = {4},
pages = {041129},
title = {{Energy transport in weakly nonlinear wave systems with narrow frequency band excitation}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.86.041129},
volume = {86},
year = {2012}
}
@article{Kartashova1990,
author = {Kartashova, E. A.},
doi = {10.1016/0167-2789(90)90112-3},
issn = {01672789},
journal = {Phys. D},
month = {oct},
number = {1},
pages = {43--56},
title = {{Partitioning of ensembles of weakly interacting dispersing waves in resonators into disjoint classes}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0167278990901123},
volume = {46},
year = {1990}
}
@article{Kartashova2007,
abstract = {We suggest a way of rationalizing intraseasonal oscillations of Earth's atmospheric flow as four meteorologically relevant triads of interacting planetary waves, isolated from the system of all of the rest of the planetary waves. Our model is independent of the topography (mountains, etc.) and gives a natural explanation of intraseasonal oscillations in both the Northern and the Southern Hemispheres. Spherical planetary waves are an example of a wave mesoscopic system obeying discrete resonances that also appears in other areas of physics.},
author = {Kartashova, E. and Lvov, V. S.},
doi = {10.1103/PhysRevLett.98.198501},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {may},
number = {19},
pages = {198501},
title = {{Model of Intraseasonal Oscillations in Earth's Atmosphere}},
volume = {98},
year = {2007}
}
@inproceedings{KDID,
author = {Kassiotis, C. and Dias, F. and Ibrahimbegovic, A. and Dutykh, D.},
booktitle = {ECCOMAS Thematic Conference on Multi-scale Computational Methods for Solids and Fluids},
editor = {Ibrahimbegovic, A and Dias, F and Matthies, H and Wriggers, P},
pages = {134--139},
title = {{A partitioned approach to model tsunami impact on coastal protections}},
year = {2007}
}
@article{Kaup1975,
author = {Kaup, D. J.},
journal = {Prog. Theor. Phys.},
pages = {396--408},
title = {{Higher-order water-wave equation and method for solving it}},
volume = {54},
year = {1975}
}
@article{Kazhikov1977,
author = {Kazhikov, A. and Smagulov, Sh.},
journal = {Sov. Phys. Dokl.},
pages = {249--252},
title = {{The correctness of boundary value problems in a diffusion problem of an homogeneous fluid}},
volume = {22},
year = {1977}
}
@article{Kazolea2013,
author = {Kazolea, M. and Delis, A. I.},
journal = {Appl. Numer. Math.},
pages = {167--186},
title = {{A well-balanced shock-capturing hybrid finite volume-finite difference numerical scheme for extended 1D Boussinesq models}},
volume = {67},
year = {2013}
}
@article{Kazolea2012,
author = {Kazolea, M. and Delis, A. I. and Nikolos, I. K. and Synolakis, C. E.},
journal = {Coastal Engineering},
pages = {42--66},
title = {{An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations}},
volume = {69},
year = {2012}
}
@article{Keller1978,
author = {Keller, H. B.},
doi = {10.1146/annurev.fl.10.010178.002221},
issn = {0066-4189},
journal = {Ann. Rev. Fluid Mech.},
month = {jan},
number = {1},
pages = {417--433},
title = {{Numerical Methods in Boundary-Layer Theory}},
url = {http://www.annualreviews.org/doi/abs/10.1146/annurev.fl.10.010178.002221},
volume = {10},
year = {1978}
}
@article{Keller2003,
author = {Keller, J. B.},
journal = {J. Fluid Mech.},
pages = {345--348},
title = {{Shallow-water theory for arbitrary slopes of the bottom}},
volume = {489},
year = {2003}
}
@article{keller,
author = {Keller, J. B.},
journal = {Int. Un. Geodesy {\&} Geophys. Monograph},
pages = {154--166},
title = {{Tsunamis: water waves produced by earthquakes}},
volume = {24},
year = {1963}
}
@techreport{Keller1964,
author = {Keller, J. B. and Keller, H. B.},
institution = {Department of the Navy, Washington, DC},
number = {NONR-3828(00)},
title = {{Water wave run-up on a beach}},
year = {1964}
}
@article{Keller1991,
author = {Keller, J. J. and Chyou, Y.-P.},
journal = {Journal of Applied Mathematics and Physics},
title = {{On the hydrodynamic lock-exchange problem}},
volume = {42},
year = {1991}
}
@article{Keller1995,
author = {Keller, S.},
journal = {Surveys in Geophysics},
pages = {661--670},
title = {{Measurements of powder snow avalanches: Laboratory}},
volume = {16},
year = {1995}
}
@article{Kelletat2008,
author = {Kelletat, D.},
journal = {Sedimentary Geology},
pages = {87--91},
title = {{Comments to Dawson, A.G. and Stewart, I. (2007), Tsunami deposits in the geological record.-Sedimentary Geology 200, 166-183}},
volume = {211},
year = {2008}
}
@article{kelvin,
author = {Kelvin, Lord},
journal = {Phil. Mag.},
number = {5},
pages = {252--257},
title = {{No Title}},
volume = {23},
year = {1887}
}
@article{kelvin,
author = {Kelvin, Lord},
journal = {Phil. Mag.},
number = {5},
pages = {252--257},
title = {{No Title}},
volume = {23},
year = {1887}
}
@article{kelvin,
author = {Kelvin, Lord},
journal = {Phil. Mag.},
number = {5},
pages = {252--257},
title = {{No Title}},
volume = {23},
year = {1887}
}
@article{kelvin,
author = {Kelvin, Lord},
journal = {Phil. Mag.},
number = {5},
pages = {252--257},
title = {{No Title}},
volume = {23},
year = {1887}
}
@article{kelvin,
author = {Kelvin, Lord},
journal = {Phil. Mag.},
number = {5},
pages = {252--257},
title = {{No Title}},
volume = {23},
year = {1887}
}
@article{Kelvin1871,
author = {Kelvin, Lord},
journal = {Philosophical Magazine},
pages = {362--377},
title = {{Hydrokinetic solutions and observations}},
volume = {42},
year = {1871}
}
@article{kelvin,
author = {Kelvin, Lord},
journal = {Phil. Mag.},
number = {5},
pages = {252--257},
title = {{No Title}},
volume = {23},
year = {1887}
}
@article{Kennedy2000,
author = {Kennedy, A. B. and Chen, Q. and Kirby, J. T. and Dalrymple, R. A.},
journal = {J. Waterway, Port, Coastal and Ocean Engineering},
pages = {39--47},
title = {{Boussinesq Modelling of Wave Transformation, Breaking, and Runup}},
volume = {126},
year = {2000}
}
@article{Kennedy2001,
abstract = {In this paper, we derive and test a set of extended Boussinesq equations with improved nonlinear performance. To do this, the concept of a reference elevation is further generalised to include a time-varying component that moves with the instantaneous free surface. It is found that, when compared to Stokes-type expansions of the second harmonic and fully nonlinear potential flow computations, both theoretical and practical nonlinear performance can be considerably improved. Finally, a special case of the extended equations is found to have properties which are invariant with respect to the still water datum.},
author = {Kennedy, A. B. and Kirby, J. T. and Chen, Q. and Dalrymple, R. A.},
doi = {10.1016/S0165-2125(00)00071-8},
issn = {01652125},
journal = {Wave Motion},
keywords = {Boussinesq equations,Numerical methods,Stokes-type expansions,Water waves},
month = {mar},
number = {3},
pages = {225--243},
title = {{Boussinesq-type equations with improved nonlinear performance}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0165212500000718},
volume = {33},
year = {2001}
}
@article{Kerswell2005,
abstract = {The problem of understanding the nature of fluid flow through a circular straight pipe remains one of the oldest problems in fluid mechanics. So far no explanation has been substantiated to rationalize the transition process by which the steady unidirectional laminar flow state gives way to a temporally and spatially disordered three-dimensional (turbulent) solution as the flow rate increases. Recently, new travelling wave solutions have been discovered which are saddle points in phase space. These plausibly represent the lowest level in a hierarchy of spatio-temporal periodic flow solutions which may be used to construct a cycle expansion theory of turbulent pipe flows. We summarize this success against the backdrop of past work and discuss its implications for future research.},
author = {Kerswell, R. R.},
doi = {10.1088/0951-7715/18/6/R01},
issn = {0951-7715},
journal = {Nonlinearity},
month = {nov},
number = {6},
pages = {R17--------R44},
title = {{Recent progress in understanding the transition to turbulence in a pipe}},
volume = {18},
year = {2005}
}
@article{KerswellL2007,
author = {Kerswell, R. R. and Tutty, O. R.},
doi = {10.1017/S0022112007006301},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {jul},
pages = {69--102},
title = {{Recurrence of travelling waves in transitional pipe flow}},
volume = {584},
year = {2007}
}
@article{Kervella2007,
author = {Kervella, Y. and Dutykh, D. and Dias, F.},
journal = {Theor. Comput. Fluid Dyn.},
pages = {245--269},
title = {{Comparison between three-dimensional linear and nonlinear tsunami generation models}},
volume = {21},
year = {2007}
}
@article{Keulegan1948,
author = {Keulegan, G. H.},
journal = {J. Res. Nat. Bureau Standards},
pages = {487--498},
title = {{Gradual damping of solitary waves}},
volume = {40(6)},
year = {1948}
}
@article{Kevrekidis2011,
abstract = {In this note we propose a new set of coordinates to study the hyperbolic or nonelliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial selfsimilar solutions. Many of the arguments can easily be adapted to more general nonlinearities.},
author = {Kevrekidis, P. and Nahmod, A. R. and Zeng, C.},
doi = {10.1088/0951-7715/24/5/007},
issn = {0951-7715},
journal = {Nonlinearity},
month = {may},
number = {5},
pages = {1523--1538},
title = {{Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D}},
url = {http://stacks.iop.org/0951-7715/24/i=5/a=007?key=crossref.98aeb888559facd65fa1c2af926324a6},
volume = {24},
year = {2011}
}
@article{Keylock2005,
author = {Keylock, C. J.},
doi = {10.1016/j.coldregions.2005.01.004},
issn = {0165232X},
journal = {Cold Regions Science and Technology},
keywords = {avalanches,iceland,peaks over threshold,snow,statistical analysis,statistical distributions},
number = {3},
pages = {185--193},
title = {{An alternative form for the statistical distribution of extreme avalanche runout distances}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0165232X05000236},
volume = {42},
year = {2005}
}
@article{Keylock2001,
author = {Keylock, C. J. and Barbolini, M.},
journal = {Can. Geotech. J.},
pages = {227--238},
title = {{Snow avalanche impact pressure - vulnerability relations for use in risk assessment}},
volume = {38(2)},
year = {2001}
}
@article{Khabakhpashev2008,
author = {Khabakhpashev, G. A.},
journal = {Oceanology},
pages = {457--465},
title = {{Dynamics of Long Spatial Nonlinear Waves in an Ocean with a Density Jump and a Gently Sloping Bottom}},
volume = {4},
year = {2008}
}
@article{Khabakhpashev1997,
author = {Khabakhpashev, G. A.},
journal = {Computational Technologies},
pages = {94--101},
title = {{Nonlinear evolution equation for sufficiently long two-dimensional waves on the free surface of a viscous liquid}},
volume = {2},
year = {1997}
}
@article{Khabakhpashev1987,
author = {Khabakhpashev, G. A.},
journal = {Fluid Dynamics},
pages = {430--437},
title = {{Effect of bottom friction on the dynamics of gravity perturbations}},
volume = {22(3)},
year = {1987}
}
@article{Khakimzyanov2002,
author = {Khakimzyanov, G. S.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {2},
pages = {145--158},
title = {{Numerical simulation of the interaction of a solitary wave with a partially immersed body}},
volume = {17},
year = {2002}
}
@article{Khakimzyanov2015b,
author = {Khakimzyanov, G. S. and Dutykh, D.},
journal = {Submitted},
pages = {1--17},
title = {{On supraconvergence phenomenon for second order centered finite differences on non-uniform grids}},
year = {2015}
}
@article{Khakimzyanov2016,
author = {Khakimzyanov, G. S. and Dutykh, D. and Gusev, O. and Shokina, N. Yu.},
journal = {Submitted},
pages = {1--40},
title = {{Shallow water wave modelling. Part II: Numerical scheme}},
year = {2016}
}
@article{Khakimzyanov2015a,
author = {Khakimzyanov, G. S. and Dutykh, D. and Mitsotakis, D. E. and Shokina, N. Yu.},
journal = {Submitted},
pages = {1--28},
title = {{Numerical solution of conservation laws on moving grids}},
year = {2015}
}
@article{Khakimzyanov2004,
author = {Khakimzyanov, G. S. and Khazhoyan, M. G.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
pages = {17--34},
title = {{Numerical Simulation of the Interaction between Surface Waves and Submerged obstacles}},
volume = {19(1)},
year = {2004}
}
@book{Khakimzyanov2001,
address = {Novosibirsk},
author = {Khakimzyanov, G. S. and Shokin, Yu. I. and Barakhnin, V. B. and Shokina, N. Yu.},
publisher = {Sib. Branch, Russ. Acad. Sci.},
title = {{Numerical Simulation of Fluid Flows with Surface Waves}},
year = {2001}
}
@article{KhakimzyanovG.S.Shokina2010,
abstract = {This paper addresses numerical modelling of wave regimes generated by the movement of underwater landslide on a curvilinear bottom. Our work differs from the works of other authors, where the problem of wave generation by a moving landslide has been investigated on flat bottoms only. The equations, describing the movement of an underwater landslide under the action of gravity force, buoyancy force, friction force and water resistance force, are obtained. Dependence of the arising wave properties versus the initial embedding of a landslide, its dimensions and slope of a bottom is investigated. Modelling of the surface waves, arising due to the movement of an underwater landslide on irregular bottom, was carried out in the framework of the shallow water model using the predictor-corrector scheme on an adaptive grid.},
author = {Khakimzyanov, G. S. and Shokina, N. Yu.},
journal = {Computational Technologies},
keywords = {adaptive grid,buoyancy,finite-difference scheme,forces of gravity,friction and water resistance,irregular bottom,numerical modelling,numerical results,shallow water equations,surface waves,underwater landslide},
number = {1},
pages = {105--119},
title = {{Numerical modelling of surface water waves arising due to a movement of the underwater landslide on an irregular bottom}},
volume = {15},
year = {2010}
}
@article{Khakimzyanov2015,
author = {Khakimzyanov, G. S. and Shokina, N. Yu. and Dutykh, D. and Mitsotakis, D.},
journal = {J. Comp. Appl. Math.},
pages = {1--27},
title = {{A new run-up algorithm based on local high-order analytic expansions}},
volume = {Accepted},
year = {2015}
}
@article{Khan2005,
abstract = {When the density of sediment laden river water exceeds that of the ambient ocean water, the river plunges to the ocean floor and generates a hyperpycnal plume. Hyperpycnal plumes can travel significant distances beyond the continental shelf and may be sustained for hours to weeks. There are several Apennine Rivers in Italy that are likely to develop hyperpycnal discharges on the Western Adriatic shelf. Among them, River Tronto is a moderately ‘dirty’ river capable of producing 64 hyperpycnal flow events (lasting ⩾ 6 h) during a 100 year period. Numerical simulations of hyperpycnal events have been conducted for the Adriatic shelf near the mouth of River Tronto using a two-dimensional depth-integrated finite volume model to study the spreading of the plume and its interaction with the alongshore current. Simulation results indicate that the alongshore current has great impact on the spreading and deposition pattern of the hyperpycnal flow. Sedimentary deposits generated from a series of simulated hyperpycnal flow events have developed undulating bed forms.},
author = {Khan, S. M. and Imran, J. and Bradford, S. F. and Syvitski, J.},
doi = {10.1016/j.margeo.2005.06.025},
issn = {00253227},
journal = {Marine Geology},
keywords = {Adriatic shelf,Apennine rivers,alongshore current,hyperpycnal flow,undulation},
month = {nov},
pages = {193--211},
title = {{Numerical modeling of hyperpycnal plume}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S002532270500201X},
volume = {222-223},
year = {2005}
}
@article{Kharif2003,
author = {Kharif, C. and Pelinovsky, E. N.},
journal = {Eur. J. Mech. B/Fluids},
pages = {603--634},
title = {{Physical mechanisms of the rogue wave phenomenon}},
volume = {22},
year = {2003}
}
@incollection{Kharif2009,
author = {Kharif, C. and Pelinovsky, E. N. and Slunyaev, A.},
booktitle = {Rogue Waves in the Ocean},
isbn = {9783540884194},
pages = {91--171},
publisher = {Springer Berlin Heidelberg},
series = {Advances in Geophysical and Environmental Mechanics and Mathematics},
title = {{Rogue Waves in Waters of Infinite and Finite Depths}},
year = {2009}
}
@book{Kharif2009a,
abstract = {The book is written for specialists in the fields of fluid mechanics, applied mathematics, nonlinear physics, physical oceanography and geophysics, and also for students learning these subjects. It includes a wide range of observational data on rogue (or freak) waves in the seas and coastal waters, as well as presenting a basic statistical description of extreme water waves. The book describes the modern approaches, including theoretical and numerical models applied to explain the physical origin of such anomalous waves on the sea surface, taking into account wind flow above waves and also variable bathymetry and currents. Apart from these analytical and numerical approaches, laboratory experiments and in-situ observations are reported too.},
author = {Kharif, C. and Pelinovsky, E. N. and Slunyaev, A.},
isbn = {978-3-540-88418-7},
keywords = {applied mathematics,fluid mechanics,natural hazards,nonlinear waves,physical oceanography},
pages = {216},
publisher = {Springer},
title = {{Rogue Waves in the Ocean}},
year = {2009}
}
@article{Kharif2001,
author = {Kharif, C. and Pelinovsky, E. and Talipova, T. and Slunyaev, A.},
doi = {10.1134/1.1368708},
issn = {00213640},
journal = {JETP Lett.},
number = {4},
pages = {170--175},
title = {{Focusing of nonlinear wave groups in deep water}},
url = {http://www.springerlink.com/index/10.1134/1.1368708},
volume = {73},
year = {2001}
}
@article{Kharif2010,
author = {Kharif, C. and Touboul, J.},
journal = {Eur. Phys. J. Special Topics},
pages = {159--168},
title = {{Under which conditions the Benjamin-Feir instability may spawn an extreme wave event: A fully nonlinear approach}},
volume = {185},
year = {2010}
}
@inproceedings{Khayyer2012,
author = {Khayyer, A. and Gotoh, H.},
booktitle = {7th SPHERIC Workshop Proceedings},
title = {{A consistent particle method for simulation of multiphase flows with high density ratios}},
year = {2012}
}
@article{Khayyer2008,
abstract = {A Corrected Moving Particle Semi-implicit (CMPS) method is proposed for the accurate tracking of water surface in breaking waves. The original formulations of standard MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. A simple numerical test demonstrates the excellent performance of the CMPS method in exact conservation of linear momentum and significantly enhanced preservation of angular momentum. The CMPS method is applied to the simulation of plunging breaking and post-breaking of solitary waves. Qualitative and quantitative comparisons with the experimental data confirm the high capability and precision of the CMPS method. A tensor-type strain-based viscosity is also proposed to further enhanced CMPS reproduction of a splash-up.},
author = {Khayyer, A. and Gotoh, H.},
doi = {10.1142/S0578563408001788},
issn = {0578-5634},
journal = {Coast. Eng. J.},
month = {jun},
number = {02},
pages = {179--207},
title = {{Development of CMPS method for accurate water-surface tracking in breaking waves}},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0578563408001788},
volume = {50},
year = {2008}
}
@article{Khazhoyan2006,
author = {Khazhoyan, M. G. and Khakimzyanov, G. S.},
journal = {Journal of Applied Mechanics and Technical Physics},
pages = {785--789},
title = {{Numerical modeling of ideal incompressible fluid flow over a step}},
volume = {47(6)},
year = {2006}
}
@article{Kibler2010,
author = {Kibler, B. and Fatome, J. and Finot, C. and Millot, G. and Dias, F. and Genty, G. and Akhmediev, N. and Dudley, J. M.},
journal = {Nature Physics},
pages = {790--795},
title = {{The Peregrine soliton in nonlinear fibre optics}},
volume = {6},
year = {2010}
}
@article{Kibler2012,
author = {Kibler, B. and Fatome, J. and Finot, C. and Millot, G. and Genty, G. and Wetzel, B. and Akhmediev, N. N.},
journal = {Sci. Rep.},
number = {463},
title = {{Observation of Kuznetsov-Ma soliton dynamics in optical fibre}},
volume = {2},
year = {2012}
}
@article{Kim2007,
author = {Kim, D.-H. and Cho, Y.-S. and Yi, Y.-K.},
journal = {Ocean Engineering},
pages = {1164--1173},
title = {{Propagation and run-up of nearshore tsunamis with HLLC approximate Riemann solver}},
volume = {34},
year = {2007}
}
@article{Kim2009,
author = {Kim, G. and Lee, C. and Suh, K.-D.},
doi = {10.1016/j.oceaneng.2009.05.002},
issn = {00298018},
journal = {Ocean Engineering},
month = {aug},
number = {11},
pages = {842--851},
title = {{Extended Boussinesq equations for rapidly varying topography}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0029801809001085},
volume = {36},
year = {2009}
}
@article{Kim2001,
author = {Kim, J. W. and Bai, K. J. and Ertekin, R. C. and Webster, W. C.},
journal = {J. Eng. Math.},
number = {1},
pages = {17--42},
title = {{A derivation of the Green-Naghdi equations for irrotational flows}},
volume = {40},
year = {2001}
}
@article{Kim2005a,
author = {Kim, K. H. and Kim, C.},
journal = {J. Comput. Phys.},
pages = {527--569},
title = {{Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows. Part I: Spatial discretization}},
volume = {208},
year = {2005}
}
@article{Kim2005,
author = {Kim, K. H. and Kim, C.},
journal = {J. Comput. Phys.},
pages = {570--615},
title = {{Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows. Part II: Multi-dimensional limiting process}},
volume = {208},
year = {2005}
}
@article{Kim1998,
author = {Kim, M. H. and Celebi, M. S. and Kim, D. J.},
journal = {Appl. Ocean Res.},
pages = {309--321},
title = {{Fully nonlinear interactions of waves with a three-dimensional body in uniform currents}},
volume = {20},
year = {1998}
}
@article{Kim2007a,
author = {Kim, P.},
journal = {BIT Numerical Mathematics},
pages = {525--546},
title = {{Invariantization of numerical schemes using moving frames}},
volume = {47},
year = {2007}
}
@article{Kim2008,
author = {Kim, P.},
journal = {Physica D},
pages = {243--254},
title = {{Invariantization of the Crank-Nicolson method for Burgers' equation}},
volume = {237},
year = {2008}
}
@techreport{Kim2003,
author = {Kim, S.-E. and Makarov, B. and Caraeni, D.},
institution = {Fluent Inc.},
title = {{A Multi-Dimensional Linear Reconstruction Scheme for Arbitrary Unstructured Grids}},
year = {2003}
}
@inbook{Kirby,
author = {Kirby, J. T.},
chapter = {Boussinesq},
pages = {1--41},
publisher = {Elsevier},
title = {{Advances in Coastal Modeling, V. C. Lakhan (ed)}},
year = {2003}
}
@inbook{Kirby1997,
author = {Kirby, J. T.},
chapter = {Nonlinear,},
editor = {Hunt, J N},
pages = {55--125},
publisher = {Computational Mechanics Publications},
title = {{Gravity Waves in Water of Finite Depth}},
volume = {10},
year = {1997}
}
@misc{Fun,
author = {Kirby, J. T. and Wei, G. and Chen, Q. and Kennedy, A. B. and Dalrymple, R. A.},
howpublished = {Research Report No. CACR-98-06},
title = {{FUNWAVE 1.0, Fully nonlinear Boussinesq wave model documentation and user's manual}},
year = {1998}
}
@book{Kirchoff1876,
address = {Leipzig},
author = {Kirchoff, G.},
pages = {489},
publisher = {B. G. Teubner},
title = {{Vorlesungen {\"{u}}ber mathematische Physik. Mechanik}},
year = {1876}
}
@article{Kit2002,
author = {Kit, E. and Shemer, L.},
journal = {J. Fluid Mech},
pages = {201--205},
title = {{Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves}},
volume = {450},
year = {2002}
}
@article{Kit1989,
author = {Kit, E. and Shemer, L.},
journal = {Acta Mechanica},
pages = {171--180},
title = {{On Dissipation Coefficients in a Rectangular Wave Tank}},
volume = {77},
year = {1989}
}
@article{Kita1995,
author = {Kita, E. and Kamiya, N.},
journal = {Advances in Engineering Software},
pages = {3--12},
title = {{Trefftz method: an overview}},
volume = {24},
year = {1995}
}
@article{Klainerman1982,
author = {Klainerman, S. and Majda, A.},
journal = {Comm. Pure Appl. Math.},
pages = {629},
title = {{Compressible and incompressible fluids}},
volume = {35},
year = {1982}
}
@article{Klein2007,
abstract = {The aim of this paper is the accurate numerical study of the Kadomtsev-Petviashvili (KP) equation. In particular, we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end, we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey–Stewartson system. In a second step, we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.},
author = {Klein, C. and Sparber, C. and Markowich, P.},
doi = {10.1007/s00332-007-9001-y},
issn = {0938-8974},
journal = {J. Nonlinear Sci.},
keywords = {Davey–Stewartson system,Kadomtsev-Petviashvili equation,Modulation theory,Multiple scales expansion,Nonlinear dispersive models},
month = {jun},
number = {5},
pages = {429--470},
title = {{Numerical Study of Oscillatory Regimes in the Kadomtsev-Petviashvili Equation}},
url = {http://www.springerlink.com/index/10.1007/s00332-007-9001-y},
volume = {17},
year = {2007}
}
@article{Klein2009,
author = {Klein, R.},
doi = {10.1007/s00162-009-0104-y},
issn = {0935-4964},
journal = {Theor. Comput. Fluid Dyn.},
month = {jul},
number = {3},
pages = {161--195},
title = {{Asymptotics, structure, and integration of sound-proof atmospheric flow equations}},
url = {http://link.springer.com/10.1007/s00162-009-0104-y},
volume = {23},
year = {2009}
}
@article{Klingbeil2013,
author = {Klingbeil, K. and Burchard, H.},
journal = {Ocean Modelling},
pages = {64--77},
title = {{Implementation of a direct nonhydrostatic pressure gradient discretisation into a layered ocean model}},
volume = {65},
year = {2013}
}
@article{Klingbeil2014,
author = {Klingbeil, K. and Mohammadi-Aragh, M. and Gr{\"{a}}we, U. and Burchard, H.},
journal = {Ocean Modelling},
pages = {49--64},
title = {{Quantification of spurious dissipation and mixing - Discrete Variance Decay in a Finite-Volume framework}},
volume = {81},
year = {2014}
}
@article{Kloczko2008,
author = {Kloczko, T. and Corre, C. and Beccantini, A.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {493--526},
title = {{Low-cost implicit schemes for all-speed flows on unstructured meshes}},
volume = {58},
year = {2008}
}
@article{Kobayashi1989,
abstract = {The numerical model developed previously for coastal structures is slightly modified and applied to predict the wave transformation in the surf and swash zones on gentle slopes as well as the wave reflection and swash oscillation on relatively steep beaches. The numerical model is one-dimensional in the cross-shore direction and is based on the finite amplitude, shallow water equations, including the effect of bottom friction, which are solved in the time domain for the incident wave train specified as input at the seaward boundary of the computation located outside the breakpoint. The slight modification is related to the effect of the time-averaged current on the seaward boundary condition and improves the agreement between the computed and measured mean water levels on gentle slopes. The modified numerical model is compared with available small-scale test data for monochromatic waves spilling on gentle slopes as well as for monochromatic waves plunging and surging on a relatively steep slope. Additional comparisons are made with small-scale tests conducted using transient monochromatic and grouped waves on a 1:8 smooth slope with and without an idealized nearshore bar at the toe of the 1:8 slope. As a whole, the numerical model is shown to be capable of predicting both time-varying and time-averaged hydrodynamic quantities in the surf and swash zones on gentle as well as steep slopes.},
author = {Kobayashi, N. and DeSilva, G. S. and Watson, K. D.},
doi = {10.1029/JC094iC01p00951},
issn = {0148-0227},
journal = {J. Geophys. Res.},
number = {C1},
pages = {951--966},
title = {{Wave transformation and swash oscillation on gentle and steep slopes}},
volume = {94},
year = {1989}
}
@article{Kolgan1975,
author = {Kolgan, N. E.},
journal = {Uchenye Zapiski TsaGI [Sci. Notes Central Inst. Aerodyn]},
pages = {1--6},
title = {{Finite-difference schemes for computation of three dimensional solutions of gas dynamics and calculation of a flow over a body under an angle of attack}},
volume = {6(2)},
year = {1975}
}
@article{Kolgan1972,
author = {Kolgan, N. E.},
journal = {Uchenye Zapiski TsaGI [Sci. Notes Central Inst. Aerodyn]},
pages = {68--77},
title = {{Application of the minimum-derivative principle in the construction of finite-difference schemes for numerical analysis of discontinuous solutions in gas dynamics}},
volume = {3(6)},
year = {1972}
}
@article{Kolmogorov1991,
abstract = {This paper is an English translation of a work (since become classic) of Kolmogorov's first published in 1941. Definitions on the local structure of turbulence are presented, and similarity hypotheses are stated.},
author = {Kolmogorov, A. N.},
doi = {10.1098/rspa.1991.0075},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {jul},
number = {1890},
pages = {9--13},
title = {{The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1991.0075},
volume = {434},
year = {1991}
}
@article{Komatitsch2002,
author = {Komatitsch, D. and Ritsema, J. and Tromp, J.},
journal = {Science},
pages = {1737--1742},
title = {{The Spectral-Element Method, Beowulf Computing, and Global Seismology}},
volume = {298},
year = {2002}
}
@book{Komen1996,
address = {Cambridge},
author = {Komen, G. J. and Cavalieri, L. and Donelan, M. and Hasselmann, K. and Hasselmann, S. and Janssen, P. A. E. M.},
isbn = {978-0521577816},
pages = {556},
publisher = {Cambridge University Press},
title = {{Dynamics and Modelling of Ocean Waves}},
year = {1996}
}
@article{Kondo2002a,
author = {Kondo, C. I. and LeFloch, Ph. G.},
doi = {10.1137/S0036141000374269},
issn = {0036-1410},
journal = {SIAM J. Math. Anal.},
month = {jan},
number = {6},
pages = {1320--1329},
title = {{Zero Diffusion-Dispersion Limits for Scalar Conservation Laws}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0036141000374269},
volume = {33},
year = {2002}
}
@article{Kong2013,
author = {Kong, L. and Wang, L. and Jiang, S. and Duan, Y.},
doi = {10.1007/s11425-013-4575-3},
issn = {1674-7283},
journal = {Science China Mathematics},
month = {may},
number = {5},
pages = {915--932},
title = {{Multisymplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schr{\"{o}}dinger equations}},
url = {http://link.springer.com/10.1007/s11425-013-4575-3},
volume = {56},
year = {2013}
}
@inproceedings{Koren1988,
address = {Aachen},
author = {Koren, B.},
booktitle = {Proceedings of the Second International Conference on Hyperbolic Problems},
editor = {Ballmann, J and Jeltsch, R},
pages = {300--309},
publisher = {Vieweg, Braunschweig},
series = {Notes on Numerical Fluid Mechanics},
title = {{Upwind schemes for the Navier-Stokes equations}},
volume = {24},
year = {1988}
}
@article{Korkmaz2010,
abstract = {The nonlinear Korteweg-de Vries (KdVE) equation is solved numerically using both Lagrange polynomials based differential quadrature and cosine expansion-based differential quadrature methods. The first test example is travelling single solitary wave solution of KdVE and the second test example is interaction of two solitary waves, whereas the other three examples are wave production from solitary waves. Maximum error norm and root mean square error norm are computed, and numerical comparison with some earlier works is done for the first two examples, the lowest four conserved quantities are computed for all test examples.},
author = {Korkmaz, A.},
doi = {10.1002/num.20505},
issn = {0749159X},
journal = {Numerical Methods for Partial Differential Equations},
keywords = {Korteweg-de Vries equation,differential quadrature method,interaction,soliton,wave generation},
number = {6},
pages = {1504--1521},
title = {{Numerical algorithms for solutions of Korteweg-de Vries equation}},
url = {http://doi.wiley.com/10.1002/num.20505},
volume = {26},
year = {2010}
}
@article{Korobkin2008,
author = {Korobkin, A. and Oguz, Y.},
doi = {10.1007/s10665-008-9237-z},
journal = {J. Eng. Math.},
title = {{The initial stage of dam-break flow}},
year = {2008}
}
@article{Korotkevich2008a,
abstract = {The results of the direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time, the simultaneous formation of both direct and inverse cascades has been observed in the framework of the primordial dynamical equations. At the same time, a strong long wave background has been developed. It has been shown that the Kolmogorov spectra obtained are very sensitive to the presence of this condensate. Such a situation has to be typical for experimental wave tanks, flumes, and small lakes.},
author = {Korotkevich, A. O.},
institution = {L. D. Landau Institute for Theoretical Physics RAS, 2 Kosygin Street, Moscow, 119334, Russian Federation. kao@itp.ac.ru},
journal = {Phys. Rev. Lett},
number = {7},
pages = {74504},
title = {{Simultaneous numerical simulation of direct and inverse cascades in wave turbulence.}},
url = {http://arxiv.org/abs/0805.0445},
volume = {101},
year = {2008}
}
@inbook{Korotkevich2007,
author = {Korotkevich, A. O. and Pushkarev, A. N. and Resio, D. and Zakharov, V. E.},
chapter = {Numerical},
editor = {Kundu, A},
pages = {135--172},
publisher = {Springer Berlin Heidelberg},
title = {{Tsunami and Nonlinear Waves}},
year = {2007}
}
@article{Korotkevich2008,
author = {Korotkevich, A. O. and Pushkarev, A. N. and Resio, D. and Zakharov, V. E.},
journal = {Eur. J. Mech. B/Fluids},
pages = {361--387},
title = {{Numerical verification of the weak turbulent model for swell evolution}},
volume = {27(4)},
year = {2008}
}
@article{Korteweg1901,
author = {Korteweg, D. J.},
journal = {Archives N{\'{e}}erlandaises des Sciences Exactes et Naturelles},
pages = {1},
title = {{Sur la forme que prennent les {\'{e}}quations du mouvement des fluides si l'on tient compte des forces capillaires caus{\'{e}}es par des variations de densit{\'{e}} consid{\'{e}}rables mais continues et sur la th{\'{e}}orie de la capillarit{\'{e}} dans l'hypoth{\`{e}}se d'une variation continue d}},
volume = {6},
year = {1901}
}
@article{KdV,
author = {Korteweg, D. J. and de Vries, G.},
journal = {Phil. Mag.},
number = {5},
pages = {422--443},
title = {{On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves}},
volume = {39},
year = {1895}
}
@article{Kosinski1977,
author = {Kosinski, W.},
doi = {10.1016/0022-247X(77)90170-6},
issn = {0022247X},
journal = {Journal of Mathematical Analysis and Applications},
month = {dec},
number = {3},
pages = {672--688},
title = {{Gradient catastrophe in the solution of nonconservative hyperbolic systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0022247X77901706},
volume = {61},
year = {1977}
}
@article{Kowalik2005,
author = {Kowalik, Z. and Knight, W. and Logan, T. and Whitmore, P.},
journal = {Science of Tsunami Hazards},
number = {1},
pages = {40--56},
title = {{Numerical Modeling of the Global Tsunami: Indonesian Tsunami of 26 December 2004}},
volume = {23},
year = {2005}
}
@article{Kowalik2007,
author = {Kowalik, Z. and Knight, W. and Logan, T. and Whitmore, P.},
journal = {Pure and Applied Geophysics},
pages = {379--393},
title = {{The tsunami of 26 December, 2004: Numerical modeling and energy considerations}},
volume = {164},
year = {2007}
}
@article{Kraenkel2005,
author = {Kraenkel, R. A. and Leon, J. and Manna, M. A.},
journal = {Physica D},
pages = {377--390},
title = {{Theory of small aspect ratio waves in deep water}},
volume = {211},
year = {2005}
}
@article{Krasitskii1994,
author = {Krasitskii, V. P.},
journal = {J. Fluid Mech},
pages = {1--20},
title = {{On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves}},
volume = {272},
year = {1994}
}
@article{Krause1970,
abstract = {The western New Britain Trench is receiving abundant sediment from the west. Evidence for earthquake-triggered turbidity currents has been detected in the New Britain Trench through breaks in a submarine telephone cable in 1966 and 1968. The average velocity of the turbidity currents is 50 and 30 km/hr, respectively, assuming that the most likely single source of the turbidity currents is the Markham River delta at Lae, New Guinea. Bottom photographs and sediment samples support these conclusions. Deep-sea channels are present.},
author = {Krause, D. C. and White, W. C. and Piper, D. J. W. and Heezen, B. C.},
journal = {Bull. Geol. Soc. Am.},
number = {7},
pages = {2153--2160},
title = {{Turbidity currents and cable breaks in the western New Britain Trench}},
volume = {81},
year = {1970}
}
@article{Kreiss1992,
author = {Kreiss, H. O. and Scherer, G.},
journal = {SIAM Journal on Numerical Analysis},
pages = {640--646},
title = {{Method of lines for hyperbolic equations}},
volume = {29},
year = {1992}
}
@article{Kremer2012,
author = {Kremer, K. and Simpson, G. and Girardclos, S.},
doi = {10.1038/ngeo1618},
issn = {1752-0894},
journal = {Nature Geoscience},
month = {oct},
number = {11},
pages = {756--757},
title = {{Giant Lake Geneva tsunami in AD 563}},
url = {http://www.nature.com/doifinder/10.1038/ngeo1618},
volume = {5},
year = {2012}
}
@book{Kroner1997,
author = {Kroner, D.},
publisher = {Wiley, Stuttgart},
title = {{Numerical Schemes for Conservation Laws}},
year = {1997}
}
@article{Kubo2004,
abstract = {Topographic effects on deposition from particle-driven density current were investigated. The laboratory experiments were carried out on topography consisting of a ramp and a series of humps. The results show a localized increase in deposit distribution downstream of the slope break and on the upslope of a hump. A numerical model is developed to predict the topographic effects on deposit distribution. The model, based on layer-averaged Navier–Stokes equations, is applied to the experiments, and the process of the topographic influence is analyzed. The preferential deposition downstream of the slope break is interpreted to result from deceleration of the flow, which increases deposit distribution through loss of capacity of the flow and longer duration of the flow passage. The former effect is more influential than the latter, while additional effects of a hydraulic jump may be imposed. Increased deposit on the upslope of a hump is attributed to partial blocking of the flow at the hump crest, as well as to the differential deposition due to deceleration on the upslope.},
author = {Kubo, Y.},
doi = {10.1016/j.sedgeo.2003.11.002},
issn = {00370738},
journal = {Sedimentary Geology},
keywords = {Numerical model,Tank experiments,Topographic effect,Turbidity current},
month = {feb},
number = {3-4},
pages = {311--326},
title = {{Experimental and numerical study of topographic effects on deposition from two-dimensional, particle-driven density currents}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0037073803003300},
volume = {164},
year = {2004}
}
@article{Kubo2002,
abstract = {This paper presents the results of laboratory experiments and numerical simulations carried out in order to understand the mechanism of sediment-wave formation by turbidity currents. Experimental turbidity currents were generated in a 10-m-long laboratory flume, so as to investigate the topographic effects of slope and ridges on turbidite deposition. The results indicate that preferential deposition occurs on the upstream side of the ridges. This preferential deposition is considered to result in possible upstream migration of the topography, a common feature of deep-sea sediment waves, provided that such deposition were repeated. The preferential deposition occurred under a subcritical turbidity current, implying that antidune flow conditions (0.8442.0.CO;2},
issn = {0027-0644},
journal = {Mon. Wea. Rev.},
month = {jul},
number = {7},
pages = {1931--1951},
title = {{Finite Elements for Shallow-Water Equation Ocean Models}},
url = {http://journals.ametsoc.org/doi/abs/10.1175/1520-0493(1998)126<1931:FEFSWE>2.0.CO;2},
volume = {126},
year = {1998}
}
@inproceedings{Leduc2010,
author = {Leduc, J. and Leboeuf, F. and Lance, M. and Parkinson, E. and Marongiu, J. C.},
booktitle = {5th SPHERIC Workshop Proceedings},
title = {{Improvement of multiphase model using preconditioned Riemann solvers}},
year = {2010}
}
@article{LeFloch1999,
author = {LeFloch, Ph. G. and Natalini, R.},
doi = {10.1016/S0362-546X(98)00012-1},
issn = {0362546X},
journal = {Nonlinear Analysis: Theory, Methods {\&} Applications},
month = {apr},
number = {2},
pages = {213--230},
title = {{Conservation laws with vanishing nonlinear diffusion and dispersion}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0362546X98000121},
volume = {36},
year = {1999}
}
@inproceedings{Leibovich1969,
abstract = {Vortex breakdown in rotating fluids associated with wave motion along axis of rotation, considering effects of nonzero wave amplitude},
author = {Leibovich, S.},
booktitle = {AIAA PAPER 69-645},
doi = {10.2514/6.1969-645},
pages = {10},
title = {{Wave motion and vortex breakdown}},
year = {1969}
}
@article{Leibovich1970,
abstract = {The Korteweg-de Vries equation is shown to govern formation of solitary and cnoidal waves in rotating fluids confined in tubes. It is proved that the method must fail when the tube wall is moved to infinity, and the failure is corrected by singular perturbation procedures. The Korteweg-de Vries equation must then give way to an integro-differential equation. Also, critical stationary flows in tubes are considered with regard to Benjamin's vortex breakdown theories.},
author = {Leibovich, S.},
doi = {10.1017/S0022112070001611},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {04},
pages = {803--822},
title = {{Weakly non-linear waves in rotating fluids}},
volume = {42},
year = {1970}
}
@article{Leibovich1968,
author = {Leibovich, S.},
doi = {10.1017/S0022112068000881},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {03},
pages = {529--548},
title = {{Axially-symmetric eddies embedded in a rotational stream}},
volume = {32},
year = {1968}
}
@article{Leibovich1984,
author = {Leibovich, S.},
doi = {10.2514/3.8761},
issn = {0001-1452},
journal = {AIAA Journal},
month = {sep},
number = {9},
pages = {1192--1206},
title = {{Vortex stability and breakdown - Survey and extension}},
volume = {22},
year = {1984}
}
@book{Leimkuhler2004,
address = {Cambridge},
author = {Leimkuhler, B. and Reich, S.},
chapter = {12},
doi = {10.1017/CBO9780511614118},
isbn = {9780511614118},
number = {14},
pages = {xvi+379},
publisher = {Cambridge University Press},
series = {Cambridge Monographs on Applied and Computational Mathematics},
title = {{Simulating Hamiltonian Dynamics}},
url = {http://ebooks.cambridge.org/ref/id/CBO9780511614118},
volume = {14},
year = {2005}
}
@article{Leite1959,
abstract = {An axially symmetric laminar flow of air was established in a long smooth pipe. This flow was steady up to Reynolds numbers of about 20,000, the capacity of the system. Small, nearly axially, symmetric disturbances were superimposed by longitudinally oscillating a thin sleeve adjacent to the inner wall of the pipe. Hot-wire anemometer measurements consisting of radial and longitudinal traverses were made downstream of the sleeve. These measurements indicated that within the Reynolds number range investigated (up to 13,000), the flow is stable to small disturbances. In general, the radial distribution of disturbance amplitudes was not independent of distance downstream; while the disturbances, as generated, exhibited imperfect axial symmetry, the non-symmetric part decayed more rapidly than the symmetric part. Results were interpreted in such a way that rates of propagation and rates of decay of the disturbances could be compared with those given by a recent theoretical stability analysis. It was found that the rates of decay are predicted fairly satisfactorily by the theory; however, the rates of propagation are not. In addition, it was found that transition to turbulent flow occurs whenever the amplitude of the disturbance exceeds a threshold value which decreases with increasing Reynolds number. Due to the departures from axial symmetry in the amplitude of the disturbance, it was not possible to obtain a quantitative measure of the threshold. A mathematical idealization of the disturbances, believed to be more akin to experimental perturbations than the classical model used in small-perturbation analyses, is proposed.},
author = {Leite, R. J.},
doi = {10.1017/S0022112059000076},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {01},
pages = {81},
title = {{An experimental investigation of the stability of Poiseuille flow}},
volume = {5},
year = {1959}
}
@article{Lenau1966,
abstract = {The maximum amplitude of the solitary wave of constant form is determined to be 0.83b, where b is the depth far from the crest. In the analysis it is assumed that the crest is pointed and the motion is two-dimensional and irrotational. The complex velocity potential is expressed in terms of known singularities and an infinite power series with unknown coefficients. Approximate solutions are obtained by truncating the power series after N terms, where N = 1, 3, 5, 7, and 9. The amplitude, a measure of the error, and several other pertinent quantities are computed for each value of N.},
author = {Lenau, C. W.},
doi = {10.1017/S0022112066001253},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {02},
pages = {309--320},
title = {{The solitary wave of maximum amplitude}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112066001253},
volume = {26},
year = {1966}
}
@article{Lenells2005,
abstract = {We classify all weak traveling wave solutions of the Degasperis-Procesi equation. In addition to smooth and peaked solutions; the equation is shown to admit more exotic traveling waves such as cuspons; stumpons; and composite waves.},
author = {Lenells, J.},
doi = {10.1016/j.jmaa.2004.11.038},
issn = {0022247X},
journal = {Journal of Mathematical Analysis and Applications},
keywords = {Degasperis–Procesi equation,Traveling waves},
mendeley-tags = {Degasperis–Procesi equation,Traveling waves},
month = {jun},
number = {1},
pages = {72--82},
title = {{Traveling wave solutions of the Degasperis-Procesi equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022247X04009606},
volume = {306},
year = {2005}
}
@book{Lesieur2008,
abstract = {This is the 4th edition of a book originally published by Kluwer Academic Publishers. It is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects, with many advanced developments using mathematical spectral methods (two-point closures like the EDQNM theory), direct-numerical simulations, and large-eddy simulations. The book is still of great actuality on a topic of the utmost importance for engineering and environmental applications, and presents a very detailed presentation of the field. The fourth edition incorporates new results coming from research work done since 1997. Many of these results come from direct and large-eddy simulations methods, which have provided significant advances in problems such as turbulent mixing or thermal exchanges (with and without gravity effects). Topics dealt with include: an introduction to turbulence in fluid mechanics; basic fluid dynamics; transition to turbulence; shear-flow turbulence; Fourier analysis for homogeneous turbulence; isotropic turbulence; phenomenology and simulations; analytical theories and stochastic models; two-dimensional turbulence; geostrophic turbulence; absolute-equilibrium ensembles; the statistical predictability theory; large-eddy simulations; and a section that explores developments towards real-world turbulence.},
author = {Lesieur, M.},
booktitle = {Fluid Mechanics and its Applications},
doi = {10.1007/978-1-4020-6435-7},
editor = {Moreau, R},
isbn = {9781402064340},
pages = {558},
publisher = {Springer},
series = {Fluid Mechanics and Its Applications},
title = {{Turbulence in Fluids}},
url = {http://books.google.com/books?hl=en{\&}amp;lr={\&}amp;id=xKUDN22Y7OYC{\&}amp;oi=fnd{\&}amp;pg=PP17{\&}amp;dq=TURBULENCE+IN+FLUIDS{\&}amp;ots=lVShFaY{\_}EI{\&}amp;sig=TimCrofR8OxYJc-Wy30Df95bWqY},
volume = {84},
year = {2008}
}
@article{Levenberg1944,
author = {Levenberg, K.},
journal = {Quart. Appl. Math.},
pages = {164--168},
title = {{A method for the solution of certain problems in least squares}},
volume = {2},
year = {1944}
}
@article{LeVeque,
author = {LeVeque, R. J.},
journal = {J. Comp. Phys.},
pages = {346--365},
title = {{Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm}},
volume = {146},
year = {1998}
}
@book{LeVeque1992,
address = {Basel},
author = {LeVeque, R. J.},
doi = {10.1007/978-3-0348-8629-1},
edition = {2},
isbn = {978-3-7643-2723-1},
pages = {XII+220},
publisher = {Birkh{\"{a}}user Basel},
title = {{Numerical Methods for Conservation Laws}},
url = {http://link.springer.com/10.1007/978-3-0348-8629-1},
year = {1992}
}
@article{LeVeque1985,
author = {LeVeque, R. J. and Temple, B.},
journal = {Trans. Amer. Math. Soc.},
number = {1},
pages = {115--123},
title = {{Stability of Godunov's method for a class of 2x2 systems of conservation laws}},
volume = {288},
year = {1985}
}
@article{Levy2004,
author = {Levy, D. and Shu, C.-W. and Yan, J.},
journal = {J. Comput. Phys.},
pages = {751--772},
title = {{Local discontinuous Galerkin methods for nonlinear dispersive equations}},
volume = {196(2)},
year = {2004}
}
@inproceedings{Lew2003,
abstract = {The purpose of this paper is to survey some recent advances in variational integrators for both finite dimensional mechanical systems as well as continuum mechanics. These advances include the general development of discrete mechanics, applications to dissipative systems, collisions, spacetime integration algorithms, AVI’s (Asynchronous Variational Integrators), as well as reduction for discrete mechanical systems. To keep the article within the set limits, we will only treat each topic briefly and will not attempt to develop any particular topic in any depth. We hope, nonetheless, that this paper serves as a useful guide to the literature as well as to future directions and open problems in the subject.},
address = {Barcelona, Spain},
author = {Lew, A. and Marsden, J. and Ortiz, M. and West, M.},
booktitle = {Finite Element Methods: 1970s and beyond (CIMNE, 2003)},
pages = {18},
title = {{An overview of variational integrators}},
year = {2004}
}
@article{Lewis1986,
author = {Lewis, D. and Marsden, J. and Montgomery, R. and Ratiu, T.},
journal = {Physica D},
pages = {391--404},
title = {{The Hamiltonian structure for dynamic free boundary problems}},
volume = {18},
year = {1986}
}
@article{Li1983,
abstract = {We construct noninteracting wave patterns (i.e., asymptotic states) for a conservation law with a general moving source term. When nonlinear resonance occurs, which is the case when the characteristic speed is near the speed of the source, instability may result. We identify a stability criterion which is independent of the flux function. This is so, even if composite wave patterns exist, as may be the case for nonconvex flux functions. We study the general scalar model as well as transonic gas flows through a duct with varying cross section. For the latter case, noninteracting wave patterns for such a flow are constructed for arbitrary equations of state. It is shown that the stability of a wave pattern depends on the geometry of the duct, and not on the equation of the state. In particular, transonic steady shock waves along a converging duct are unstable, and flow along a diverging duct is always stable.},
author = {Li, C.-Zh. and Liu, T.-P.},
doi = {10.1016/0196-8858(83)90015-5},
issn = {01968858},
journal = {Advances in Applied Mathematics},
month = {dec},
number = {4},
pages = {353--379},
title = {{Asymptotic states for hyperbolic conservation laws with a moving source}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0196885883900155},
volume = {4},
year = {1983}
}
@article{Li2011,
author = {Li, W. and Yeh, H. and Kodama, Y.},
journal = {J. Fluid Mech.},
pages = {326--357},
title = {{On the Mach reflection of a solitary wave: revisited}},
volume = {672},
year = {2011}
}
@article{Li2008,
author = {Li, X.-S. and Gu, C.-W.},
journal = {J. Comput. Phys.},
pages = {5144--5159},
title = {{An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour}},
volume = {227},
year = {2008}
}
@article{Li2001,
author = {Li, Y. A.},
journal = {Commun. Pure Appl. Math.},
number = {5},
pages = {501--536},
title = {{Linear stability of solitary waves of the Green-Naghdi equations}},
volume = {54},
year = {2001}
}
@article{Li2006,
author = {Li, Y. A.},
journal = {Communications on pure and applied mathematics},
number = {9},
pages = {1225--1285},
title = {{A shallow-water approximation to the full water wave problem}},
volume = {59},
year = {2006}
}
@article{Li2002,
author = {Li, Y. A.},
journal = {J. Nonlin. Math. Phys.},
number = {1},
pages = {99--105},
title = {{Hamiltonian structure and linear stability of solitary waves of the Green-Naghdi equations}},
volume = {9},
year = {2002}
}
@article{Li2006a,
author = {Li, Y. A.},
doi = {10.1002/cpa.20148},
issn = {0010-3640},
journal = {Communications on Pure and Applied Mathematics},
month = {sep},
number = {9},
pages = {1225--1285},
title = {{A shallow-water approximation to the full water wave problem}},
url = {http://doi.wiley.com/10.1002/cpa.20148},
volume = {59},
year = {2006}
}
@article{Li2004,
author = {Li, Y. A. and Hyman, J. M. and Choi, W.},
journal = {Stud. Appl. Maths.},
pages = {303--324},
title = {{A Numerical Study of the Exact Evolution Equations for Surface Waves in Water of Finite Depth}},
volume = {113},
year = {2004}
}
@article{Li2002a,
author = {Li, Y. and Raichlen, F.},
journal = {J. Fluid Mech.},
pages = {295--318},
title = {{Non-breaking and breaking solitary wave run-up}},
volume = {456},
year = {2002}
}
@book{Liao2012,
address = {Berlin, Heidelberg},
author = {Liao, S.},
doi = {10.1007/978-3-642-25132-0},
isbn = {978-3-642-25131-3},
pages = {565},
publisher = {Springer Berlin Heidelberg},
title = {{Homotopy Analysis Method in Nonlinear Differential Equations}},
url = {http://link.springer.com/10.1007/978-3-642-25132-0},
year = {2012}
}
@article{Liao2014,
abstract = {Many models of shallow water waves, such as the famous Camassa-Holm equation, admit peaked solitary waves. However, it is an open question whether or not the widely accepted peaked solitary waves can be derived from the fully nonlinear wave equations. In this paper, a unified wave model (UWM) based on the symmetry and the fully nonlinear wave equations is put forward for progressive waves with permanent form in finite water depth. Different from traditional wave models, the flows described by the UWM are not necessarily irrotational at crest, so that it is more general. The unified wave model admits not only the traditional progressive waves with smooth crest, but also a new kind of solitary waves with peaked crest that include the famous peaked solitary waves given by the Camassa-Holm equation. Besides, it is proved that Kelvin's theorem still holds everywhere for the newly found peaked solitary waves. Thus, the UWM unifies, for the first time, both of the traditional smooth waves and the peaked solitary waves. In other words, the peaked solitary waves are consistent with the traditional smooth ones. So, in the frame of inviscid fluid, the peaked solitary waves are as acceptable and reasonable as the traditional smooth ones. It is found that the peaked solitary waves have some unusual and unique characteristics. First of all, they have a peaked crest with a discontinuous vertical velocity at crest. Especially, unlike the traditional smooth waves that are dispersive with wave height, the phase speed of the peaked solitary waves has nothing to do with wave height, but depends (for a fixed wave height) on its decay length, i.e., the actual wavelength: in fact, the peaked solitary waves are dispersive with the actual wavelength when wave height is fixed. In addition, unlike traditional smooth waves whose kinetic energy decays exponentially from free surface to bottom, the kinetic energy of the peaked solitary waves either increases or almost keeps the same. All of these unusual properties show the novelty of the peaked solitary waves, although it is still an open question whether or not they are reasonable in physics if the viscosity of fluid and surface tension are considered. ?? 2013 Elsevier B.V.},
archivePrefix = {arXiv},
arxivId = {1204.3354},
author = {Liao, S.},
doi = {10.1016/j.cnsns.2013.09.042},
eprint = {1204.3354},
issn = {10075704},
journal = {Comm. Nonlin. Sci. Num. Sim.},
keywords = {Homotopy analysis method (HAM),Progressive wave,Solitary peaked wave,Unified wave model (UWM)},
number = {6},
pages = {1792--1821},
title = {{Do peaked solitary water waves indeed exist?}},
volume = {19},
year = {2014}
}
@book{Liapidevskii2000,
address = {Novosibirsk},
author = {Liapidevskii, V. Yu. and Teshukov, V. M.},
pages = {419},
publisher = {Izd. Sib. Otd. Ross. Akad. Nauk},
title = {{Mathematical models of long wave propagation in an inhomogeneous fluid}},
year = {2000}
}
@techreport{Lied2006,
author = {Lied, K.},
institution = {European Commission},
title = {{SATSIE: Avalanche Studies and Model Validation in Europe}},
year = {2006}
}
@article{Lied1980,
author = {Lied, K. and Bakkeh{\o}i, S.},
journal = {Journal of Glaciology},
pages = {165--177},
title = {{Empirical calculations of snow avalanche run-out distances based on topographic parameters}},
volume = {26},
year = {1980}
}
@article{Lien1999,
author = {Lien, W.-C.},
journal = {Comm. Pure Appl. Math.},
number = {9},
pages = {1075--1098},
title = {{Hyperbolic conservation laws with a moving source}},
volume = {52},
year = {1999}
}
@book{Lievois2006,
author = {Li{\'{e}}vois, J.},
publisher = {La Documentation Fran$\backslash$c{\{}c{\}}aise, Paris},
title = {{Guide m{\'{e}}thodologique des plans de pr{\'{e}}vention des risques d'avalanches}},
year = {2006}
}
@book{Lifshitz1988,
address = {New York},
author = {Lifshitz, I. M. and Gredeskul, S. A. and Pastur, L. A.},
pages = {462},
publisher = {John Wiley {\&} Sons Inc.},
title = {{Introduction to the Theory of Disordered Systems}},
year = {1988}
}
@book{LighthillEd.1967,
address = {London},
author = {{Lighthill (Ed.)}, M. J.},
pages = {145},
publisher = {Royal Society},
title = {{A discussion on nonlinear theory of wave propagation in dispersive systems}},
year = {1967}
}
@article{Lighthill1979,
author = {Lighthill, J.},
journal = {Journal of Fluid Mechanics},
pages = {253--317},
title = {{Two-dimensional analyses related to wave-energy extraction by submerged resonant ducts}},
volume = {91:2},
year = {1979}
}
@book{Lighthill1978,
author = {Lighthill, J.},
publisher = {Cambridge University Press},
title = {{Waves in Fluids}},
year = {1978}
}
@article{Likhachev2005,
author = {Likhachev, O. A. and Jacobs, J. W.},
journal = {Phys. Fluids},
pages = {31704},
title = {{A vortex model for Richtmyer-Meshkov instability accounting for finite Atwood number}},
volume = {17},
year = {2005}
}
@article{Lin2006,
abstract = {We present numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space-dependent noise and a combination of the two. We employ polynomial chaos for discretization in random space, and discontinuous Galerkin and finite difference for discretization in physical space. The accuracy of the stochastic solutions is investigated by comparing the first two moments against analytical and Monte Carlo simulation results. Of particular interest is the interplay of spatial discretization error with the stochastic approximation error, which is examined for different orders of spatial and stochastic approximation.},
author = {Lin, G. and Grinberg, L. and Karniadakis, G. E.},
doi = {10.1016/j.jcp.2005.08.029},
issn = {00219991},
journal = {Journal of Computational Physics},
keywords = {discontinuous galerkin method,kdv,polynomial chaos,uncertainty},
number = {2},
pages = {676--703},
title = {{Numerical studies of the stochastic Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999105004122},
volume = {213},
year = {2006}
}
@book{Lind1995,
abstract = {Symbolic dynamics is a rapidly growing area of dynamical systems. Although it originated as a method to study general dynamical systems, it has found significant uses in coding for data storage and transmission as well as in linear algebra. This book is the first general textbook on symbolic dynamics and its applications to coding. Mathematical prerequisites are relatively modest (mainly linear algebra at the undergraduate level) especially for the first half of the book. Topics are carefully developed and motivated with many examples, and there are over 500 exercises to test the reader's understanding. The last chapter contains a survey of more advanced topics, and a comprehensive bibliography is included. This book will serve as an introduction to symbolic dynamics for advanced undergraduate students in mathematics, engineering, and computer science.},
address = {Cambridge},
author = {Lind, D. A. and Marcus, B. H.},
isbn = {978-0521559003},
pages = {516},
publisher = {Cambridge University Press},
title = {{An introduction to symbolic dynamics and coding}},
year = {1995}
}
@book{Linton2001,
abstract = {Although a wide range of mathematical techniques can apply to solving problems involving the interaction of waves with structures, few texts discuss those techniques within that context-most often they are presented without reference to any applications. Handbook of Mathematical Techniques for Wave/Structure Interactions brings together some of the most important techniques useful to applied mathematicians and engineers. Each chapter is dedicated to a particular technique, such as eigenfunction expansions, multipoles, integral equations, and Wiener-Hopf methods. Other chapters discuss approximation techniques and variational methods. The authors describe all of the techniques in terms of wave/structure interactions, with most illustrated by application to research problems. They provide detailed explanations of the important steps within the mathematical development, and, where possible, physical interpretations of mathematical results. Handbook of Mathematical Techniques for Wave/Structure Interactions effectively bridges the gap between the heavy computational methods preferred by some engineers and the more mathematical approach favored by others. These techniques provide a powerful means of dealing with wave/structure interactions, are readily applied to relevant problems, and illuminate those problems in a way that neither a purely computational approach nor a straight theoretical treatment can.},
author = {Linton, C. M. and McIver, P.},
pages = {320},
publisher = {Chapman $\backslash${\&} Hall/CRC},
title = {{Mathematical Techniques for Wave/Structure Interactions}},
year = {2001}
}
@book{Lions1998,
author = {Lions, P.-L.},
publisher = {Oxford University Press},
title = {{Mathematical topics in fluid dynamics, Vol. 2. Compressible models}},
year = {1998}
}
@article{Litvinenko1999,
author = {Litvinenko, A. A. and Khabakhpashev, G. A.},
journal = {Computational Technologies},
pages = {95--105},
title = {{Numerical modeling of sufficiently long nonlinear two-dimensional waves on water in a basin with a gently sloping bottom}},
volume = {4},
year = {1999}
}
@article{Liu2006a,
author = {Liu, P. L.-F.},
journal = {Proc. Roy. Soc. London},
pages = {3481--3491},
title = {{Turbulent boundary layer effects on transient wave propagation in shallow water}},
volume = {462(2075)},
year = {2006}
}
@inbook{Liu,
author = {Liu, P. L.-F. and Liggett, J. A.},
chapter = {Chapter 3},
pages = {37--67},
title = {{Applications of boundary element methods to problems of water waves}},
year = {1983}
}
@article{MR2011541,
author = {Liu, P. L.-F. and Lynett, P. and Synolakis, C. E.},
issn = {0022-1120},
journal = {J. Fluid Mech.},
pages = {101--109},
title = {{Analytical solutions for forced long waves on a sloping beach}},
volume = {478},
year = {2003}
}
@article{Liu2004,
author = {Liu, P. L.-F. and Orfila, A.},
journal = {J. Fluid Mech.},
pages = {83--92},
title = {{Viscous effects on transient long-wave propagation}},
volume = {520},
year = {2004}
}
@article{Liu2007,
author = {Liu, P. L.-F. and Park, Y. S. and Cowen, E. A.},
journal = {J. Fluid Mech.},
pages = {449--463},
title = {{Boundary layer flow and bed shear stress under a solitary wave}},
volume = {574},
year = {2007}
}
@article{Liu2006,
author = {Liu, P. L.-F. and Simarro, G. and Vandever, J. and Orfila, A.},
journal = {Coastal Engineering},
pages = {181--190},
title = {{Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank}},
volume = {53},
year = {2006}
}
@techreport{Liu1998,
author = {Liu, P. L.-F. and Woo, S.-B. and Cho, Y.-K.},
institution = {School of Civil and Environmental Engineering, Cornell University},
title = {{Computer Programs for Tsunami Propagation and Inundation}},
year = {1998}
}
@article{Liu1987,
abstract = {The purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source. Resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system. For the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear interactions which lead to rich wave phenomena. Motivated by physical examples a scalar model is proposed and analyzed to describe the qualitative behavior of waves for a general system in resonance with the source. Analytical understanding is used to design a numerical scheme based on the random choice method. An important physical example is transonic gas flow through a nozzle. This analysis provides a transparent and revealing qualitative understanding of wave behavior of gas flow, including such phenomena as nonlinear stability, instability, and changing types of waves.},
author = {Liu, T.-P.},
doi = {10.1063/1.527751},
issn = {00222488},
journal = {J. Math. Phys.},
number = {11},
pages = {2593},
title = {{Nonlinear resonance for quasilinear hyperbolic equation}},
url = {http://scitation.aip.org/content/aip/journal/jmp/28/11/10.1063/1.527751},
volume = {28},
year = {1987}
}
@article{Liu1979,
abstract = {We construct global solutions for quasilinear hyperbolic systems and study their asymptotic behaviors. The systems include models of gas flows in a variable area duct and flows with a moving source. Our analysis is based on a numerical scheme which generalizes the Glimm scheme for hyperbolic conservation laws.},
author = {Liu, T.-P.},
doi = {10.1007/BF01418125},
issn = {0010-3616},
journal = {Comm. Math. Phys.},
month = {jun},
number = {2},
pages = {141--172},
title = {{Quasilinear hyperbolic systems}},
url = {http://link.springer.com/10.1007/BF01418125},
volume = {68},
year = {1979}
}
@article{LOC,
author = {Liu, X.-D. and Osher, S. and Chan, T.},
journal = {J. Comp. Phys.},
pages = {200--212},
title = {{Weighted essentially non-oscillatory schemes}},
volume = {115},
year = {1994}
}
@article{Liu2005,
author = {Liu, Z. B. and Sun, Z. C.},
doi = {10.1016/j.oceaneng.2004.12.004},
issn = {00298018},
journal = {Ocean Engineering},
month = {aug},
number = {11-12},
pages = {1296--1310},
title = {{Two sets of higher-order Boussinesq-type equations for water waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0029801805000272},
volume = {32},
year = {2005}
}
@article{Liu2002,
author = {Liu, Z. and Qian, T.},
doi = {10.1016/S0307-904X(01)00086-5},
issn = {0307904X},
journal = {Applied Mathematical Modelling},
month = {mar},
number = {3},
pages = {473--480},
title = {{Peakons of the Camassa-Holm equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0307904X01000865},
volume = {26},
year = {2002}
}
@book{Llor2005,
author = {Llor, A.},
publisher = {Springer Verlag},
title = {{Statistical hydrodynamic models for developed mixing instability flows : analytical "0D" evaluation criteria, and comparison of single- and two-phase flow approaches}},
year = {2005}
}
@article{Lo1985,
author = {Lo, E. and Mei, C. C.},
journal = {J. Fluid Mech},
pages = {395--416},
title = {{A numerical study of water-wave modulation based on a higher-order nonlinear Schr{\"{o}}dinger equation}},
volume = {150},
year = {1985}
}
@incollection{Locat2009,
abstract = {Submarine mass movements pose a threat to coastal communities and infrastructures, both onshore and offshore. They can be found from the coastal zone down onto the abyssal plain and can take place on slope angles as low as 0.5°. They can move at velocities up to 50 km/h and reach distances over 1000 km. Their volume can be enormous, as illustrated by the 2.5 × 103 km3 Storegga slide. Similar to their sub-aerial counterparts, submarine mass movements can consist of soil or rock and can take the form of slides, spreads, flows, topples or falls, but in addition they can develop into turbidity currents. Their main consequences are linked either to the direct loss of material at the site where the mass movement is initiated or along its path and to the generation of tsunamis.},
author = {Locat, J. and Lee, H.},
booktitle = {Landslides - Disaster Risk Reduction},
doi = {10.1007/978-3-540-69970-5{\_}6},
isbn = {978-3-540-69970-5},
pages = {115--142},
publisher = {Springer Berlin Heidelberg},
title = {{Submarine Mass Movements and Their Consequences: An Overview}},
year = {2009}
}
@article{Lombard2007,
author = {Lombard, B. and Piraux, J. and G{\'{e}}lis, C. and Virieux, J.},
journal = {Geophys. J. Int.},
pages = {252--261},
title = {{Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves}},
volume = {172},
year = {2007}
}
@book{Lombardi2000,
abstract = {During the last two decades, in several branches of science (water waves, crystal growth, travelling waves in one dimensional lattices, splitting of separatrices,...) different problems appeared in which the key point is the computation of exponentially small terms. This self-contained monograph gives new and rigorous mathematical tools which enable a systematic study of such problems. Starting with elementary illuminating examples, the book contains (i) new asymptotical tools for obtaining exponentially small equivalents of oscillatory integrals involving solutions of nonlinear differential equations; (ii) implementation of these tools for solving old open problems of bifurcation theory such as existence of homoclinic connections near resonances in reversible systems.},
author = {Lombardi, E.},
isbn = {978-3-540-67785-7},
keywords = {Oscillatory integrals,exponential equivalents,homoclinic connections,reversible systems},
pages = {418},
publisher = {Springer},
title = {{Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems}},
year = {2000}
}
@article{LH,
author = {Longuet-Higgins, M. S.},
journal = {Proc. R. Soc. Lond. A},
pages = {1--13},
title = {{On the mass, momentum, energy and circulation of a solitary wave}},
volume = {337},
year = {1974}
}
@article{Longuet-Higgins1980,
author = {Longuet-Higgins, M. S.},
journal = {J. Fluid Mech.},
pages = {1--25},
title = {{Spin and angular momentum in gravity waves}},
volume = {97},
year = {1980}
}
@article{Longuet-Higgins1963,
author = {Longuet-Higgins, M. S.},
doi = {10.1017/S0022112063001452},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {03},
pages = {459--480},
title = {{The effect of non-linearities on statistical distributions in the theory of sea waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112063001452},
volume = {17},
year = {1963}
}
@article{LH1992,
author = {Longuet-Higgins, M. S.},
journal = {J. Fluid Mech.},
pages = {319--324},
title = {{Theory of weakly damped Stokes waves: a new formulation and its physical interpretation}},
volume = {235},
year = {1992}
}
@article{Longuet-Higgins1976,
abstract = {Plunging breakers are beyond the reach of all known analytical approximations. Previous numerical computations have succeeded only in integrating the equations of motion up to the instant when the surface becomes vertical. In this paper we present a new method for following the time-history of space-periodic irrotational surface waves. The only independent variables are the coordinates and velocity potential of marked particles at the free surface. At each time-step an integral equation is solved for the new normal component of velocity. The method is faster and more accurate than previous methods based on a two dimensional grid. It has also the advantage that the marked particles become concentrated near regions of sharp curvature. Viscosity and surface tension are both neglected. The method is tested on a free, steady wave of finite amplitude, and is found to give excellent agreement with independent calculations based on Stokes's series. It is then applied to unsteady waves, produced by initially applying an asymmetric distribution of pressure to a symmetric, progressive wave. The freely running wave then steepens and overturns. It is demonstrated that the surface remains rounded till well after the over-turning takes place.},
author = {Longuet-Higgins, M. S. and Cokelet, E. D.},
doi = {10.1098/rspa.1976.0092},
issn = {1364-5021},
journal = {Proc. R. Soc. A},
month = {jul},
number = {1660},
pages = {1--26},
title = {{The Deformation of Steep Surface Waves on Water. I. A Numerical Method of Computation}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1976.0092},
volume = {350},
year = {1976}
}
@article{Longuet-Higgins1974,
author = {Longuet-Higgins, M. S. and Fenton, J.},
journal = {Proc. R. Soc. A},
pages = {471--493},
title = {{On the Mass, Momentum, Energy and Circulation of a Solitary Wave. II}},
volume = {340(1623)},
year = {1974}
}
@article{Longuet-Higgins1996,
abstract = {The behaviour of the energy in a steep solitary wave as a function of the wave height has a direct bearing on the breaking of solitary waves on a gently shoaling beach. Here it is shown that the speed, energy and momentum of a steep solitary wave in water of finite depth all behave in an oscillatory manner as functions of the wave height and as the limiting height is approached. Asymptotic formulae for these and other wave parameters are derived by means of a theory for the ‘almost-highest wave’ similar to that formulated previously for periodic waves in deep water (Longuet-Higgins {\&} Fox 1977, 1978). It is demonstrated that the theory fits very precisely some recent calculations of solitary waves by Tanaka (1995).},
author = {Longuet-Higgins, M. S. and Fox, J. H.},
doi = {10.1017/S002211209600064X},
journal = {J. Fluid Mech},
pages = {1--19},
title = {{Asymptotic theory for the almost-highest solitary wave}},
volume = {317},
year = {1996}
}
@article{Longuet-Higgins1978,
author = {Longuet-Higgins, M. S. and Fox, M. J. H.},
doi = {10.1017/S0022112078000920},
issn = {0022-1120},
journal = {Journal of Fluid Mechanics},
month = {apr},
pages = {769--786},
title = {{Theory of the almost-highest wave. Part 2. Matching and analytic extension}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112078000920},
volume = {85},
year = {1978}
}
@article{Longuet-Higgins1977,
author = {Longuet-Higgins, M. S. and Fox, M. J. H.},
doi = {10.1017/S0022112077002444},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {721--741},
title = {{Theory of the almost-highest wave: the inner solution}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112077002444},
volume = {80},
year = {1977}
}
@article{Longuet-Higgins1997,
author = {Longuet-Higgins, M. S. and Tanaka, M.},
journal = {J. Fluid Mech.},
pages = {51--68},
title = {{On the crest instabilities of steep surface waves}},
volume = {336},
year = {1997}
}
@article{Lonngren1983,
author = {Lonngren, K. E.},
doi = {10.1088/0032-1028/25/9/001},
issn = {0032-1028},
journal = {Plasma Physics},
month = {sep},
number = {9},
pages = {943--982},
title = {{Soliton experiments in plasmas}},
url = {http://stacks.iop.org/0032-1028/25/i=9/a=001?key=crossref.9e20288c8f816bfe365a95abdf2620f4},
volume = {25},
year = {1983}
}
@article{LordRayleigh1876,
author = {{Lord Rayleigh}, J. W. S.},
journal = {Phil. Mag.},
pages = {257--279},
title = {{On Waves}},
volume = {1},
year = {1876}
}
@article{Lorenz1960,
author = {Lorenz, E. N.},
journal = {Tellus},
pages = {364--373},
title = {{Energy and numerical weather prediction}},
volume = {12},
year = {1960}
}
@misc{Lourakis2004,
author = {Lourakis, M. L. A.},
title = {{levmar: Levenberg-Marquardt nonlinear least squares algorithms in C/C++}},
url = {http://www.ics.forth.gr/{~}lourakis/levmar/},
urldate = {2015-07-04},
year = {2004}
}
@inproceedings{Lourakis2005,
abstract = {In order to obtain optimal 3D structure and viewing parameter estimates, bundle adjustment is often used as the last step of feature-based structure and motion estimation algorithms. Bundle adjustment involves the formulation of a large scale, yet sparse minimization problem, which is traditionally solved using a sparse variant of the Levenberg-Marquardt optimization algorithm that avoids storing and operating on zero entries. This paper argues that considerable computational benefits can be gained by substituting the sparse Levenberg-Marquardt algorithm in the implementation of bundle adjustment with a sparse variant of Powell's dog leg non-linear least squares technique. Detailed comparative experimental results provide strong evidence supporting this claim},
address = {Beijing},
author = {Lourakis, M. L. A. and Argyros, A. A.},
booktitle = {Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1},
doi = {10.1109/ICCV.2005.128},
isbn = {0-7695-2334-X},
pages = {1526--1531},
publisher = {IEEE},
title = {{Is Levenberg-Marquardt the most efficient optimization algorithm for implementing bundle adjustment?}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=1544898},
year = {2005}
}
@book{love,
author = {Love, A. E. H.},
publisher = {Dover Publications, New York},
title = {{A treatise on the mathematical theory of elasticity}},
year = {1944}
}
@article{Lovholt2006,
author = {L{\o}vholt, F. and Bungum, H. and Harbitz, C. B. and Glimsdal, S. and Lindholm, C. and Pedersen, G.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {1--18},
title = {{Earthquake related tsunami hazard along the western coast of Thailand}},
volume = {6},
year = {2006}
}
@article{Lovholt2009,
abstract = {The von Neumann method for stability analysis of linear waves in a uniform medium is a widely applied procedure. However, the method does not apply to stability of linear waves in a variable medium. Herein we describe instabilities due to variable depth for different Boussinesq equations, including the standard model by Peregrine and the popular generalization by Nwogu. Eigenmodes are first found for bathymetric features on the grid scale. For certain combinations of Boussinesq formulations and bottom profiles stability limits are found in closed form, otherwise numerical techniques are used for the eigenvalue problems. Naturally, the unstable modes in such settings must be considered to be as much a result of the difference method as of the underlying differential (Boussinesq) equations. Hence, modes are also computed for smooth depth profiles that are well resolved. Generally, the instabilities do not vanish with refined resolution. In some cases convergence is observed and we thus have indications of unstable solutions of the differential equations themselves. The stability properties differ strongly. While the standard Boussinesq equations seem perfectly stable, all the other formulations do display unstable modes. In most cases the instabilities are linked to steep bottom gradients and small grid increments. However, while a certain formulation, based on velocity potentials, is very prone to instability, the Boussinesq equations of Nwogu become unstable only under quite demanding conditions. Still, for the formulation of Nwogu, instabilities are probably inherent in the differential equations and are not a result of the numerical model.},
author = {L{\o}vholt, F. and Pedersen, G.},
doi = {10.1002/fld.1968},
issn = {02712091},
journal = {Int. J. Num. Meth. Fluids},
keywords = {Boussinesq equations,eigenvalue analysis,linear dispersive waves,stability and convergence of numerical models,surface waves,tsunamis},
month = {oct},
number = {6},
pages = {606--637},
title = {{Instabilities of Boussinesq models in non-uniform depth}},
url = {http://doi.wiley.com/10.1002/fld.1968},
volume = {61},
year = {2009}
}
@article{Lovholt2010,
author = {Lovholt, F. and Pedersen, G. and Glimsdal, S.},
doi = {10.2174/1874252101004010071},
issn = {18742521},
journal = {The Open Oceanography Journal},
month = {may},
number = {1},
pages = {71--82},
title = {{Coupling of Dispersive Tsunami Propagation and Shallow Water Coastal Response}},
url = {http://benthamopen.com/ABSTRACT/TOOCEAJ-4-71},
volume = {4},
year = {2010}
}
@article{Lu2007,
author = {Lu, Y. and Liu, H. and Wu, W. and Zhang, J.},
journal = {Journal of Hydrodynamics, Ser. B},
number = {3},
pages = {322--329},
title = {{Numerical simulation of two-dimensional overtopping against seawalls armored with artificial units in regular waves}},
volume = {19},
year = {2007}
}
@article{Lucy1977,
author = {Lucy, L. B.},
journal = {Astron. J.},
pages = {1013--1024},
title = {{A numerical approach to the testing of the fission hypothesis}},
volume = {82},
year = {1977}
}
@article{Lugni2006,
author = {Lugni, C. and Brocchini, M. and Faltinsen, O. M.},
doi = {10.1063/1.2399077},
issn = {10706631},
journal = {Phys. Fluids},
number = {12},
pages = {122101},
title = {{Wave impact loads: The role of the flip-through}},
url = {http://link.aip.org/link/PHFLE6/v18/i12/p122101/s1{\&}Agg=doi},
volume = {18},
year = {2006}
}
@article{Luk'acov'a-Medvid'ov'a2007,
author = {Luk{\'{a}}cov{\'{a}}-Medvid'ov{\'{a}}, M. and Noelle, S. and Kraft, M.},
journal = {J. Comput. Phys.},
pages = {122--147},
title = {{Well-balanced finite volume evolution Galerkin methods for the shallow water equations}},
volume = {221},
year = {2007}
}
@article{Luke1967,
author = {Luke, J. C.},
journal = {J. Fluid Mech.},
pages = {375--397},
title = {{A variational principle for a fluid with a free surface}},
volume = {27},
year = {1967}
}
@article{Lumley2001,
abstract = {A brief, superficial survey of some very personal nominations for highpoints of the last hundred years in turbulence. Some conclusions can be dimly seen. This field does not appear to have a pyramidal structure, like the best of physics. We have very few great hypotheses. Most of our experiments are exploratory experiments. What does this mean? We believe it means that, even after 100 years, turbulence studies are still in their infancy. We are naturalists, observing butterflies in the wild. We are still discovering how turbulence behaves, in many respects. We do have a crude, practical, working understanding of many turbulence phenomena but certainly nothing approaching a comprehensive theory, and nothing that will provide predictions of an accuracy demanded by designers.},
author = {Lumley, J. L.},
doi = {10.1023/A:1012437421667},
institution = {Sibley School of Mechanical {\&} Aerospace Engineering, Cornell University, Ithaca, NY 14853, U.S.A.; Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.},
journal = {Advances},
keywords = {history,turbulence},
number = {3},
pages = {241--286},
publisher = {Springer},
title = {{A Century of Turbulence}},
url = {http://www.springerlink.com/index/gr5051t71821442n.pdf},
volume = {66},
year = {2001}
}
@inbook{Lundgren1989,
author = {Lundgren, T. S.},
booktitle = {Mathematical aspects of vortex dynamics},
chapter = {A free sur},
editor = {Caflisch, E},
pages = {68--79},
publisher = {SIAM},
title = {{A Free Surface Vortex Method with Weak ViscousEffects}},
year = {1989}
}
@article{Lundmark2003,
abstract = {We present an inverse scattering approach for computing n-peakon solutions of the Degasperis-Procesi equation (a modification of the Camassa-Holm (CH) shallow water equation). The associated non-self-adjoint spectral problem is shown to be amenable to analysis using the isospectral deformations induced from the n-peakon solution, and the inverse problem is solved by a method generalizing the continued fraction solution of the peakon sector of the CH equation.},
author = {Lundmark, H. and Szmigielski, J.},
doi = {10.1088/0266-5611/19/6/001},
issn = {0266-5611},
journal = {Inverse Problems},
month = {dec},
number = {6},
pages = {1241--1245},
title = {{Multi-peakon solutions of the Degasperis-Procesi equation}},
url = {http://stacks.iop.org/0266-5611/19/i=6/a=001?key=crossref.033ed11eb1a50160e7054b859e57d156},
volume = {19},
year = {2003}
}
@article{Lvov2009,
abstract = {Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave ''clusters'' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. It is shown that the dynamics of the clusters is determined by the types of connections between neighboring triads within a cluster; these correspond to substantially different scenarios of energy flux between different triads. All the possible cases of the energy cascade termination are classified. Free and forced chaotic dynamics in the clusters are investigated: due to the huge fluctuations of the energy exchange between resonant triads these two types of evolution have a lot in common. It is confirmed that finite-dimensional wave turbulence in finite wave systems is fundamentally different from kinetic wave turbulence in infinite systems; the latter is described by wave-kinetic equations that account for interactions with overlapping quasiresonances of finite amplitude waves. The present results are directly applicable to finite-dimensional wave turbulence in any wave system in finite domains with three-mode interactions as encountered in hydrodynamics, astronomy, plasma physics, chemistry, medicine, etc.},
author = {Lvov, V. S. and Pomyalov, A. and Procaccia, I. and Rudenko, O.},
doi = {10.1103/PhysRevE.80.066319},
issn = {1539-3755},
journal = {Phys. Rev. E},
month = {dec},
number = {6},
pages = {066319},
title = {{Finite-dimensional turbulence of planetary waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.80.066319},
volume = {80},
year = {2009}
}
@article{Lyatkher1974,
author = {Lyatkher, V. M. and Militeev, A. N.},
journal = {Oceanology},
number = {1},
pages = {37--42},
title = {{Calculation of run-up on a slope for long gravitational waves}},
volume = {14},
year = {1974}
}
@article{Lynett,
author = {Lynett, P. J.},
journal = {J. Waterway, Port, Coastal, and Ocean Eng.},
pages = {346--357},
title = {{Nearshore wave modeling with high-order Boussinesq-type equations}},
volume = {132},
year = {2006}
}
@article{LWL,
author = {Lynett, P. J. and Wu, T. R. and Liu, P. L.-F.},
journal = {Coastal Engineering},
number = {2},
pages = {89--107},
title = {{Modeling wave runup with depth-integrated equations}},
volume = {46},
year = {2002}
}
@article{Lynett2002,
abstract = {A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth-integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequency-dispersion, effects. The model is capable of describing wave propagation from relatively deep water to shallow water. Simplified models for waves generated by small seafloor displacement or creeping ground movement are also presented. A numerical algorithm is developed for the general fully nonlinear model. Comparisons are made with a boundary integral equation method model, and a deep-water limit for the depth-integrated model is determined in terms of a characteristic side length of the submarine mass. The importance of nonlinearity and frequency dispersion in the wave-generation region and on the shoreline movement is discussed.},
author = {Lynett, P. and Liu, P. L. - F.},
doi = {10.1098/rspa.2002.0973},
issn = {1364-5021},
journal = {Proc. R. Soc. A},
month = {dec},
number = {2028},
pages = {2885--2910},
title = {{A numerical study of submarine-landslide-generated waves and run-up}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2002.0973},
volume = {458},
year = {2002}
}
@book{Case1967,
address = {Reading, Massachusetts},
author = {M., Case K. and Zweifel, P. F.},
isbn = {978-0201009057},
pages = {342},
publisher = {Addison-Wesley Pub. Co.},
title = {{Linear transport theory}},
year = {1967}
}
@article{Ma1999,
abstract = {We investigated the source mechanism of the 1975 Kalapana, Hawaii, earthquake (MS = 7.2) by modeling the tsunamis observed at three tide-gauge stations, Hilo, Kahului, and Honolulu. We computed synthetic tsunamis for various fault models. The arrival times and the amplitudes of the synthetic tsunamis computed for Ando's fault model (fault length = 40 km, fault width = 20 km, strike = N70°E, dip = 20°SE, rake = −90°, fault depth = 10 km, and slip = 5.6 m) are ∼10 min earlier and 5 times smaller than those of the observed, respectively. We tested fault models with different dip angles and depths. Models with a northwest dip direction yield larger tsunami amplitudes than those with a southeast dip direction. Models with shallower fault depths produce later first arrivals than deeper models. We also considered the effects of the Hilina fault system, but its contribution to tsunami excitation is insignificant. This suggests that another mechanism is required to explain the tsunamis. One plausible model is a propagating slump model with a 1 m subsidence along the coast and a l m uplift offshore. This model can explain the arrival times and the amplitudes of the observed tsunamis satisfactorily. An alternative model is a wider fault model that dips 10°NW, with its fault plane extending 25 km offshore, well beyond the aftershock area of the Kalapana earthquake. These two models produce a similar uplift pattern offshore and, kinematically, are indistinguishable as far as tsunami excitation is concerned. The total volume of displaced water is estimated to be ∼2.5 km3. From the comparison of slump model and the single-force model suggested earlier from seismological data we prefer a combination of faulting and large-scale slumping on the south flank of Kilauea volcano as the most appropriate model for the 1975 Kalapana earthquake. Two basic mechanisms have been presented for explaining the deformation of the south flank of Kilauea: (1) pressure and density variation along the rift zone caused by magma injection and (2) gravitational instability due to the steep topography of the south flank of Kilauea. In either mechanism, large displacements on the south flank are involved that are responsible for the observed large tsunamis.},
author = {Ma, K.-F. and Kanamori, H. and Satake, K.},
doi = {10.1029/1999JB900073},
issn = {0148-0227},
journal = {J. Geophys. Res.},
number = {B6},
pages = {13153--13167},
title = {{Mechanism of the 1975 Kalapana, Hawaii, earthquake inferred from tsunami data}},
url = {http://www.agu.org/pubs/crossref/1999/1999JB900073.shtml},
volume = {104},
year = {1999}
}
@incollection{Ma2010,
author = {Ma, Q.},
booktitle = {Adv. Coastal Ocean Engng},
publisher = {World Scientific},
title = {{Advances in numerical simulation of nonlinear water waves}},
year = {2010}
}
@article{Ma1979,
author = {Ma, Y.-C.},
journal = {Stud. Appl. Math.},
number = {1},
pages = {43--58},
title = {{The perturbed plane-wave solutions of the cubic Schr{\{}{\"{o}}{\}}dinger equation}},
volume = {60},
year = {1979}
}
@article{Ma1979,
author = {Ma, Y.-C.},
journal = {Stud. Appl. Math.},
number = {1},
pages = {43--58},
title = {{The perturbed plane-wave solutions of the cubic Schr{\"{o}}dinger equation}},
volume = {60},
year = {1979}
}
@article{Ma2012,
abstract = {An experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin-Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229-271), i.e. dissipation can stabilize the Benjamin-Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe's equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.},
author = {Ma, Y. and Dong, G. and Perlin, M. and Ma, X. and Wang, G.},
doi = {10.1017/jfm.2012.372},
issn = {0022-1120},
journal = {Journal of Fluid Mechanics},
month = {sep},
pages = {101--121},
title = {{Experimental investigation on the evolution of the modulation instability with dissipation}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112012003722},
volume = {711},
year = {2012}
}
@article{MacCormack1969,
author = {MacCormack, R. W.},
journal = {AIAA Paper},
pages = {69--354},
title = {{The effect of viscosity in hypervelocity impact cratering}},
year = {1969}
}
@article{Mackrodt1976,
abstract = {The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.},
author = {Mackrodt, P.-A.},
doi = {10.1017/S0022112076001304},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {01},
pages = {153--164},
title = {{Stability of Hagen-Poiseuille flow with superimposed rigid rotation}},
volume = {73},
year = {1976}
}
@article{MacNulty2012,
abstract = {Despite the popular view that social predators live in groups because group hunting facilitates prey capture, the apparent tendency for hunting success to peak at small group sizes suggests that the formation of large groups is unrelated to prey capture. Few empirical studies, however, have tested for nonlinear relationships between hunting success and group size, and none have demonstrated why success trails off after peaking. Here, we use a unique dataset of observations of individually known wolves (Canis lupus) hunting elk (Cervus elaphus) in Yellowstone National Park to show that the relationship between success and group size is indeed nonlinear and that individuals withholding effort (free riding) is why success does not increase across large group sizes. Beyond 4 wolves, hunting success leveled off, and individual performance (a measure of effort) decreased for reasons unrelated to interference from inept hunters, individual age, or size. But performance did drop faster among wolves with an incentive to hold back, i.e., nonbreeders with no dependent offspring, those performing dangerous predatory tasks, i.e., grab- bing and restraining prey, and those in groups of proficient hunters. These results suggest that decreasing performance was free riding and that was why success leveled off in groups with.4 wolves that had superficially appeared to be cooperating. This is the first direct evidence that nonlinear trends in group hunting success reflect a switch from cooperation to free riding. It also highlights how hunting success per se is unlikely to promote formation and maintenance of large groups.},
author = {MacNulty, D. R. and Smith, D. W. and Mech, L. D. and Vucetich, J. A. and Packer, C.},
doi = {10.1093/beheco/arr159},
issn = {10452249},
journal = {Behavioral Ecology},
keywords = {Canis lupus,carnivore,cooperation,free riding,group hunting,group living,interference,predation,sociality,wolf},
number = {1},
pages = {75--82},
title = {{Nonlinear effects of group size on the success of wolves hunting elk}},
volume = {23},
year = {2012}
}
@article{MacNulty2009,
author = {MacNulty, D. R. and Smith, D. W. and Vucetich, J. A. and Mech, L. D. and Stahler, D. R. and Packer, C.},
doi = {10.1111/j.1461-0248.2009.01385.x},
issn = {1461023X},
journal = {Ecol. Lett.},
month = {dec},
pages = {1347--1356},
title = {{Predatory senescence in ageing wolves}},
url = {http://doi.wiley.com/10.1111/j.1461-0248.2009.01385.x},
volume = {12},
year = {2009}
}
@article{MacNulty2014,
author = {MacNulty, D. R. and Tallian, A. and Stahler, D. R. and Smith, D. W.},
doi = {10.1371/journal.pone.0112884},
issn = {1932-6203},
journal = {PLoS ONE},
number = {11},
pages = {e112884},
title = {{Influence of Group Size on the Success of Wolves Hunting Bison}},
url = {http://dx.plos.org/10.1371/journal.pone.0112884},
volume = {9},
year = {2014}
}
@article{Madariaga2003,
author = {Madariaga, R.},
journal = {Pure Appl. Geophys.},
pages = {555--577},
title = {{Radiation from a finite reverse fault in half space}},
volume = {160},
year = {2003}
}
@article{Maday1988,
abstract = {The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.},
author = {Maday, Y. and Quarteroni, A.},
journal = {Mathematical Modelling And Numerical Analysis},
number = {3},
pages = {499--529},
title = {{Error analysis for spectral approximation of the Korteweg-De Vries equation}},
url = {http://hdl.handle.net/2060/19870016379},
volume = {22},
year = {1988}
}
@article{Maddocks1995,
author = {Maddocks, J. H. and Pego, R. L.},
journal = {Comm. Math. Phys.},
pages = {207--217},
title = {{An unconstrained Hamiltonian formulation for incompressible fluid flow}},
volume = {170},
year = {1995}
}
@techreport{Madsen2004,
author = {Madsen, K. and Nielsen, H. and Tingleff, O.},
institution = {Technical University of Denmark},
pages = {58},
title = {{Methods for Non-Linear Least Squares Problems}},
year = {2004}
}
@article{Madsen2002,
author = {Madsen, P. A. and Bingham, H. B. and Liu, H.},
journal = {J. Fluid Mech.},
pages = {1--30},
title = {{A new Boussinesq method for fully nonlinear waves from shallow to deep water}},
volume = {462},
year = {2002}
}
@article{Madsen03,
author = {Madsen, P. A. and Bingham, H. B. and Schaffer, H. A.},
journal = {Proc. R. Soc. Lond. A},
pages = {1075--1104},
title = {{Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis}},
volume = {459},
year = {2003}
}
@article{Madsen2008,
abstract = {In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3-6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement},
author = {Madsen, P. A. and Fuhrman, D. R.},
doi = {10.1016/j.coastaleng.2007.09.007},
issn = {03783839},
journal = {Coastal Engineering},
keywords = {Long waves,Run-up,Surf-similarity,Tsunamis},
month = {mar},
number = {3},
pages = {209--223},
title = {{Run-up of tsunamis and long waves in terms of surf-similarity}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S037838390700107X},
volume = {55},
year = {2008}
}
@article{MFS2008,
author = {Madsen, P. A. and Fuhrman, D. R. and Sch{\"{a}}ffer, H. A.},
journal = {J. Geophys. Res.},
pages = {C12012},
title = {{On the solitary wave paradigm for tsunamis}},
volume = {113},
year = {2008}
}
@article{Madsen1991,
author = {Madsen, P. A. and Murray, R. and Sorensen, O. R.},
journal = {Coastal Engineering},
pages = {371--388},
title = {{A new form of the Boussinesq equations with improved linear dispersion characteristics}},
volume = {15},
year = {1991}
}
@article{Madsen1999,
author = {Madsen, P. A. and Schaffer, H. A.},
journal = {Adv. Coastal {\&} Ocean Engin.},
pages = {1--94},
title = {{A review of Boussinesq-type equations for surface gravity waves}},
volume = {5},
year = {1999}
}
@article{Madsen2010,
author = {Madsen, P. A. and Schaffer, H. A.},
journal = {J. Fluid Mech},
pages = {27--57},
title = {{Analytical solutions for tsunami runup on a plane beach: single waves, N-waves and transient waves}},
volume = {645},
year = {2010}
}
@article{Madsen1998,
author = {Madsen, P. A. and Schaffer, H. A.},
journal = {Phil. Trans. R. Soc. Lond. A},
pages = {3123--3184},
title = {{Higher-Order Boussinesq-Type Equations for Surface Gravity Waves: Derivation and Analysis}},
volume = {356},
year = {1998}
}
@article{Madsen1997,
author = {Madsen, P. A. and Sorensen, H. A. and Schaffer, H. A.},
journal = {Coastal Engineering},
pages = {255--287},
title = {{Surf zone dynamics simulated by a Boussinesq-type model. Part I. Model description and cross-shore motion of regular waves}},
volume = {32},
year = {1997}
}
@article{Madsen1992,
author = {Madsen, P. A. and Sorensen, O. R.},
journal = {Coastal Engineering},
pages = {183--204},
title = {{A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry}},
volume = {18},
year = {1992}
}
@book{Majda2003,
address = {Providence, Rhode Island},
author = {Majda, A.},
pages = {234},
publisher = {American Mathematical Society},
title = {{Introduction to PDEs and Waves for the Atmosphere and Ocean}},
year = {2003}
}
@techreport{Majda1982,
author = {Majda, A.},
institution = {Center for Pure and Applied Mathematics, University of California, Berkeley},
number = {112},
title = {{Equations of low Mach number combustion}},
year = {1982}
}
@article{Majda1984,
author = {Majda, A.},
journal = {Appl. Math. Sci.},
title = {{Compressible fluid flow and systems of conservation laws in several space dimensions}},
volume = {53},
year = {1984}
}
@book{Majda2001,
abstract = {This comprehensive introduction to the mathematical theory of vorticity and incompressible flow begins with the elementary introductory material and leads into current research topics. While the book centers on mathematical theory, many parts also showcase the interaction among rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprises a modern applied mathematics graduate course on the weak solution theory for incompressible flow.},
address = {Cambridge},
author = {Majda, A. J. and Bertozzi, A. L.},
isbn = {9780521639484},
pages = {560},
publisher = {Cambridge University Press},
title = {{Vorticity and Incompressible Flow}},
year = {2001}
}
@article{Majda1997,
abstract = {Summary{\~{}}{\~{}}A family of one-dimensional nonlinear dispersive wave equations is introduced as a model for assessing the validity of weak turbulence theory for random waves in an unambiguous and transparent fashion. These models have an explicitly solvable weak turbulence theory which is developed here, with Kolmogorov-type wave number spectra exhibiting interesting dependence on parameters in the equations. These predictions of weak turbulence theory are compared with numerical solutions with damping and driving that exhibit a statistical inertial scaling range over as much as two decades in wave number. It is established that the quasi-Gaussian random phase hypothesis of weak turbulence theory is an excellent approximation in the numerical statistical steady state. Nevertheless, the predictions of weak turbulence theory fail and yield a much flatter (k1/3) spectrum compared with the steeper (k3/4) spectrum observed in the numerical statistical steady state. The reasons for the failure of weak turbulence theory in this context are elucidated here. Finally, an inertial range closure and scaling theory is developed which successfully predicts the inertial range exponents observed in the numerical statistical steady states.},
author = {Majda, A. J. and McLaughlin, D. W. and Tabak, E. G.},
doi = {10.1007/BF02679124},
issn = {09388974},
journal = {Journal of Nonlinear Science},
number = {1},
pages = {9--44},
title = {{A one-dimensional model for dispersive wave turbulence}},
url = {http://www.springerlink.com/index/10.1007/BF02679124},
volume = {7},
year = {1997}
}
@article{Majda1985,
author = {Majda, A. and Sethian, J.},
journal = {Combust. Sci. and Tech.},
pages = {185--205},
title = {{The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion}},
volume = {42},
year = {1985}
}
@article{Maklakov2002,
abstract = {The paper presents a method of computing periodic water waves based on solving an integral equation by means of discretization and automatically finding the mesh on which the functions to be found are approximated by the best way. The power of the method to describe ‘bad functions’ well makes it possible to reproduce all the main results of asymptotic theory for the almost-highest waves (Longuet-Higgins {\&} Fox, 1977, 1978, 1996) by a direct numerical simulation. The method is able to compute two full periods of the oscillations of wave properties for all wave height-to-length ratios. The end of the second period corresponds to the wave steepness that achieves 99.99997{\%} of the limiting value. So, the validity of the asymptotic formulae by Longuet-Higgins {\&} Fox is proved for the steep waves of any finite depth. The refined value of the maximum slope of the free-surfaces is found to be 30.3787°.},
author = {Maklakov, D.},
doi = {10.1017/S0956792501004739},
journal = {European Journal of Applied Mathematics},
pages = {67--93},
title = {{Almost-highest gravity waves on water of finite depth}},
url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online{\&}aid=101935},
volume = {13},
year = {2002}
}
@article{Malfliet1992a,
abstract = {A method is proposed for obtaining traveling‐wave solutions of nonlinear wave equations that are essentially of a localized nature. It is based on the fact that most solutions are functions of a hyperbolic tangent. This technique is straightforward to use and only minimal algebra is needed to find these solutions. The method is applied to selected cases.},
author = {Malfliet, W.},
doi = {10.1119/1.17120},
issn = {00029505},
journal = {American Journal of Physics},
number = {7},
pages = {650},
title = {{Solitary wave solutions of nonlinear wave equations}},
url = {http://link.aip.org/link/?AJP/60/650/1{\&}Agg=doi},
volume = {60},
year = {1992}
}
@article{Mangeney-Castelnau2003,
author = {Mangeney-Castelnau, A. and Vilotte, J.-P. and Bristeau, M.-O. and Perthame, B. and Bouchut, F. and Simeoni, C. and Yerneni, S.},
doi = {10.1029/2002JB002024},
journal = {J. Geophys. Res.},
pages = {2527},
title = {{Numerical modeling of avalanches based on Saint-Venant equations using a kinetic scheme}},
volume = {108},
year = {2003}
}
@article{Mangeney2000,
author = {Mangeney, A. and Heinrich, P. and Roche, R.},
journal = {Pure Appl. Geophys.},
pages = {1081--1096},
title = {{Analytical Solution for Testing Debris Avalanche Numerical Models}},
volume = {157},
year = {2000}
}
@article{Mansinha1967,
author = {Mansinha, L. and Smylie, D. E.},
journal = {J. Geophys. Res.},
pages = {4731--4743},
title = {{Effect of earthquakes on the Chandler wobble and the secular polar shift}},
volume = {72},
year = {1967}
}
@article{Mansinha1971,
author = {Mansinha, L. and Smylie, D. E.},
journal = {Bull. Seism. Soc. Am.},
pages = {1433--1440},
title = {{The displacement fields of inclined faults}},
volume = {61},
year = {1971}
}
@article{Marchant1990,
abstract = {The extended Korteweg-de Vries equation which includes nonlinear and dispersive terms cubic in the wave amplitude is derived from the water-wave equations and the Lagrangian for the water-wave equations. For the special case in which only the higher-order nonlinear term is retained, the extended Korteweg-de Vries equation is transformed into the Korteweg-de Vries equation. Modulation equations for this equation are then derived from the modulation equations for the Korteweg-de Vries equation and the undular bore solution of the extended Korteweg-de Vries equation is found as a simple wave solution of these modulation equations. The modulation equations are also used to extend the solution for the resonant flow of a fluid over topography. This resonant flow occurs when, in the weakly nonlinear, long-wave limit, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. In addition to the effect of higher-order terms, the effect of boundary-layer viscosity is also considered. These solutions (with and without viscosity) are compared with recent experimental and numerical results.},
author = {Marchant, T. R. and Smyth, N. F.},
doi = {10.1017/S0022112090003561},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {263--287},
title = {{The extended Korteweg-de Vries equation and the resonant flow of a fluid over topography}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112090003561},
volume = {221},
year = {1990}
}
@article{Marche2007,
author = {Marche, F.},
journal = {European Journal of Mechanics - B/Fluids},
pages = {49--63},
title = {{Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects}},
volume = {26(1)},
year = {2007}
}
@article{MarcheBonneton2007,
author = {Marche, F. and Bonneton, P. and Fabrie, P. and Seguin, N.},
journal = {Int. J. Numer. Methods Fluids},
pages = {867--894},
title = {{Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes}},
volume = {53(5)},
year = {2007}
}
@inproceedings{Marongiu2008,
address = {Lausane, Switzerland},
author = {Marongiu, J. C. and Parkinson, E.},
booktitle = {3rd SPHERIC Workshop Proceedings},
title = {{Riemann solvers and efficient boundary treatments: an hybrid SPH-finite volume numerical method}},
year = {2008}
}
@article{Marquardt1963,
author = {Marquardt, D. W.},
doi = {10.1137/0111030},
issn = {0368-4245},
journal = {Journal of the Society for Industrial and Applied Mathematics},
month = {jun},
number = {2},
pages = {431--441},
title = {{An Algorithm for Least-Squares Estimation of Nonlinear Parameters}},
url = {http://epubs.siam.org/doi/abs/10.1137/0111030},
volume = {11},
year = {1963}
}
@article{Marris2005,
author = {Marris, E.},
journal = {Nature},
pages = {1071},
title = {{Tsunami damage was enhanced by coral theft}},
volume = {436},
year = {2005}
}
@article{Marrone2011,
author = {Marrone, S. and Antuono, M. and Colagrossi, A. and Colicchio, G. and {Le Touz{\'{e}}}, D. and Graziani, G.},
doi = {10.1016/j.cma.2010.12.016},
issn = {00457825},
journal = {Comput. Methods Appl. Mech. Engrg.},
month = {mar},
number = {13-16},
pages = {1526--1542},
title = {{$\delta$-SPH model for simulating violent impact flows}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0045782510003725},
volume = {200},
year = {2011}
}
@book{Marsden1994,
abstract = {This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis. The first two chapters cover the background geometry - developed as needed - and use this discussion to obtain the basic results on kinematics and dynamics of continuous media. Subsequent chapters deal with elastic materials, linearization, variational principles, the use of functional analysis in elasticity, and bifurcation theory. Carefully selected problems are interspersed throughout, while a large bibliography rounds out the text.},
address = {Englewood Cliffs},
author = {Marsden, J. E. and Hughes, T. J. R.},
isbn = {978-0486678658},
pages = {556},
publisher = {Dover Publications},
title = {{Mathematical Foundations of Elasticity}},
year = {1994}
}
@article{Marsden1998,
abstract = {This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle. In particular, we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function, and use this structure to prove covariant generalizations of conservation of symplecticity and Noether's theorem. Natural discretization schemes for PDEs, which have these important preservation properties, then follow by choosing a discrete action functional. In the case of mechanics, we recover the variational symplectic integrators of Veselov type, while for PDEs we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries. We show that the usual notion of symplecticity along an infinite-dimensional space of fields can be naturally obtained by making a spacetime split. All of the aspects of our method are demonstrated with a nonlinear sine-Gordon equation, including computational results and a comparison with other discretization schemes.},
author = {Marsden, J. E. and Patrick, G. W. and Shkoller, S.},
journal = {Comm. Math. Phys.},
number = {2},
pages = {52},
publisher = {Springer},
title = {{Multisymplectic geometry, variational integrators, and nonlinear PDEs}},
url = {http://arxiv.org/abs/math/9807080},
volume = {199},
year = {1998}
}
@article{Marshall1997,
author = {Marshall, J. and Hill, C. and Perelman, L. and Adcroft, A.},
journal = {J. Geophys. Res.},
number = {C3},
pages = {5733--5752},
title = {{Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling}},
volume = {102},
year = {1997}
}
@article{Martin1952,
author = {Martin, J. C. and Moyce, W. J.},
journal = {Phil. Trans. R. Soc. London. Series A.},
pages = {312--324},
title = {{Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane}},
volume = {244(882)},
year = {1952}
}
@article{maru,
author = {Maruyama, T.},
journal = {Bull. Earthquake Res. Inst., Tokyo Univ.},
pages = {289--368},
title = {{Statical elastic dislocations in an infinite and semi-infinite medium}},
volume = {42},
year = {1964}
}
@article{Mascia1997,
abstract = {We study entropy travelling wave solutions for first-order hyperbolic balance laws. Results concerning existence, regularity and asymptotic stability of such solutions are proved for convex fluxes and source terms with simple isolated zeros.},
author = {Mascia, C.},
doi = {10.1017/S0308210500029917},
issn = {0308-2105},
journal = {Proc. R. Soc. Edinburgh Sect. A},
month = {jan},
number = {03},
pages = {567--593},
title = {{Travelling wave solutions for a balance law}},
url = {http://www.journals.cambridge.org/abstract{\_}S0308210500029917},
volume = {127},
year = {1997}
}
@article{Mascia1999,
author = {Mascia, C. and Terracina, A.},
journal = {J. Diff. Eqns.},
number = {2},
pages = {485--514},
title = {{Large-Time Behavior for Conservation Laws with Source in a Bounded Domain}},
volume = {159},
year = {1999}
}
@book{Massel1996,
author = {Massel, S.},
publisher = {World Scientific},
title = {{Ocean Surface Waves: Their Physics and Prediction}},
year = {1996}
}
@article{tim,
author = {Masterlark, T.},
journal = {J. Geophys. Res.},
number = {B11},
pages = {2540},
title = {{Finite element model predictions of static deformation from dislocation sources in a subduction zone: Sensivities to homogeneous, isotropic, Poisson-solid, and half-space assumptions}},
volume = {108},
year = {2003}
}
@article{Matsuno1993,
author = {Matsuno, Y.},
journal = {J. Fluid Mech.},
pages = {121--133},
title = {{Nonlinear evolution of surface gravity waves over an uneven bottom}},
volume = {249},
year = {1993}
}
@article{Matsuuchi1976,
author = {Matsuuchi, K.},
journal = {J. Phys. Soc. Japan},
month = {aug},
number = {2},
pages = {681--686},
title = {{Numerical Investigations on Long Gravity Waves under the Influence of Viscosity}},
volume = {41},
year = {1976}
}
@article{Maximov2008,
author = {Maximov, V. V. and Nudner, I.},
journal = {Fundamental and Applied Hydrophysics},
pages = {31--46},
title = {{Tsunami Action on the Off-Shore Hydraulic Structures}},
volume = {2},
year = {2008}
}
@article{Maxworthy1976,
author = {Maxworthy, T.},
journal = {J Fluid Mech},
pages = {177--185},
title = {{Experiments on collisions between solitary waves}},
volume = {76},
year = {1976}
}
@article{Mayer1998,
author = {Mayer, S. and Garapon, A. and Sorensen, L. S.},
journal = {Int. J. Num. Meth. Fluids},
number = {2},
pages = {293--315},
title = {{A fractional step method for unsteady free-surface flow with applications to non-linear wave dynamics}},
volume = {28},
year = {1998}
}
@article{McCloskey2008,
author = {McCloskey, J. and Antonioli, A. and Piatanesi, A. and Sieh, K. and Steacy, S. and {Nalbant S. Cocco}, M. and Giunchi, C. and Huang, J. D. and Dunlop, P.},
journal = {Earth and Planetary Science Letters},
pages = {61--81},
title = {{Tsunami threat in the Indian Ocean from a future megathrust earthquake west of Sumatra}},
volume = {265},
year = {2008}
}
@article{McClung2001,
author = {McClung, D. M.},
journal = {Can. Geotech. J.},
pages = {1254--1265},
title = {{Extreme avalanche runout: a comparison of empirical models}},
volume = {38},
year = {2001}
}
@article{McClung2003,
author = {McClung, D. M.},
doi = {10.1029/2002JB002298},
issn = {01480227},
journal = {Journal of Geophysical Research},
number = {B10},
pages = {1--12},
title = {{Size scaling for dry snow slab release}},
url = {http://www.agu.org/pubs/crossref/2003/2002JB002298.shtml},
volume = {108},
year = {2003}
}
@article{McClung2000,
author = {McClung, D. M.},
journal = {Can. Geotech. J.},
pages = {161--170},
title = {{Extreme avalanche runout in space and time}},
volume = {37},
year = {2000}
}
@article{McClung1987,
author = {McClung, D. M. and Lied, K.},
journal = {Cold Regions Science and Technology},
pages = {107--119},
title = {{Statistical and geometrical definition of snow avalanche runout}},
volume = {13},
year = {1987}
}
@book{McClung1993,
author = {McClung, D. M. and Schaerer, P. A.},
publisher = {The Mountaineers, Seattle},
title = {{The Avalanche Handbook}},
year = {1993}
}
@article{McClung1984,
author = {McClung, D. and Schaerer, P. A.},
journal = {J. Glaciology},
pages = {109--120},
title = {{Determination of avalanche dynamics, friction coefficients from measured speeds}},
volume = {20},
year = {1984}
}
@article{McCowan1891,
author = {McCowan, J.},
journal = {Phil. Mag. S.},
number = {194},
pages = {45--58},
title = {{On the solitary wave}},
volume = {32},
year = {1891}
}
@book{McDuff1998,
address = {New York},
author = {McDuff, D. and Salamon, D.},
edition = {2nd},
pages = {486},
publisher = {Oxford University Press},
title = {{Introduction to symplectic topology}},
year = {1998}
}
@inbook{McElwaine2001,
author = {McElwaine, J. N. and Nishimura, K.},
chapter = {Ping-pong},
editor = {McCaffrey, W D and Kneller, B C and Peakall, J},
pages = {135--148},
publisher = {Blackwell Science},
title = {{Particulate Gravity Currents}},
year = {2001}
}
@article{McElwaine2001a,
author = {McElwaine, J. and Nishimura, K.},
doi = {10.3189/172756401781819526},
issn = {02603055},
journal = {Annals Of Glaciology},
number = {1},
pages = {241--250},
title = {{Ping-pong ball avalanche experiments}},
url = {http://openurl.ingenta.com/content/xref?genre=article{\&}issn=0260-3055{\&}volume=32{\&}issue=1{\&}spage=241},
volume = {32},
year = {2001}
}
@phdthesis{mcginl,
address = {Pasadena, California},
author = {McGinley, J. R.},
school = {California Institute of Technology},
title = {{A comparison of observed permanent tilts and strains due to earthquakes with those calculated from displacement dislocations in elastic earth models}},
year = {1969}
}
@article{McLachlan1993,
author = {McLachlan, R.},
doi = {10.1007/BF01385708},
issn = {0029599X},
journal = {Numerische Mathematik},
number = {1},
pages = {465--492},
publisher = {Springer},
title = {{Symplectic integration of Hamiltonian wave equations}},
url = {http://www.springerlink.com/index/10.1007/BF01385708},
volume = {66},
year = {1993}
}
@article{McLean1982,
author = {McLean, J. W.},
doi = {10.1017/S0022112082000172},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {315--330},
title = {{Instabilities of finite-amplitude water waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112082000172},
volume = {114},
year = {1982}
}
@book{Mech2003,
address = {Chicago},
author = {Mech, L. D. and Boitani, L.},
pages = {472},
publisher = {University of Chicago Press},
title = {{Wolves: Behavior, Ecology and Conservation}},
year = {2003}
}
@article{Medeiros2013,
abstract = {A review of wetting and drying (WD) algorithms used by contemporary numerical models based on the shallow water equations is presented. The numerical models reviewed employ WD algorithms that fall into four general frameworks: (1) Specifying a thin film of fluid over the entire domain; (2) checking if an element or node is wet, dry or potentially one of the two, and subsequently adding or removing elements from the computational domain; (3) linearly extrapolating the fluid depth onto a dry element and its nodes from nearby wet elements and computing the velocities; and (4) allowing the water surface to extend below the topographic ground surface. This review presents the benefits and drawbacks in terms of accuracy, robustness, computational efficiency, and conservation properties. The WD algorithms also tend to be highly tailored to the numerical model they serve and therefore difficult to generalize. Furthermore, the lack of temporally and spatially defined validation data has hampered comparisons of the models in terms of their ability to simulate WD over real domains. A short discussion of this topic is included in the conclusion.},
author = {Medeiros, S. C. and Hagen, S. C.},
doi = {10.1002/fld.3668},
issn = {02712091},
journal = {Int. J. Num. Meth. Fluids},
month = {feb},
number = {4},
pages = {473--487},
title = {{Review of wetting and drying algorithms for numerical tidal flow models}},
url = {http://doi.wiley.com/10.1002/fld.3668},
volume = {71},
year = {2013}
}
@article{Megna2005,
author = {Megna, A. and Barba, S. and Santini, S.},
journal = {Annals Geophys.},
pages = {1009--1016},
title = {{Normal-fault stress and displacement through finite-element analysis}},
volume = {48},
year = {2005}
}
@book{Mehaute1995,
author = {Mehaut{\'{e}}, B. and Wang, S.},
publisher = {World Scientific, Singapore},
title = {{Water Waves Generated by Underwater Explosion, Advanced Series on Ocean Engineering, Vol. 10}},
year = {1995}
}
@article{Mehmeti2003,
author = {Mehmeti, F. A. and R{\'{e}}gnier, V.},
doi = {10.1002/zamm.200310010},
issn = {00442267},
journal = {ZAMM},
month = {feb},
number = {2},
pages = {105--118},
title = {{Splitting of energy of dispersive waves in a star-shaped network}},
url = {http://doi.wiley.com/10.1002/zamm.200310010},
volume = {83},
year = {2003}
}
@book{Mei1989,
author = {Mei, C. C.},
publisher = {World Scientific},
title = {{The applied dynamics of water waves}},
year = {1989}
}
@book{Mei1994,
author = {Mei, C. C.},
publisher = {World Scientific},
title = {{The applied dynamics of ocean surface waves}},
year = {1994}
}
@article{Mei1981,
author = {Mei, C. C. and Foda, M. A.},
journal = {Geophysical Journal International},
pages = {597--631},
title = {{Wave-induced responses in a fluid-filled poro-elastic solid with a free surface - a boundary layer theory}},
volume = {66(3)},
year = {1981}
}
@article{Mei1973,
abstract = {In deducing the viscous damping rate in surface waves confined by side walls, Ursell found in an example that two different calculations, one by energy dissipation within and the other by pressure working on the edge of the side-wall boundary layers, gave different answers. This discrepancy occurs in other examples also and is resolved here by examining the energy transfer in the neighbourhood of the free-surface meniscus. With due care near the meniscus a boundary-layer Poincar{\'{e}} method is employed to give an alternative derivation for the rate of attenuation and to obtain in addition the frequency (or wave-number) shift due to viscosity. Surface tension is not considered.},
author = {Mei, C. C. and Liu, P. L.-F.},
journal = {J. Fluid Mech.},
pages = {239--256},
title = {{The Damping of surface gravity waves in a bounded liquid}},
volume = {59(2)},
year = {1973}
}
@book{Mei2005a,
author = {Mei, C. C. and Stiassnie, M. and Yue, D. K. P.},
pages = {1136},
publisher = {World Scientific},
title = {{Theory and applications of ocean surface waves, Part 2: Nonlinear aspects}},
year = {2005}
}
@book{Mei2005,
author = {Mei, C. C. and Stiassnie, M. and Yue, D. K. P.},
editor = {Mei, C. C. and Stiassnie, M. and Yue, D. K.-P.},
pages = {1071},
publisher = {World Scientific},
title = {{Theory and applications of ocean surface waves: Linear aspects}},
year = {2005}
}
@article{Mei2003,
author = {Mei, Z. and Roberts, A. J. and Li, Z.},
journal = {SIAM J. Appl. Math},
number = {2},
pages = {423--458},
title = {{Modelling the dynamics of turbulent floods}},
volume = {63},
year = {2003}
}
@article{Melville1996,
author = {Melville, W. K.},
journal = {Ann. Rev. Fluid Mech.},
pages = {279--321},
title = {{The Role of Surface-Wave Breaking in Air-Sea Interaction}},
volume = {28},
year = {1996}
}
@article{Mendes2005,
author = {Mendes, N. and Philippi, P. C.},
doi = {10.1016/j.ijheatmasstransfer.2004.08.011},
journal = {Int. J. Heat Mass Transfer},
number = {1},
pages = {37--51},
title = {{A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients}},
volume = {48},
year = {2005}
}
@article{Meyapin2009,
author = {Meyapin, Y. and Dutykh, D. and Gisclon, M.},
journal = {Stud. Appl. Maths.},
pages = {179--212},
title = {{Velocity and energy relaxation in two-phase flows}},
volume = {125(2)},
year = {2010}
}
@inproceedings{Meyapin2009a,
author = {Meyapin, Y. and Dutykh, D. and Gisclon, M.},
booktitle = {The Fourth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing},
series = {Springer series "Notes on Numerical Fluid Mechanics and Multidisciplinary Design"},
title = {{Two-fluid barotropic models for powder-snow avalanche flows}},
year = {2009}
}
@inproceedings{Meyer-Peter1948,
author = {Meyer-Peter, E. and Muller, R.},
booktitle = {Proceedings of the 2nd congress of the International Association for Hydraulic Research},
pages = {39--64},
title = {{Formulas for bed load transport}},
year = {1948}
}
@article{Michalopoulos1993,
author = {Michalopoulos, P. G. and Yi, P. and Lyrintzis, A. S.},
doi = {10.1016/0191-2615(93)90041-8},
issn = {01912615},
journal = {Transportation Research Part B: Methodological},
month = {aug},
number = {4},
pages = {315--332},
title = {{Continuum modelling of traffic dynamics for congested freeways}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0191261593900418},
volume = {27},
year = {1993}
}
@article{Micu2001,
author = {Micu, S.},
doi = {10.1137/S0363012999362499},
issn = {0363-0129},
journal = {SIAM Journal on Control and Optimization},
month = {jan},
number = {6},
pages = {1677--1696},
title = {{On the Controllability of the Linearized Benjamin-Bona-Mahony Equation}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0363012999362499},
volume = {39},
year = {2001}
}
@article{Middleton1967,
abstract = {Turbidity currents were formed by releasing suspensions of plastic beads (density 1.52, median diameter 0.18 mm) from a lock into a horizontal water-filled flume. Graded beds were formed; the mechanism of deposition was studied by motion photography and the size grading by 150 size analyses.Deposition of sediment took place behind the head even at a time when there was no deceleration of the head: the greater part of the thickness of the bed was deposited during a period of rapid decline in velocity of flow within the body of the current. The mechanism of deposition and the type of grading differed for beds deposited from suspensions with concentrations less than and greater than about 30{\%} by volume. Low concentration suspensions formed 'distribution grading' in which all percentiles showed vertical grading and at least the coarser half of the distribution showed lateral size decrease away from the gate. High concentration suspensions formed 'coarse-tail grading' in which there was almost no lateral size variation and the vertical grading was shown only by the coarsest few percentiles (except at the top of the bed).In high concentration flows the bed did not accumulate layer by layer, as it did in low concentration flows, but was deposited first as an expanded 'quick' layer, which was deformed by shearing and waves produced by the entrained water flowing over the still plastic bed.In both types of graded beds the sorting coefficient (standard deviation of the logarithm of the settling velocity) decreased upward within the bed, and to a lesser extent also laterally away from the gate. The skewness reached a maximum near the center of the bed and became negative at the top.},
author = {Middleton, G. V.},
journal = {Canadian Journal of Earth Sciences},
number = {3},
pages = {475--505},
title = {{Experiments on density and turbidity currents: III. Deposition of sediment}},
url = {http://www.nrcresearchpress.com/doi/abs/10.1139/e67-025},
volume = {4},
year = {1967}
}
@article{Miles1977,
author = {Miles, J. W.},
journal = {J. Fluid Mech.},
pages = {153--158},
title = {{On Hamilton's principle for water waves}},
volume = {83},
year = {1977}
}
@article{Miles1981,
author = {Miles, J. W.},
doi = {10.1017/S0022112081001559},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {131--147},
title = {{The Korteweg-de Vries equation: a historical essay}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112081001559},
volume = {106},
year = {1981}
}
@article{Miles1967,
author = {Miles, J. W.},
doi = {10.1017/S0022112067002423},
journal = {J. Fluid Mech},
number = {04},
pages = {755--767},
title = {{Surface-wave scattering matrix for a shelf}},
volume = {28},
year = {1967}
}
@article{Miles1971,
author = {Miles, J. W.},
journal = {J. Fluid Mech.},
number = {02},
pages = {241--265},
title = {{Resonant response of harbours: an equivalent-circuit analysis}},
volume = {46},
year = {1971}
}
@article{Miles1976,
abstract = {The Korteweg-de Vries equation is modified to include both the dissipative and dispersive effects of viscous boundary layers. Physics of Fluids is copyrighted by The American Institute of Physics.},
author = {Miles, J. W.},
doi = {DOI:10.1063/1.861580},
journal = {Phys. Fluids},
number = {7},
title = {{Korteweg-de Vries equation modified by viscosity}},
volume = {19},
year = {1976}
}
@article{Miles1985,
author = {Miles, J. W. and Salmon, R.},
journal = {J. Fluid Mech.},
pages = {519--531},
title = {{Weakly dispersive nonlinear gravity waves}},
volume = {157},
year = {1985}
}
@article{Milewski1999,
author = {Milewski, P. and Tabak, E.},
journal = {SIAM J. Sci. Comput.},
pages = {1102--1114},
title = {{A pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows}},
volume = {21(3)},
year = {1999}
}
@article{Milewski2010,
abstract = {In this paper, the unsteady evolution of two-dimensional fully nonlinear free-surface gravity–capillary solitary waves is computed numerically in infinite depth. Gravity-capillary wavepacket-type solitary waves were found previously for the full Euler equations, bifurcating from the minimum of the linear dispersion relation. Small and moderate amplitude elevation solitary waves, which were known to be linearly unstable, are shown to evolve into stable depression solitary waves, together with a radiated wave field. Depression waves and certain large amplitude elevation waves were found to be robust to numerical perturbations. Two kinds of collisions are computed: head-on collisions whereby the waves are almost unchanged, and overtaking collisions which are either almost elastic if the wave amplitudes are both large or destroy the smaller wave in the case of a small amplitude wave overtaking a large one.},
author = {Milewski, P. and Vanden-Broeck, J.-M. and Wang, Z.},
doi = {10.1017/S0022112010004714},
journal = {J. Fluid Mech.},
pages = {466--477},
title = {{Dynamics of steep two-dimensional gravity-capillary solitary waves}},
volume = {664},
year = {2010}
}
@article{Miloh1978,
abstract = {Unusual large waves (tsunamis) triggered by submarine tectonic activity, such as a fault displacement in the sea bottom, may have considerable effect on a coastalsite. The possibility of such phenomena to occur at the southern coast of Israel due to a series of shore-parallel faults, about 20 km offshore, is examined in this paper. The analysis relates the energy or the momentum imparted to the body of water due to a fault displacement of the sea bottom to the energy or the momentum of the water waves thus created. The faults off the Ashdod coast may cause surface waves with amplitudes of about 5 m and periods of about one third of an hour. It is also considered that because of the downward movement of the faulted blocks a recession of the sea level rather than a flooding would be the first and the predominant effect at the shore, and this is in agreement with some historical reports. The analysis here presented might be of interest to those designing coastal power plants.},
author = {Miloh, T. and Striem, H. L.},
doi = {10.1016/0040-1951(78)90212-3},
issn = {00401951},
journal = {Tectonophysics},
month = {apr},
number = {3-4},
pages = {347--356},
title = {{Tsunamis effects at coastal sites due to offshore faulting}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0040195178902123},
volume = {46},
year = {1978}
}
@article{mindl1,
author = {Mindlin, R. D.},
journal = {Physics},
pages = {195--202},
title = {{Force at a point in the interior of a semi-infinite medium}},
volume = {7},
year = {1936}
}
@article{mindl2,
author = {Mindlin, R. D. and Cheng, D. H.},
journal = {J. Appl. Phys.},
pages = {926--930},
title = {{Nuclei of strain in the semi-infinite solid}},
volume = {21},
year = {1950}
}
@article{Mingham1998,
abstract = {A high-resolution time-marching method is presented for solving the two-dimensional shallow water equations. The method uses a cell-centered formulation with collocated data rather than a space-staggered approach. Spurious oscillations are avoided by employing Monotonic Upstream Schemes for Conservation Laws (MUSCL) reconstruction with an approximate Riemann solver in a two-step Runge-Kutta time stepping scheme. A finite-volume implementation on a boundary conforming mesh is chosen to more accurately map the complex geometries that will occur in practice. These features enable the model to deal with dam break phenomena involving flow discontinuities, subcritical and supercritical flows, and other cases. The method is applied to several bore wave propagation and dam break problems. Read More: http://ascelibrary.org/doi/abs/10.1061/(ASCE)0733-9429(1998)124{\%}3A6(605)},
author = {Mingham, C. G. and Causon, D. M.},
doi = {10.1061/(ASCE)0733-9429(1998)124:6(605)},
issn = {0733-9429},
journal = {J. Hydraul. Eng.},
month = {jun},
number = {6},
pages = {605--614},
title = {{High-Resolution Finite-Volume Method for Shallow Water Flows}},
url = {http://ascelibrary.org/doi/abs/10.1061/(ASCE)0733-9429(1998)124:6(605)},
volume = {124},
year = {1998}
}
@book{Minikin1963,
address = {London},
author = {Minikin, R. R.},
edition = {2nd revise},
pages = {301},
publisher = {Arnold},
title = {{Winds, Waves and Maritime Structures}},
year = {1963}
}
@article{Mirchina1984,
author = {Mirchina, N. R. and Pelinovsky, E.},
journal = {Izvestiya, Atmospheric and Oceanic Physics},
number = {3},
pages = {252--253},
title = {{Increase in the amplitude of a long wave near a vertical wall}},
volume = {20},
year = {1984}
}
@article{Mirie1982,
author = {Mirie, S. M. and Su, C. H.},
journal = {J. Fluid Mech.},
pages = {475--492},
title = {{Collision between two solitary waves. Part 2. A numerical study}},
volume = {115},
year = {1982}
}
@article{Mishra2012,
author = {Mishra, S. and Schwab, Ch. and {\v{S}}ukys, J.},
doi = {10.1016/j.jcp.2012.01.011},
issn = {00219991},
journal = {J. Comput. Phys.},
month = {apr},
number = {8},
pages = {3365--3388},
title = {{Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999112000320},
volume = {231},
year = {2012}
}
@article{Mitsotakis2007,
author = {Mitsotakis, D. E.},
journal = {Math. Comp. Simul.},
pages = {860--873},
title = {{Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves}},
volume = {80},
year = {2009}
}
@article{Mitsotakis2014a,
author = {Mitsotakis, D. and Dutykh, D. and Carter, J. D.},
journal = {Submitted},
pages = {1--42},
title = {{On the nonlinear dynamics of the traveling-wave solutions of the Serre equations}},
url = {http://arxiv.org/abs/1404.6725},
year = {2015}
}
@article{Mitsotakis2014,
abstract = {A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finite-element method based on smooth periodic splines in space, and an explicit fourth-order Runge–Kutta method in time. Computations compared with exact solitary and cnoidal wave solutions show that the scheme achieves the optimal orders of accuracy in space and time. These computations also show that the stability of this scheme does not impose very restrictive conditions on the temporal stepsize. In addition, solitary, cnoidal, and dispersive shock waves are studied in detail using this numerical scheme for the Serre system and compared with the ‘classical’ Boussinesq system for small-amplitude shallow water waves. The results show that the interaction of solitary waves in the Serre system is more inelastic. The efficacy of the numerical scheme for modeling dispersive shocks is shown by comparison with asymptotic results. These results have application to the modeling of shallow water waves of intermediate or large amplitude.},
archivePrefix = {arXiv},
arxivId = {arXiv:1306.3321v1},
author = {Mitsotakis, D. and Ilan, B. and Dutykh, D.},
doi = {10.1007/s10915-014-9823-3},
eprint = {arXiv:1306.3321v1},
issn = {08857474},
journal = {J. Sci. Comput.},
keywords = {Green-Naghdi equations,Traveling waves,Undular bores},
month = {feb},
number = {1},
pages = {166--195},
title = {{On the Galerkin/Finite-Element Method for the Serre Equations}},
url = {http://link.springer.com/10.1007/s10915-014-9823-3},
volume = {61},
year = {2014}
}
@article{Miura1974,
author = {Miura, R. M.},
journal = {Stud. Appl. Maths.},
pages = {45--56},
title = {{Conservation laws for the fully nonlinear long wave equations}},
volume = {53},
year = {1974}
}
@article{Miura1968a,
author = {Miura, R. M.},
doi = {10.1063/1.1664700},
issn = {00222488},
journal = {J. Math. Phys.},
number = {8},
pages = {1202--1204},
title = {{Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation}},
url = {http://link.aip.org/link/?JMP/9/1202/1{\&}Agg=doi},
volume = {9},
year = {1968}
}
@article{Miura1968b,
abstract = {An explicit nonlinear transformation relating solutions of the Korteweg‐de Vries equation and a similar nonlinear equation is presented. This transformation is generalized to solutions of a one‐parameter family of similar nonlinear equations. A transformation is given which relates solutions of a ``forced'' Korteweg‐de Vries equation to those of the Korteweg‐de Vries equation.},
author = {Miura, R. M.},
doi = {10.1063/1.1664700},
issn = {00222488},
journal = {J. Math. Phys.},
number = {8},
pages = {1202},
title = {{Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation}},
url = {http://scitation.aip.org/content/aip/journal/jmp/9/8/10.1063/1.1664700},
volume = {9},
year = {1968}
}
@article{Miura1976,
author = {Miura, R. M.},
journal = {SIAM Rev},
pages = {412--459},
title = {{The Korteweg-de Vries equation: a survey of results}},
volume = {18},
year = {1976}
}
@article{Miura1968,
abstract = {With extensive use of the nonlinear transformations presented in Paper I of the series, a variety of conservation laws and constants of motion are derived for the Kortewegde Vries and related equations. A striking connection with the SturmLiouville eigenvalue problem is exploited.},
author = {Miura, R. M. and Gardner, C. S. and Kruskal, M. D.},
doi = {10.1063/1.1664701},
issn = {00222488},
journal = {Journal of Mathematical Physics},
number = {8},
pages = {1204},
title = {{Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion}},
url = {http://link.aip.org/link/?JMP/9/1204/1{\&}Agg=doi},
volume = {9},
year = {1968}
}
@book{Mohammadi1994,
author = {Mohammadi, B. and Pironneau, O.},
booktitle = {Research in Applied Mathematics},
editor = {Mohammadi, B. and Pironneau, O.},
isbn = {0471944602},
pages = {194},
publisher = {John Wiley and Sons},
title = {{Analysis of the K-Epsilon Turbulence Model}},
year = {1994}
}
@article{Monaghan2000,
author = {Monaghan, J. J.},
doi = {10.1006/jcph.2000.6439},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {apr},
number = {2},
pages = {290--311},
title = {{SPH without a Tensile Instability}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999100964398},
volume = {159},
year = {2000}
}
@article{Monaghan2005,
abstract = {In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.},
author = {Monaghan, J. J.},
journal = {Rep. Prog. Phys.},
pages = {1703--1759},
title = {{Smoothed particle hydrodynamics}},
volume = {68},
year = {2005}
}
@article{Monaghan,
author = {Monaghan, J. J.},
journal = {Phys. D},
pages = {399--406},
title = {{Simulating free surface flows with SPH}},
volume = {110},
year = {1994}
}
@article{Monaghan2013,
author = {Monaghan, J. J. and Rafiee, A.},
doi = {10.1002/fld.3671},
issn = {02712091},
journal = {Int. J. Num. Meth. Fluids},
month = {feb},
number = {5},
pages = {537--561},
title = {{A simple SPH algorithm for multi-fluid flow with high density ratios}},
url = {http://doi.wiley.com/10.1002/fld.3671},
volume = {71},
year = {2013}
}
@book{Monin2007,
address = {Mineola, New York},
author = {Monin, A. S. and Yaglom, A. M.},
pages = {784},
publisher = {Dover Publications},
title = {{Statistical fluid mechanics, Volume I}},
year = {2007}
}
@book{Montgomery1964,
author = {Montgomery, D. C. and Tidman, D. A.},
publisher = {McGraw-Hill, New York},
title = {{Plasme kinetic theory}},
year = {1964}
}
@article{Moore2003a,
abstract = {Recent results on numerical integrationmethods that exactly preserve the symplectic structure in both space and time for Hamiltonian PDEs are discussed. The Preissman box scheme is considered as an example, and it is shown that the method exactly preserves a multi-symplectic conservation law and any conservation law related to linear symmetries of the PDE. Local energy and momentum are not, in general, conserved exactly, but semi-discrete versions of these conservation laws are. Then, using Taylor series expansions, one obtains a modified multi-symplectic PDE and modified conservation laws that are preserved to higher order. These results are applied to the nonlinear Schr{\"{o}}dinger (NLS) equation and the sine-Gordon equation in relation to the numerical approximation of solitary wave solutions.},
author = {Moore, B. and Reich, S.},
doi = {10.1016/S0167-739X(02)00166-8},
issn = {0167739X},
journal = {Future Generation Computer Systems},
keywords = {backward error analysis,conservation laws,modified equations,multi symplectic pdes,preissman box scheme},
number = {3},
pages = {395--402},
title = {{Multi-symplectic integration methods for Hamiltonian PDEs}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167739X02001668},
volume = {19},
year = {2003}
}
@article{Moore2003,
author = {Moore, B. and Reich, S.},
journal = {Numerische Mathematik},
number = {4},
pages = {625--652},
publisher = {Springer},
title = {{Backward error analysis for multi-symplectic integration methods}},
url = {http://www.springerlink.com/index/QW1KJPHLT6VBHBYQ.pdf},
volume = {95},
year = {2003}
}
@article{Moore1994,
author = {Moore, J. G. and Normark, W. R. and Holcomb, R. T.},
journal = {Annu. Rev. Earth Planet. Sci.},
pages = {119--144},
title = {{Giant Hawaiian landslides}},
volume = {22},
year = {1994}
}
@article{MoralesdeLuna2009,
abstract = {We present a model for hyperpycnal plumes or turbidity currents that takes into account the interaction between the turbidity current and the bottom, considering deposition and erosion effects as well as solid transport of particles at the bed load due to the current. Water entrainment from the ambient water in which the turbidity current plunges is also considered. Motion of ambient water is neglected and the rigid lid assumption is considered. The model is obtained as a depth-average system of equations under the shallow water hypothesis describing the balance of fluid mass, sediment mass and mean flow. The character of the system is analyzed and numerical simulations are carried out using finite volume schemes and path-conservative Roe schemes.},
author = {{Morales de Luna}, T. and Castro-Diaz, M. J. and {Pares Madronal}, C. and Fernandez-Nieto, E. D.},
journal = {Commun. Comput. Phys.},
keywords = {Turbidity currents,finite volume methods,hyperbolic systems,numerical modeling,path-conservative schemes},
pages = {848--882},
title = {{On a Shallow Water Model for the Simulation of Turbidity Currents}},
volume = {6},
year = {2009}
}
@inproceedings{More1978,
author = {Mor{\'{e}}, J. J.},
booktitle = {Proceedings of the Biennial Conference Held at Dundee, June 28-July 1, 1977},
doi = {10.1007/BFb0067700},
editor = {Watson, G. A.},
pages = {105--116},
publisher = {Springer Berlin Heidelberg},
title = {{The Levenberg-Marquardt algorithm: Implementation and theory}},
year = {1978}
}
@article{Mori2006,
author = {Mori, N. and Janssen, P. A. E. M.},
journal = {J. Phys. Oceanogr.},
pages = {1471--1483},
title = {{On Kurtosis and occurrence probability of freak waves}},
volume = {36},
year = {2006}
}
@article{Morris1997,
abstract = {The method of smoothed particle hydrodynamics (SPH) is extended to model incompressible flows of low Reynolds number. For such flows, modification of the standard SPH formalism is required to minimize errors associated with the use of a quasi-incompressible equation of state. Treatment of viscosity, state equation, kernel interpolation, and boundary conditions are described. Simulations using the method show close agreement with series solutions for Couette and Poiseuille flows. Furthermore, comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields. The SPH results exhibit small pressure fluctuations near curved boundaries. Further improvements to the boundary conditions may be possible which will reduce these errors. A similar method to that used here may permit the simulation of other flows at low Reynolds numbers using SPH. Further development will be needed for cases involving free surfaces or substantially different equations of state.},
author = {Morris, J. P. and Fox, P. J. and Zhu, Y.},
doi = {10.1006/jcph.1997.5776},
issn = {00219991},
journal = {J. Comp. Phys.},
pages = {214--226},
title = {{Modeling Low Reynolds Number Incompressible Flows Using SPH}},
url = {http://www.sciencedirect.com/science/article/pii/S0021999197957764},
volume = {136},
year = {1997}
}
@article{Morrison1998,
author = {Morrison, P. J.},
journal = {Rev. Mod. Phys.},
pages = {467--521},
title = {{Hamiltonian description of the ideal fluid}},
volume = {70(2)},
year = {1998}
}
@article{Morse1940,
author = {Morse, M. and Hedlund, G. A.},
journal = {Amer. J. Math.},
pages = {1--42},
title = {{Symbolic Dynamics II. Sturmian trajectories}},
volume = {62},
year = {1940}
}
@book{Mougin1922,
address = {Paris},
author = {Mougin, P.},
editor = {{Minist{\`{e}}re de l'Agriculture, Direction G{\'{e}}n{\'{e}}rale des Eaux et For{\^{e}}ts, Service des Grandes Forces Hydrauliques}, Paris},
publisher = {Imprimerie Nationale},
title = {{Etudes glaciologiques : Les avalanches en Savoie, T. 4}},
year = {1922}
}
@book{Mougin1931,
author = {Mougin, P.},
publisher = {Imprimerie Nationale, Paris},
title = {{Restauration des montagnes}},
year = {1931}
}
@article{Mugnolo2013,
archivePrefix = {arXiv},
arxivId = {1302.2104},
author = {Mugnolo, D. and Rault, J.-F.},
eprint = {1302.2104},
journal = {Submitted},
pages = {1--18},
title = {{Construction of exact travelling waves for the Benjamin-Bona-Mahony equation on networks}},
url = {http://arxiv.org/abs/1302.2104},
year = {2013}
}
@article{Munk1964,
author = {Munk, W. and Snodgrass, F. and Gilbert, F.},
journal = {J. Fluid Mech.},
number = {04},
pages = {529--554},
title = {{Long waves on the continental shelf: an experiment to separate trapped and leaky modes}},
volume = {20},
year = {1964}
}
@book{Mura1992,
abstract = {The recent success and popularity of the finite-element method, crucial to solving mathematical problems in many branches of engineering today, is based on the variational methods discussed in this textbook. The author, Toshio Mura, is a distinguished engineer and applied mathematician who brings to the work a highly pragmatic approach designed to facilitate teaching the subject, which is essential for all materials science and mechanical and civil engineering students. In addition to all basic topics, the authors cover state-of-the-art research findings, such as those involving composite materials.},
address = {Oxford},
author = {Mura, T. and Koya, T.},
isbn = {978-0195068306},
pages = {256},
publisher = {Oxford University Press},
title = {{Variational Methods in Mechanics}},
year = {1992}
}
@article{Muraki2007,
author = {Muraki, D. J.},
journal = {SIAM J. Appl. Math},
number = {5},
pages = {1504--1521},
title = {{A Simple Illustration of a Weak Spectral Cascade}},
volume = {67},
year = {2007}
}
@article{Muro2011,
author = {Muro, C. and Escobedo, R. and Spector, L. and Coppinger, R. P.},
doi = {10.1016/j.beproc.2011.09.006},
issn = {03766357},
journal = {Behavioural Processes},
month = {nov},
number = {3},
pages = {192--197},
title = {{Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0376635711001884},
volume = {88},
year = {2011}
}
@book{Murray2007,
abstract = {Mathematical Biology is a richly illustrated textbook in an exciting and fast growing field. Providing an in-depth look at the practical use of math modeling, it features exercises throughout that are drawn from a variety of bioscientific disciplines - population biology, developmental biology, physiology, epidemiology, and evolution, among others. It maintains a consistent level throughout so that graduate students can use it to gain a foothold into this dynamic research area.},
address = {Berlin, Heidelberg},
author = {Murray, J. D.},
editor = {Antman, S.S. and Marsden, J.E. and Sirovich, L. and Wiggins, S.},
isbn = {978-0387952239},
pages = {553},
publisher = {Springer-Verlag},
title = {{Mathematical Biology: I. An Introduction}},
year = {2007}
}
@book{murray,
author = {Murray, J. D.},
isbn = {0387909370},
publisher = {Springer},
title = {{Asymptotic Analysis}},
year = {1992}
}
@inproceedings{Murray1989,
author = {Murray, R. J.},
booktitle = {Proc., 9th Australian Conf. on Coast. and Oc. Engrg.},
title = {{Short wave modelling using new equations of Boussinesq type}},
year = {1989}
}
@article{Murrone2005,
author = {Murrone, A. and Guillard, H.},
journal = {J. Comput. Phys.},
pages = {664--698},
title = {{A five equation reduced model for compressible two phase flow problems}},
volume = {202},
year = {2005}
}
@article{Musaferija1996,
author = {Musaferija, S. and Gosman, D.},
journal = {J. Comp. Phys.},
pages = {766--787},
title = {{Finite-Volume CFD Procedure and Adaptive Error Control Strategy for Grids of Arbitrary Topology}},
volume = {138},
year = {1996}
}
@phdthesis{Naaim-Bouvet2003,
author = {Naaim-Bouvet, F.},
school = {Cemagref},
title = {{Approche macro-structurelle des {\'{e}}coulements bi-phasiques turbulents de neige et de leur interaction avec des obstacles}},
type = {Habilitation $\backslash$`a Diriger des Recherches},
year = {2003}
}
@article{Naaim-Bouvet2002,
author = {Naaim-Bouvet, F. and Naaim, M. and Bacher, M. and Heiligenstein, L.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {193--202},
title = {{Physical modelling of the interaction between powder avalanches and defence structures}},
volume = {2},
year = {2002}
}
@article{Naaim-Bouvet2003a,
author = {Naaim-Bouvet, F. and Pain, S. and Naaim, M. and Faug, T.},
journal = {Surveys in Geophysics},
pages = {479--498},
title = {{Numerical and physical modelling of the effect of dam on powder avalanche motion: Comparison with previous approaches}},
volume = {24 (5/6)},
year = {2003}
}
@inproceedings{Naaim1995,
address = {Chamonix},
author = {Naaim, M.},
booktitle = {Comptes Rendus Les apports de la recherche scientifique {\`{a}} la securit{\'{e}} neige, glace et avalanche},
editor = {ANENA},
pages = {31--36},
title = {{Numerical model of powder snow avalanche. Theoretical analysis and application}},
year = {1995}
}
@article{Naaim1998,
author = {Naaim, M. and Gurer, I.},
journal = {Natural Hazards},
pages = {129--145},
title = {{Two-phase Numerical Model of Powder Avalanche. Theory and Application}},
volume = {117},
year = {1998}
}
@article{Nachbin2003,
author = {Nachbin, A.},
journal = {SIAM Appl. Math.},
pages = {905--922},
title = {{A terrain-following Boussinesq system}},
volume = {63(3)},
year = {2003}
}
@article{Nachbin2010,
author = {Nachbin, A.},
journal = {Discrete and Continuous Dynamical Systems (DCDS-A)},
pages = {1603--1633},
title = {{Discrete and continuous random water wave dynamics}},
volume = {28(4)},
year = {2010}
}
@article{Nachbin2012a,
abstract = {The dynamics of solitary waves is studied in intricate domains such as open channels with sharp-bends and branching points. Of particular interest, the wave characteristics at sharp-bends is rationalized by using the Jacobian of the Schwarz-Christoffel transformation. It is observed that it acts in a similar fashion as a topography in other wave models previously studied. Previous numerical studies are revisited. A new very efficient algorithm is described, which computationally solves the problem in much more general channel configurations than presented in the literature. Also the conformal mapping naturally leads to a new strategy regarding the geometrical singularity at the sharp-bends. Finally preliminary results illustrate the use of the mapping's Jacobian at a channel's branching point. A future goal of this study regards deducing accurate reduced (one-dimensional) models for the reflection and transmission of solitary waves on graphs/networks.},
author = {Nachbin, A. and {Da Silva Simoes}, V.},
doi = {10.1142/S1402925112400116},
issn = {1402-9251},
journal = {J. Nonlin. Math. Phys.},
month = {jan},
number = {sup1},
pages = {1240011},
title = {{Solitary waves in open channels with abrupt turns and branching points}},
url = {http://www.tandfonline.com/doi/abs/10.1142/S1402925112400116},
volume = {19},
year = {2012}
}
@article{Nachbin2012,
abstract = {The dynamics of solitary waves is studied in intricate domains such as open channels with sharp-bends and branching points. Of particular interest, the wave characteristics at sharp-bends is rationalized by using the Jacobian of the Schwarz-Christoffel transformation. It is observed that it acts in a similar fashion as a topography in other wave models previously studied. Previous numerical studies are revisited. A new very efficient algorithm is described, which computationally solves the problem in much more general channel configurations than presented in the literature. Also the conformal mapping naturally leads to a new strategy regarding the geometrical singularity at the sharp-bends. Finally preliminary results illustrate the use of the mapping's Jacobian at a channel's branching point. A future goal of this study regards deducing accurate reduced (one-dimensional) models for the reflection and transmission of solitary waves on graphs/networks.},
author = {Nachbin, A. and {Da Silva Simoes}, V.},
doi = {10.1142/S1402925112400116},
issn = {1402-9251},
journal = {J. Nonlinear Math. Phys.},
keywords = {Water waves,solitary waves,tsunami in channels},
month = {jan},
pages = {1240011},
title = {{Solitary waves in open channels with abrupt turns and branching points}},
url = {http://www.tandfonline.com/doi/abs/10.1142/S1402925112400116},
volume = {19},
year = {2012}
}
@article{Nachbin2015,
abstract = {Solitary water waves travelling through a forked channel region are studied via a new nonlinear wave model. This novel (reduced) one-dimensional (1D) model captures the effective features of the reflection and transmission of solitary waves passing through a two-dimensional (2D) branching channel region. Using an appropriate change of coordinates, the 2D wave system is defined in a simpler geometric configuration that allows a straightforward reduction to a 1D graph-like configuration. The Jacobian of the change of coordinates leads to a variable coefficient in the 1D model, which contains information about the angles of the diverting reaches, a feature that is not present in any previous water wave model on networks. Furthermore, this new formulation is more general, in allowing both symmetric and asymmetric branching configurations to be considered. A new compatibility condition is deduced, which is used at the corresponding branching node. The 2D and 1D dynamics are compared, with very good agreement.},
author = {Nachbin, A. and Sim{\~{o}}es, V. S.},
doi = {10.1017/jfm.2015.359},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {aug},
pages = {544--568},
title = {{Solitary waves in forked channel regions}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112015003596},
volume = {777},
year = {2015}
}
@article{Natalini1994,
author = {Natalini, R. and Tesei, A.},
doi = {10.1080/03605309408821023},
issn = {0360-5302},
journal = {Comm. Partial Diff. Eqns.},
month = {jan},
number = {3-4},
pages = {417--453},
title = {{Blow-up of solutions for a class of balance laws}},
url = {http://www.tandfonline.com/doi/abs/10.1080/03605309408821023},
volume = {19},
year = {1994}
}
@book{Nayfeh2000,
address = {New York},
author = {Nayfeh, A.},
edition = {1},
isbn = {978-0471399179},
pages = {437},
publisher = {Wiley-VCH},
title = {{Perturbation Methods}},
year = {2000}
}
@book{Nazarenko2011,
abstract = {Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as ''frozen'' turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.},
address = {Berlin},
author = {Nazarenko, S.},
isbn = {978-3-642-15942-8},
pages = {279},
publisher = {Springer Series Lecture Notes in Phyics, vol. 825},
title = {{Wave Turbulence}},
year = {2011}
}
@article{Ndjinga2008,
author = {Ndjinga, M. and Kumbaro, A. and {De Vuyst}, F. and Laurent-Gengoux, P.},
journal = {Nuclear Engineering and Design},
pages = {2075--2083},
title = {{Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver}},
volume = {238},
year = {2008}
}
@article{Neetu2011,
author = {Neetu, S. and Suresh, I. and Shankar, R. and Nagarajan, B. and Sharma, R. and Shenoi, S. and Unnikrishnan, A. and Sundar, D.},
journal = {Nat. Hazards},
pages = {1--10},
publisher = {Springer Netherlands},
title = {{Trapped waves of the 27 November 1945 Makran tsunami: observations and numerical modeling}},
year = {2011}
}
@article{indiens2,
author = {Neetu, S. and Suresh, I. and Shankar, R. and Shankar, D. and Shenoi, S. S. C. and Shetye, S. R. and Sundar, D. and Nagarajan, B.},
journal = {Science},
pages = {1431a--------1431b},
title = {{Comment on ``The Great Sumatra-Andaman Earthquake of 26 December 2004''}},
volume = {310},
year = {2005}
}
@article{Nersisyan2012,
abstract = {In this study we investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to a given trajectory. The practical question we address in this study is how to compute the wavemaker shape and its trajectory in order to generate a wave with prescribed characteristics? For the sake of simplicity we model the hydrodynamics by a generalized forced BBM equation. This practical problem is reformulated as a constrained nonlinear optimization problem. Some constraints are imposed in order to make practically feasible the computed solution. Finally, we show some numerical results to support our theoretical and algorithmic developments.},
author = {Nersisyan, H. and Dutykh, D. and Zuazua, E.},
doi = {10.1093/imamat/hxu051},
issn = {0272-4960},
journal = {IMA J. Appl. Math.},
month = {aug},
number = {4},
pages = {1235--1253},
title = {{Generation of 2D water waves by moving bottom disturbances}},
url = {http://imamat.oxfordjournals.org/lookup/doi/10.1093/imamat/hxu051},
volume = {80},
year = {2015}
}
@article{NT,
author = {Nessyahu, H. and Tadmor, E.},
journal = {J. Comp. Phys.},
number = {2},
pages = {408--463},
title = {{Nonoscillatory central differencing for hyperbolic conservation laws}},
volume = {87},
year = {1990}
}
@book{Nesterenko2001,
address = {New York, NY},
author = {Nesterenko, V. F.},
doi = {10.1007/978-1-4757-3524-6},
isbn = {978-1-4419-2926-6},
pages = {510},
publisher = {Springer New York},
title = {{Dynamics of Heterogeneous Materials}},
url = {http://link.springer.com/10.1007/978-1-4757-3524-6},
year = {2001}
}
@article{Newell1977,
author = {Newell, A. C.},
journal = {SIAM Journal of Applied Mathematics},
pages = {133--160},
title = {{Finite amplitude instabilities of partial difference equations}},
volume = {33},
year = {1977}
}
@article{Newell2011,
abstract = {In this article, we state and review the premises on which a successful asymptotic closure of the moment equations of wave turbulence is based, describe how and why this closure obtains, and examine the nature of solutions of the kinetic equation. We discuss obstacles that limit the theory's validity and suggest how the theory might then be modified. We also compare the experimental evidence with the theory's predictions in a range of applications. Finally, and most importantly, we suggest open challenges and encourage the reader to apply and explore wave turbulence with confidence. The narrative is terse but, we hope, delivered at a speed more akin to the crisp pace of a Hemingway story than the wordjumblingtumbling rate of a Joycean novel.},
author = {Newell, A. C. and Rumpf, B.},
doi = {10.1146/annurev-fluid-122109-160807},
issn = {0066-4189},
journal = {Ann. Rev. Fluid Mech.},
month = {jan},
number = {1},
pages = {59--78},
title = {{Wave Turbulence}},
url = {http://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-122109-160807},
volume = {43},
year = {2011}
}
@book{Newton1687,
address = {London},
author = {Newton, I.},
title = {{Philosophiae Naturalis Principia Mathematica}},
year = {1687}
}
@article{Nghia2006,
abstract = {We consider the Riemann problem for non-genuinely nonlinear conservation laws where the flux function admits two inflection points. This is a simplification of van der Waals fluid pressure, which can be seen as a function of the specific volume for a specific entropy at which the system lacks the non-genuine nonlinearity. Corresponding to each inflection point, A nonclassical Riemann solver can be uniquely constructed. Furthermore, two kinetic relations can be used to construct nonclassical Riemann solutions.},
author = {Nghia, H. D. and Thanh, M. D.},
journal = {Electronic Journal of Differential Equations},
keywords = {Conservation law,kinetic relation,non-genuine nonlinearity,nonclassical solution},
pages = {1--18},
title = {{Nonclassical shock waves of conservation laws: flux function having two inflection points}},
volume = {149},
year = {2006}
}
@phdthesis{Nguyen2008a,
author = {Nguyen, H. Y.},
school = {Ecole Normale Sup{\'{e}}rieure de Cachan},
title = {{Mod{\`{e}}les pour les ondes interfaciales et leur int{\'{e}}gration num{\'{e}}rique}},
year = {2008}
}
@article{Nguyen2008,
author = {Nguyen, H. Y. and Dias, F.},
journal = {Physica D},
pages = {2365--2389},
title = {{A Boussinesq system for two-way propagation of interfacial waves}},
volume = {237(18)},
year = {2008}
}
@article{Nichols1971,
author = {Nichols, B. D. and Hirt, C. W.},
journal = {J. Comput. Phys.},
pages = {434--448},
title = {{Improved free surface conditions for numerical incompressible flow computations}},
volume = {8},
year = {1971}
}
@book{Nichols2011,
abstract = {For over fifty years, McDonald's Blood Flow in Arteries has remained the definitive reference work in the field of arterial hemodynamics, including arterial structure and function with special emphasis on pulsatile flow and pressure. Prestigious, authoritative and comprehensive, the sixth edition has been totally updated and revised with several new chapters. This edition continues to provide the theoretical basis required for a thorough understanding of arterial blood flow in both normal and pathological conditions, while keeping clinical considerations and readability paramount throughout the text.},
address = {London},
author = {Nichols, W. and O'Rourke, M. and Vlachopoulos, C.},
edition = {Sixth},
pages = {768},
publisher = {CRC Press},
title = {{McDonald's Blood Flow in Arteries}},
year = {2011}
}
@article{Nickalls1996,
author = {Nickalls, R. W. D. and Dye, R. H.},
journal = {The Mathematical Gazette},
number = {488},
pages = {279--285},
title = {{The geometry of the discriminant of a polynomial}},
volume = {80},
year = {1996}
}
@techreport{Nielsen1999,
author = {Nielsen, H.},
institution = {Technical University of Denmark},
keywords = {IMM-REP-1999-05},
mendeley-tags = {IMM-REP-1999-05},
pages = {31},
title = {{Damping Parameter in Marquardt's Method}},
year = {1999}
}
@book{Nielsen1992,
author = {Nielsen, P.},
booktitle = {Advanced Series on Ocean Engineering},
editor = {Liu, P L F},
isbn = {9810204736},
pages = {324},
publisher = {World Scientific},
title = {{Coastal bottom boundary layers and sediment transport}},
url = {http://books.google.com/books?id=53MQC15q54wC{\&}pgis=1},
volume = {4},
year = {1992}
}
@article{Nikitin1999,
author = {Nikitin, A. G.},
journal = {Zh. Vychisl. Mat. Mat. Fiz.},
number = {4},
pages = {588--591},
title = {{On the principal eigenfunction of a singularly perturbed Sturm-Liouville problem}},
volume = {39},
year = {1999}
}
@article{Nikolkina2011,
author = {Nikolkina, I. and Didenkulova, I.},
doi = {10.5194/nhess-11-2913-2011},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {2913--2924},
title = {{Rogue waves in 2006 - 2010}},
volume = {11},
year = {2011}
}
@inproceedings{Ning2012,
author = {Ning, D. and Zhou, X. and Hou, T. and Teng, B.},
booktitle = {Proc. 22nd International Offshore and Polar Engineering Conference},
title = {{Numerical investigation of focused waves on uniform currents}},
year = {2012}
}
@article{Nishimura1998,
author = {Nishimura, K. and Keller, S. and McElwaine, J. and Nohguchi, Y.},
journal = {Granular matter},
pages = {51--56},
title = {{Ping-pong ball avalanche at a ski jump}},
volume = {1},
year = {1998}
}
@article{Nishimura1993,
author = {Nishimura, K. and Maneo, N. and Kawada, K. and Izumi, K.},
journal = {Annals of Glaciology},
pages = {173--178},
title = {{Structures of snow cloud in dry-snow avalanches}},
volume = {18},
year = {1993}
}
@article{Nishimura1995,
author = {Nishimura, K. and Sandersen, F. and Kristensen, K. and Lied, K.},
journal = {Surveys in Geophysics},
pages = {649--660},
title = {{Measurements of powder snow avalanche - Nature}},
volume = {16},
year = {1995}
}
@article{Noble2014,
abstract = {In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler equations are discretized with a classical scheme (e.g. Roe, Rusanov or Lax-Friedrichs scheme) whereas the dispersive term is discretized with centered finite differences. We first prove that a certain amount of numerical viscosity is needed for a difference scheme to be stable in the Von Neumann sense. Then we consider the entropy stability of difference approximations. For that purpose, we introduce an additional unknown, the gradient of a function of the density. The Euler-Korteweg system is transformed into a hyperbolic system perturbed by a second order skew symmetric term. We prove entropy stability of Lax-Friedrichs type schemes under a suitable Courant-Friedrichs-Levy condition. We validate our approach numerically on a simple case and then carry out numerical simulations of a shallow water system with surface tension which models thin films down an incline. In addition, we propose a spatial discretization of the Euler-Korteweg system seen as a Hamiltonian system of evolution PDEs. This spatial discretization preserves the Hamiltonian structure and thus is naturally entropy conservative. This scheme makes possible the numerical simulation of the dispersive shock waves of the Euler Korteweg system.},
author = {Noble, P. and Vila, J. P.},
journal = {Arxiv:1304.3805},
pages = {1--22},
title = {{Stability theory for difference approximations of some dispersive shallow water equations and application to thin film flows}},
year = {2014}
}
@book{Nocedal2006,
address = {New York},
author = {Nocedal, J. and Wright, S. J.},
edition = {2nd},
isbn = {978-0387-30303-1},
pages = {664},
publisher = {Springer},
title = {{Numerical Optimization}},
year = {2006}
}
@book{Nocedal1999,
address = {New York},
author = {Nocedal, J. and Wright, S. J.},
isbn = {0-387-98793-2},
pages = {651},
publisher = {Springer},
title = {{Numerical Optimization}},
year = {1999}
}
@article{Noelle2006,
author = {Noelle, S. and Pankratz, N. and Puppo, G. and Natvig, J. R.},
journal = {J. Comput. Phys.},
pages = {474--499},
title = {{Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows}},
volume = {213},
year = {2006}
}
@techreport{Norem1990,
author = {Norem, H. and Tronstad, K. and Kristensen, K.},
institution = {Norwegian Geotechnical Institute},
title = {{The Ryggfonn project: Avalanche data from the 1983 - 1989 winters}},
year = {1990}
}
@article{Nosov1999,
author = {Nosov, M. A.},
journal = {Phys. Chem. Earth. (B)},
pages = {437--441},
title = {{Tsunami generation in compressible ocean}},
volume = {24},
year = {1999}
}
@article{Nosov2009,
author = {Nosov, M. A. and Kolesov, S. V.},
doi = {10.3103/S0027134909020222},
issn = {0027-1349},
journal = {Moscow University Physics Bulletin},
month = {may},
number = {2},
pages = {208--213},
title = {{Method of specification of the initial conditions for numerical tsunami modeling}},
url = {http://www.springerlink.com/index/10.3103/S0027134909020222},
volume = {64},
year = {2009}
}
@article{Nosov2007a,
author = {Nosov, M. A. and Kolesov, S. V.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {243--249},
title = {{Elastic oscillations of water column in the 2003 Tokachi-oki tsunami source: in-situ measurements and 3-D numerical modelling}},
volume = {7},
year = {2007}
}
@article{Nosov2007,
author = {Nosov, M. A. and Kolesov, S. V. and Denisova, A. V. and Alekseev, A. B. and Levin, B. V.},
journal = {Oceanology},
number = {1},
pages = {26--32},
title = {{On the Near-Bottom Pressure Variations in the Region of the 2003 Tokachi-Oki Tsunami Source}},
volume = {47},
year = {2007}
}
@article{Nosov2001,
author = {Nosov, M. A. and Skachko, S. N.},
journal = {Natural Hazards and Earth System Sciences},
pages = {251--253},
title = {{Nonlinear tsunami generation mechanism}},
volume = {1},
year = {2001}
}
@article{Noussair2000,
author = {Noussair, A.},
doi = {10.1111/1467-9590.00137},
issn = {0022-2526},
journal = {Stud. Appl. Math.},
month = {may},
number = {4},
pages = {313--352},
title = {{Analysis of Nonlinear Resonance in Conservation Laws with Point Sources and Well-Balanced Scheme}},
url = {http://doi.wiley.com/10.1111/1467-9590.00137},
volume = {104},
year = {2000}
}
@article{Nwogu1993,
author = {Nwogu, O.},
journal = {J. Waterway, Port, Coastal and Ocean Engineering},
pages = {618--638},
title = {{Alternative form of Boussinesq equations for nearshore wave propagation}},
volume = {119},
year = {1993}
}
@phdthesis{O'Brien2012,
author = {O'Brien, L.},
school = {University College Dublin},
title = {{Mathematical and numerical modelling of extreme ocean waves with a historical survey of damaging events in Ireland}},
type = {PhD},
year = {2012}
}
@article{O'Brien2013,
author = {O'Brien, L. and Dudley, J. M. and Dias, F.},
doi = {10.5194/nhess-13-625-2013},
issn = {1684-9981},
journal = {Natural Hazards and Earth System Science},
month = {mar},
number = {3},
pages = {625--648},
title = {{Extreme wave events in Ireland: 14 680 BP-2012}},
url = {http://www.nat-hazards-earth-syst-sci.net/13/625/2013/},
volume = {13},
year = {2013}
}
@article{Ohmachi2001,
author = {Ohmachi, T. and Tsukiyama, H. and Matsumoto, H.},
journal = {Bull. Seism. Soc. Am.},
pages = {1898--1909},
title = {{Simulation of tsunami induced by dynamic displacement of seabed due to seismic faulting}},
volume = {91},
year = {2001}
}
@article{Okada85,
author = {Okada, Y.},
journal = {Bull. Seism. Soc. Am.},
pages = {1135--1154},
title = {{Surface deformation due to shear and tensile faults in a half-space}},
volume = {75},
year = {1985}
}
@article{okada92,
author = {Okada, Y.},
journal = {Bull. Seism. Soc. Am.},
pages = {1018--1040},
title = {{Internal deformation due to shear and tensile faults in a half-space}},
volume = {82},
year = {1992}
}
@article{Okal2003a,
author = {Okal, E. A.},
journal = {Pure Appl. Geophys.},
pages = {2189--2221},
title = {{Normal Mode Energetics for Far-field Tsunamis Generated by Dislocations and Landslides}},
volume = {160},
year = {2003}
}
@article{Okal1982,
author = {Okal, E. A.},
journal = {Physics of the Earth and Planetary Interiors},
pages = {1--11},
title = {{Mode-wave equivalence and other asymptotic problems in tsunami theory}},
volume = {30},
year = {1982}
}
@article{Okal1988,
author = {Okal, E. A.},
journal = {Natural Hazards},
pages = {67--96},
title = {{Seismic Parameters Controlling Far-field Tsunami Amplitudes: A Review}},
volume = {1},
year = {1988}
}
@article{Okal2003,
author = {Okal, E. A. and Synolakis, C. E.},
journal = {Pure and Applied Geophysics},
pages = {2177--2188},
title = {{A theoretical comparison of tsunamis from dislocations and landslides}},
volume = {160},
year = {2003}
}
@article{Okal2003b,
author = {Okal, E. A. and Synolakis, C. E.},
journal = {Pure Appl. Geophys.},
pages = {2177--2188},
title = {{Field survey and numerical simulations: a theoretical comparison of tsunamis from dislocations and landslides}},
volume = {160},
year = {2003}
}
@article{Okal2008,
author = {Okal, E. A. and Synolakis, C. E.},
journal = {Geophys. J. Int.},
pages = {995--1015},
title = {{Far-field tsunami hazard from mega-thrust earthquakes in the Indian Ocean}},
volume = {172},
year = {2008}
}
@article{Okal2004,
author = {Okal, E. A. and Synolakis, C. E.},
journal = {Geophys. J. Int.},
pages = {899--912},
title = {{Source discriminants for near-field tsunamis}},
volume = {158},
year = {2004}
}
@article{OTR2007,
author = {Okal, E. A. and Talandier, J. and Reymond, D.},
journal = {Pure Appl. Geophys.},
pages = {309--323},
title = {{Quantification of hydrophone records of the 2004 Sumatra tsunami}},
volume = {164},
year = {2007}
}
@book{Okamoto2001,
address = {Singapore},
author = {Okamoto, H. and Shoji, M.},
editor = {Okamoto, H. and Shoji, M.},
pages = {229},
publisher = {World Scientific},
title = {{The Mathematical Theory of Permanent Progressive Water Waves}},
year = {2001}
}
@article{Okumura2007,
author = {Okumura, Y. and Kawata, Y.},
journal = {Proceedings of the Seventeenth International Offshore and Polar Engineering Conference},
title = {{Effects of rise time and rupture velocity on tsunami}},
volume = {III},
year = {2007}
}
@article{Olver1984,
author = {Olver, P. J.},
journal = {Contemp. Math.},
pages = {231--249},
title = {{Hamiltonian perturbation theory and water waves}},
volume = {28},
year = {1984}
}
@misc{Olver2012,
author = {Olver, P. J.},
title = {{Personal web page}},
url = {http://www.math.umn.edu/{~}olver/},
year = {2012}
}
@article{Olver1988a,
abstract = {We show how the restriction of certain bidirectional hamiltonian systems modelling nonlinear, one-dimensional wave propagation to waves moving in a single direction preserves the hamiltonian structure, even though the perturbation expansion of the bidirectional hamiltonian is not correct. A combination of the two approaches of direct hamiltonian perturbation theory and the method of multiple scales helps explain the apperance of integrable bihamiltonian wave models.},
author = {Olver, P. J.},
doi = {10.1016/0375-9601(88)90047-3},
journal = {Phys. Lett. A},
pages = {501--506},
title = {{Unidirectionalization of hamiltonian waves}},
volume = {126},
year = {1988}
}
@book{Olver1993,
author = {Olver, P. J.},
publisher = {Springer-Verlag},
series = {Graduate Texts in Mathematics},
title = {{Applications of Lie groups to differential equations}},
volume = {107 (2nd e},
year = {1993}
}
@article{Olver1979,
author = {Olver, P. J.},
doi = {10.1017/S0305004100055572},
issn = {0305-0041},
journal = {Math. Proc. Camb. Phil. Soc.},
month = {oct},
pages = {143--160},
title = {{Euler operators and conservation laws of the BBM equation}},
url = {http://www.journals.cambridge.org/abstract{\_}S0305004100055572},
volume = {85},
year = {1979}
}
@article{Olver1988,
abstract = {The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.},
author = {Olver, P. J. and Nutku, Y.},
doi = {10.1063/1.527909},
journal = {J. Math. Phys.},
pages = {1610},
title = {{Hamiltonian structures for systems of hyperbolic conservation laws}},
volume = {29},
year = {1988}
}
@article{Ono1975,
author = {Ono, H.},
journal = {J. Phys. Soc. Japan},
pages = {1082--1091},
title = {{Algebraic solitary waves in stratified fluids}},
volume = {39},
year = {1975}
}
@article{Ono1976,
author = {Ono, H.},
doi = {10.1143/JPSJ.41.1817},
issn = {0031-9015},
journal = {J. Phys. Soc. Jpn.},
month = {nov},
number = {5},
pages = {1817--1818},
title = {{Algebraic Soliton of the Modified Korteweg-de Vries Equation}},
url = {http://journals.jps.jp/doi/abs/10.1143/JPSJ.41.1817},
volume = {41},
year = {1976}
}
@article{Onorato2001,
author = {Onorato, M. and Osborne, A. R. and Serio, M. and Bertone, S.},
journal = {Phys. Rev. Lett.},
number = {25},
pages = {5831--5834},
title = {{Freak waves in random oceanic sea states}},
volume = {86},
year = {2001}
}
@article{Onorato2004,
author = {Onorato, M. and Osborne, A. R. and Serio, M. and Cavalieri, L. and Brandini, C. and Stansberg, C. T.},
journal = {Phys. Rev. E},
pages = {067302},
title = {{Observation of strongly non-gaussian statistics for random sea surface gravity waves in wave flume experiments}},
volume = {70},
year = {2004}
}
@article{Onorato2002,
abstract = {We study the long-time evolution of deep-water ocean surface waves in order to better understand the behavior of the nonlinear interaction processes that need to be accurately predicted in numerical models of wind-generated ocean surface waves. Of particular interest are those nonlinear interactions which are predicted by weak turbulence theory to result in a wave energy spectrum of the form of k(-2.5). We numerically implement the primitive Euler equations for surface waves and demonstrate agreement between weak turbulence theory and the numerical results.},
author = {Onorato, M. and Osborne, A. R. and Serio, M. and Resio, D. and Pushkarev, A. N. and Zakharov, V. E. and Brandini, C.},
institution = {Dipartimento di Fisica Generale, Universit{\`{a}} di Torino, Via Pietro Giuria 1, 10125 Torino, Italy.},
journal = {Phys. Rev. Lett},
number = {14},
pages = {4},
title = {{Freely decaying weak turbulence for sea surface gravity waves}},
url = {http://arxiv.org/abs/nlin/0201017},
volume = {89},
year = {2002}
}
@article{Onorato2003,
author = {Onorato, M. and Osborne, A. and Fedele, R. and Serio, M.},
doi = {10.1103/PhysRevE.67.046305},
issn = {1063-651X},
journal = {Phys. Rev. E},
month = {apr},
number = {4},
pages = {046305},
title = {{Landau damping and coherent structures in narrow-banded 1+1 deep water gravity waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.67.046305},
volume = {67},
year = {2003}
}
@article{Onorato2012,
author = {Onorato, M. and Proment, D.},
doi = {10.1016/j.physleta.2012.05.063},
issn = {03759601},
journal = {Phys. Lett. A},
month = {oct},
number = {45},
pages = {3057--3059},
title = {{Approximate rogue wave solutions of the forced and damped nonlinear Schr{\"{o}}dinger equation for water waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960112008377},
volume = {376},
year = {2012}
}
@phdthesis{Ooi2006,
author = {Ooi, S. K.},
school = {University of Iowa},
title = {{High resolution numerical simulations of lock-exchange gravity-driven flows}},
year = {2006}
}
@article{Osborne1993,
author = {Osborne, A.},
doi = {10.1103/PhysRevLett.71.3115},
issn = {0031-9007},
journal = {Phys. Rev. Lett},
month = {nov},
number = {19},
pages = {3115--3118},
title = {{Behavior of solitons in random-function solutions of the periodic Korteweg-de Vries equation}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.71.3115},
volume = {71},
year = {1993}
}
@book{Osborne2010,
author = {Osborne, A.},
booktitle = {International Geophysics Series},
editor = {Osborne, A.},
isbn = {9780125286299},
pages = {917 pp.},
publisher = {Elsevier},
title = {{Nonlinear ocean waves and the inverse scattering transform}},
url = {http://scholar.google.com/scholar?hl=en{\&}btnG=Search{\&}q=intitle:Nonlinear+ocean+waves+and+the+inverse+scattering+transform{\#}1},
volume = {97},
year = {2010}
}
@article{Osborne1995,
author = {Osborne, A. R.},
doi = {10.1016/0960-0779(94)E0118-9},
editor = {M{\"{u}}ller, P and Henderson, D},
issn = {09600779},
journal = {Chaos Solitons Fractals},
number = {12},
pages = {2623--2637},
publisher = {University of Hawaii Press},
title = {{The numerical inverse scattering transform: nonlinear Fourier analysis and nonlinear filtering of oceanic surface waves}},
url = {http://www.sciencedirect.com/science?{\_}ob=MImg{\&}{\_}imagekey=B6TJ4-3YXBR8R-T-1{\&}{\_}cdi=5300{\&}{\_}user=2787739{\&}{\_}orig=search{\&}{\_}coverDate=12/31/1995{\&}{\_}sk=999949987{\&}view=c{\&}wchp=dGLbVzb-zSkWA{\&}md5=e39d244d74ba7769b4699a4fb41b8058{\&}ie=/sdarticle.pdf},
volume = {5},
year = {1995}
}
@article{Osborne2000,
abstract = {Rogue waves are rare “giant”, “freak”, “monster” or “steep wave” events in nonlinear deep water gravity waves which occasionally rise up to surprising heights above the background wave field. Holes are deep troughs which occur before and/or after the largest rogue crests. The dynamical behavior of these giant waves is here addressed as solutions of the nonlinear Schr{\"{o}}dinger equation in both 1+1 and 2+1 dimensions. We discuss analytical results for 1+1 dimensions and demonstrate numerically, for certain sets of initial conditions, the ubiquitous occurrence of rogue waves and holes in 2+1 spatial dimensions. A typical wave field evidently consists of a background of stable wave modes punctuated by the intermittent upthrusting of unstable rogue waves.},
author = {Osborne, A. R. and Onorato, M. and Serio, M.},
doi = {10.1016/S0375-9601(00)00575-2},
issn = {03759601},
journal = {Phys. Lett. A},
keywords = {Benjamin–Feir instability,Freak waves,Nonlinear Schr{\"{o}}dinger equation,Rogue waves,Steep wave events,Sudden steep events},
mendeley-tags = {Benjamin–Feir instability,Freak waves,Nonlinear Schr{\"{o}}dinger equation,Rogue waves,Steep wave events,Sudden steep events},
month = {oct},
number = {5-6},
pages = {386--393},
title = {{The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960100005752},
volume = {275},
year = {2000}
}
@article{Osher1984,
author = {Osher, S.},
journal = {SIAM J. Numer. Anal.},
pages = {217--235},
title = {{Riemann solvers, the entropy condition, and difference approximations}},
volume = {21(2)},
year = {1984}
}
@article{Osher1988,
author = {Osher, S. and Sethian, J.},
journal = {J. Comput. Phys.},
pages = {12--49},
title = {{Front propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations}},
volume = {78},
year = {1988}
}
@article{Osher1994,
author = {Osher, S. and Smereka, P.},
journal = {J. Comput. Phys.},
pages = {146--159},
title = {{A level set approach for computing solutions to incompressible two-phase flow}},
volume = {114},
year = {1994}
}
@article{Ott1970,
author = {Ott, E. and Sudan, R. N.},
journal = {Phys. Fluids},
pages = {1432--1434},
title = {{Damping of Solitary Waves}},
volume = {13},
year = {1970}
}
@article{Ovsyannikov1974,
author = {Ovsyannikov, L. V.},
journal = {Arch. Mech.},
pages = {407--422},
title = {{To the shallow water theory foundation}},
volume = {26},
year = {1974}
}
@article{Ovsyannikov1979,
author = {Ovsyannikov, L. V.},
doi = {10.1007/BF00910010},
issn = {0021-8944},
journal = {Journal of Applied Mechanics and Technical Physics},
number = {2},
pages = {127--135},
title = {{Two-layer "Shallow water" model}},
url = {http://www.springerlink.com/index/10.1007/BF00910010},
volume = {20},
year = {1979}
}
@article{Ozgokmen2006,
author = {{\"{O}}zg{\"{o}}kmen, T. and Fischer, P. F. and Duan, J. and Iliescu, T.},
journal = {J. Phys. Ocean.},
pages = {2006--2026},
title = {{Three-Dimensional Turbulent Bottom Density Currents from a High-Order Nonhydrostatic Spectral Element Method}},
volume = {34},
year = {2006}
}
@article{Ozgokmen2004,
author = {{\"{O}}zg{\"{o}}kmen, T. and Fischer, P. J. and Duan, J. and Iliescu, T.},
doi = {10.1029/2004GL020186},
journal = {Geophys. Res. Lett.},
pages = {L13212},
title = {{Entrainment in bottom gravity currents over complex topography from three-dimensional nonhydrostatic simulations}},
volume = {31},
year = {2004}
}
@article{Ozgokmen2007,
author = {{\"{O}}zg{\"{o}}kmen, T. and Iliescu, T. and Fischer, P. F. and Srinivasan, A. and Duan, J.},
journal = {Ocean Modelling},
pages = {106--140},
title = {{Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain}},
volume = {16},
year = {2007}
}
@techreport{Ozgun2006,
address = {USGS},
author = {{Ozgun Konca}, A.},
institution = {http://www.tectonics.caltech.edu/slip{\_}history/2006},
title = {{Preliminary Result 06/07/17 (Mw 7.9) , Southern Java Earthquake}},
url = {http://www.tectonics.caltech.edu/slip{\_}history/2006{\_}s{\_}java/s{\_}java.html},
year = {2006}
}
@article{Ozkan-Haller1997,
author = {Ozkan-Haller, H. T. and Kirby, J. T.},
journal = {Applied Ocean Research},
pages = {21--34},
title = {{A Fourier-Chebyshev collocation method for the shallow water equations including shoreline runup}},
volume = {19},
year = {1997}
}
@article{Pagani1970,
author = {Pagani, C. D.},
journal = {Boll. Un. Mat. Ital.},
number = {6},
pages = {961--986},
title = {{Studio di alcune questioni concernenti l'equazione generalizzata di Fokker-Planck}},
volume = {3},
year = {1970}
}
@article{Pantin1979,
abstract = {The present paper describes a new mathematical model of turbidity flow, this model having been constructed so as to investigate the interaction between the velocity and effective density of the flow. The differential equations involved represent a version of the so-called “slab model” and involve many simplifying assumptions; however, these equations are non-linear, and have therefore been investigated by phase-plane analysis, a very useful technique which provides graphical and numerical solutions of suitable equations to any desired degree of accuracy. Following a summary of earlier models of turbidity flow, Bagnold's (1963) criterion for autosuspension is discussed, and a revised version proposed. The new model is then developed, initially in a simplified form, in order to illustrate the mathematical properties of the equations, the (four) possible types of turbidity flow, and their relationship to the revised criterion for autosuspension. A physical version of the model, with plausible values for the controlling parameters, is then described. The model as a whole provides a satisfactory qualitative explanation of the essential difference between relatively weak, secular turbidity flow, and the episodes of strong turbidity flow which are evidently responsible for the deposition of turbidites. Flows of the latter variety can be explained as phases of autosuspension. The physical version of the model indicates that the current velocities, effective densities, and bottom gradients necessary for autosuspension are not wildly improbable, either on the shelf or the slope, and autosuspension may indeed occur in appropriate places.},
author = {Pantin, H. M.},
doi = {10.1016/0025-3227(79)90057-4},
issn = {00253227},
journal = {Marine Geology},
month = {apr},
number = {1-2},
pages = {59--99},
title = {{Interaction between velocity and effective density in turbidity flow: Phase-plane analysis, with criteria for autosuspension}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0025322779900574},
volume = {31},
year = {1979}
}
@article{Papageorgiou2004,
author = {Papageorgiou, D. T. and Vanden-Broeck, J.-M.},
doi = {10.1017/S0022112004008997},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {jun},
pages = {71--88},
title = {{Large-amplitude capillary waves in electrified fluid sheets}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112004008997},
volume = {508},
year = {2004}
}
@article{Paramonov1984,
abstract = {A number of frequency detunings, in particular those caused by vibrational anharmonicity, can be compensated under coherent excitation of molecules by picosecond infrared laser pulses. Multi-photon excitation by a sequence of picosecond pulses is much more effective than nanosecond pulse excitation with the same energy fluence.},
author = {Paramonov, G. K. and Savva, V. A.},
doi = {10.1016/S0009-2614(84)80242-0},
issn = {00092614},
journal = {Chem. Phys. Lett.},
month = {jun},
number = {4-5},
pages = {394--397},
title = {{Effective overcoming of frequency detuning and resonance effects under molecular vibrational excitation by picosecond infrared laser pulses}},
volume = {107},
year = {1984}
}
@article{Parau2005,
author = {Parau, E. I. and Vanden-Broeck, J.-M. and Cooker, M. J.},
doi = {10.1017/S0022112005005136},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {jul},
pages = {99--105},
title = {{Nonlinear three-dimensional gravity-capillary solitary waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112005005136},
volume = {536},
year = {2005}
}
@article{Parau2005a,
abstract = {Numerical solutions for three-dimensional gravity capillary waves in water of finite depth are presented. The full Euler equations are used and the waves are calculated by a boundary integral equation method. The findings generalize previous results of Parau, Vanden-Broeck, and Cooker [J. Fluid Mech. 536, 99 (2005)] in water of infinite depth. It is found that there are both lumps that bifurcate from linear sinusoidal waves and other fully localized solitary waves which exist for large values of the Bond number. These findings are consistent with rigorous analytical results and asymptotic calculations. The relation between the solitary waves and free surface flows generated by moving disturbances is also explored.},
author = {Parau, E. I. and Vanden-Broeck, J.-M. and Cooker, M. J.},
doi = {10.1063/1.2140020},
issn = {10706631},
journal = {Phys. Fluids},
pages = {122101},
title = {{Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems}},
volume = {17},
year = {2005}
}
@article{Parau2002,
author = {Parau, E. and Vanden-Broeck, J.-M.},
doi = {10.1016/S0997-7546(02)01212-8},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
month = {nov},
number = {6},
pages = {643--656},
title = {{Nonlinear two- and three-dimensional free surface flows due to moving disturbances}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754602012128},
volume = {21},
year = {2002}
}
@article{Parker1982,
abstract = {The basic impediment to a clear understanding of eroding and depositing turbidity currents has been the lack of a proper formulation of bed sediment entrainment. This problem is addressed herein: a detailed analysis indicates that the Bagnold criterion is necessary but insufficient for self-sustaining turbidity currents. The analysis reveals two possible equilibrium states, a relatively low-velocity ignitive state, and a high-velocity, dense catastrophic state. A stability analysis indicates that the ignitive state is unstable; flows below it invariably die out, and flows above it “ignite”, i.e. accelerate and entrain sediment to the catastrophic state, which is stable. The ignitive state thus defines the criterion for a self-sustaining turbidity current. Estimates of the catastrophic state suggest that it is highly erosive and competent to scour out submarine canyons.},
author = {Parker, G.},
doi = {10.1016/0025-3227(82)90086-X},
issn = {00253227},
journal = {Marine Geology},
month = {apr},
number = {3-4},
pages = {307--327},
title = {{Conditions for the ignition of catastrophically erosive turbidity currents}},
url = {http://linkinghub.elsevier.com/retrieve/pii/002532278290086X},
volume = {46},
year = {1982}
}
@article{Parker1986,
author = {Parker, G. and Fukushima, Y. and Pantin, H. M.},
journal = {J. Fluid Mech.},
pages = {145--181},
title = {{Self-accelerating turbidity currents}},
volume = {171},
year = {1986}
}
@article{Parkes1987,
abstract = {The modulation of a one-dimensional weakly non-linear purely dispersive quasi-monochromatic wave (the carrier) is usually governed by the non-linear Schrodinger (NS) equation. The critical wavenumber for which the carrier is marginally modulationally unstable is determined by the condition that the product of the coefficients of the non-linear and dispersive terms in the NS equation is zero. However, near this marginal state the assumptions that lead to the NS equation are invalid and a modified form of the NS equation that involves higher-order non-linearities is appropriate. This modified NS equation is here derived formally for a general system involving a single dependent variable and a revised form of the instability criterion is obtained. The results are illustrated by considering a particular system described by a generalised Korteweg-de Vries equation.},
author = {Parkes, E. J.},
doi = {10.1088/0305-4470/20/8/021},
issn = {0305-4470},
journal = {J. Phys. A: Math. Gen.},
month = {jun},
number = {8},
pages = {2025--2036},
title = {{The modulation of weakly non-linear dispersive waves near the marginal state of instability}},
url = {http://stacks.iop.org/0305-4470/20/i=8/a=021?key=crossref.e0b5f47ef5fd15b17d46873bc56e393d},
volume = {20},
year = {1987}
}
@phdthesis{Pascal2002,
author = {Pascal, F.},
school = {Universit{\'{e}} de Paris-Sud},
title = {{Sur des m{\'{e}}thodes d'approximation effectives et d'analyse num{\'{e}}rique pour les {\'{e}}quations de la m{\'{e}}canique de fluides}},
type = {Habilitation {\`{a}} diriger des recherches},
year = {2002}
}
@article{Patankar2001,
author = {Patankar, N. A. and Joseph, D. D.},
doi = {10.1016/S0301-9322(01)00025-8},
issn = {03019322},
journal = {Int. J. Multiphase Flow},
month = {oct},
number = {10},
pages = {1685--1706},
title = {{Lagrangian numerical simulation of particulate flows}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0301932201000258},
volume = {27},
year = {2001}
}
@article{Patankar2001a,
abstract = {In this paper we present an Eulerian-Lagrangian numerical simulation (LNS) scheme for particulate flows. The overall algorithm in the present approach is a variation of the scheme presented earlier. In this numerical scheme we solve the fluid phase continuity and momentum equations on an Eulerian grid. The particle motion is governed by Newton's law thus following the Lagrangian approach. Momentum exchange from the particle to fluid is modeled in the fluid phase momentum equation. Forces acting on the particles include drag from the fluid, body force and the interparticle force that prevents the particle volume fraction from exceeding the close-packing limit. There is freedom to use different models for these forces and to introduce other forces. In this paper we have used two types of interparticle forces. The effect of viscous stresses are included in the fluid phase equations. The volume fraction of the particles appear in the fluid phase continuity and momentum equations. The fluid and particle momentum equations are coupled in the solution procedure unlike an earlier approach. A finite volume method is used to solve these equations on an Eulerian grid. Particle positions are updated explicitly. This numerical scheme can handle a range of particle loadings and particle types. We solve the fluid phase continuity and momentum equations using a Chorin-type fractional-step method. The numerical scheme is verified by comparing results with test cases and experiments.},
author = {Patankar, N. A. and Joseph, D. D.},
doi = {10.1016/S0301-9322(01)00021-0},
issn = {03019322},
journal = {International Journal of Multiphase Flow},
month = {oct},
number = {10},
pages = {1659--1684},
title = {{Modeling and numerical simulation of particulate flows by the Eulerian-Lagrangian approach}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0301932201000210},
volume = {27},
year = {2001}
}
@article{Patera2006,
abstract = {The stability of pipe flow to axisymmetric disturbances is studied by direct numerical simulation of the incompressible Navier-Stokes equations. There is no evidence of finite-amplitude equilibria at any of the wavenumber/Reynolds number combinations investigated, with all perturbations decaying on a time scale much shorter than the diffusive (viscous) time scale. In particular, decay is obtained where amplitude-expansion perturbation techniques predict equilibria, indicating that these methods are not valid away from the neutral curve of linear stability theory.},
author = {Patera, A. T. and Orszag, S. A.},
doi = {10.1017/S0022112081000529},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {467--474},
title = {{Finite-amplitude stability of axisymmetric pipe flow}},
volume = {112},
year = {1981}
}
@article{Patrick1992,
abstract = {Stability of relative equilibria for Hamiltonian systems is generally equated with Liapunov stability of the corresponding fixed point of the flow on the reduced phase space. Under mild assumptions, a sharp interpretation of this stability is given in terms of concepts on the unreduced space.},
author = {Patrick, G. W.},
doi = {10.1016/0393-0440(92)90015-S},
issn = {03930440},
journal = {Journal of Geometry and Physics},
keywords = {Hamiltonian systems,nonlinear stability},
month = {may},
number = {2},
pages = {111--119},
title = {{Relative equilibria in Hamiltonian systems: The dynamic interpretation of nonlinear stability on a reduced phase space}},
url = {http://linkinghub.elsevier.com/retrieve/pii/039304409290015S},
volume = {9},
year = {1992}
}
@article{Pava2006,
author = {Pava, J. A. and Bona, J. L. and Scialom, M.},
journal = {Advances in Differential Equations},
number = {12},
pages = {1321--1374},
title = {{Stability of cnoidal waves}},
volume = {11},
year = {2006}
}
@article{Pavlov2012,
author = {Pavlov, M. V. and Taranov, V. B. and El, G. A.},
doi = {10.1007/s11232-012-0064-z},
issn = {0040-5779},
journal = {Theor. Math. Phys.},
month = {may},
number = {2},
pages = {675--682},
title = {{Generalized hydrodynamic reductions of the kinetic equation for a soliton gas}},
url = {http://link.springer.com/10.1007/s11232-012-0064-z},
volume = {171},
year = {2012}
}
@article{Pearce-10,
author = {Pearce, J. D. and Esler, J. G.},
journal = {Journal of Computational Physics},
number = {20},
pages = {7594--7608},
title = {{A pseudo-spectral algorithm and test cases for the numerical solution of the two-dimensional rotating Green-Naghdi shallow water equations}},
volume = {229},
year = {2010}
}
@article{Pearson1905,
author = {Pearson, K.},
journal = {Nature},
pages = {294},
title = {{The Problem of the Random Walk}},
volume = {72},
year = {1905}
}
@article{Pedersen1983,
abstract = {A numerical model based on a Lagrangian description has been developed for studying run-up of long water waves governed by a set of Boussinesq equations. The performance of the numerical scheme has been tested by comparing with analytical solutions and experimental data. Simulations of the run-up of solitary waves on relatively steep planes (inclination angle > 20°) show surface displacements and run-up heights in good agreement with experiments. For waves with relatively large amplitude the simulations reveal the development of a breaking bore during the backwash. Results for run-up heights in converging and diverging channels are also presented.},
author = {Pedersen, G. and Gjevik, B.},
doi = {10.1017/S0022112083003080},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {283--299},
title = {{Run-up of solitary waves}},
volume = {135},
year = {1983}
}
@book{Pedlosky1990,
address = {New York},
author = {Pedlosky, J.},
isbn = {978-0387963877},
pages = {710},
publisher = {Springer},
title = {{Geophysical Fluid Dynamics}},
year = {1992}
}
@article{Pego1994,
author = {Pego, R. L. and Weinstein, M. I.},
doi = {10.1007/BF02101705},
issn = {0010-3616},
journal = {Communications in Mathematical Physics},
month = {aug},
number = {2},
pages = {305--349},
title = {{Asymptotic stability of solitary waves}},
url = {http://link.springer.com/10.1007/BF02101705},
volume = {164},
year = {1994}
}
@article{Pego1997,
author = {Pego, R. L. and Weinstein, M. I.},
journal = {Stud. Appl. Maths.},
pages = {311--375},
title = {{Convective linear stability of solitary waves for Boussinesq equations}},
volume = {99},
year = {1997}
}
@article{Pelinovsky2001a,
abstract = {Properties of the linear eigenvalue problem associated to a hyperbolic non-linear Schr{\"{o}}dinger equation are reviewed. The instability band of adeep-watersoliton is shown to merge to the continuous spectrum of a linear Schr{\"{o}}dinger operator. A new analytical approximation of the instability growth near athreshold is derived by means of a bifurcation theory of weakly localized wave functions.},
author = {Pelinovsky, D. E.},
doi = {10.1016/S0378-4754(00)00287-1},
issn = {03784754},
journal = {Math. Comp. Simul.},
keywords = {Deep-watersoliton,Non-linear Schr{\"{o}}dinger equation in two dimensions,Threshold,Transverseinstability},
month = {mar},
number = {4-6},
pages = {585--594},
title = {{A mysterious threshold for transverse instability of deep-water solitons}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378475400002871},
volume = {55},
year = {2001}
}
@article{Pelinovsky2013a,
abstract = {The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation. The spectrum of spatial amplitudes at the breaking time {\$}t = t{\_}b{\$} has an asymptotic decay of {\$}k{\^{}}{\{}-4/3{\}}{\$}, with corresponding energy spectrum decaying as {\$}k{\^{}}{\{}-8/3{\}}{\$}. This spectrum is formed by the singularity of the form {\$}(x-x{\_}b){\^{}}{\{}1/3{\}}{\$} in the wave shape at the breaking time. This result remains valid for arbitrary nonlinear wave speed. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg-de Vries equations.},
author = {Pelinovsky, D. E. and Pelinovsky, E. N. and Kartashova, E. and Talipova, T. and Giniyatullin, A.},
doi = {10.1134/S0021364013170116},
journal = {JETP Lett.},
number = {4},
pages = {237--241},
title = {{Universal power law for the energy spectrum of breaking Riemann waves}},
url = {http://arxiv.org/abs/1307.0248},
volume = {98},
year = {2013}
}
@article{Pelinovsky2004,
author = {Pelinovsky, D. E. and Stepanyants, Y. A.},
journal = {SIAM J. Num. Anal.},
pages = {1110--1127},
title = {{Convergence of Petviashvili's iteration method for numerical approximation of stationary solutions of nonlinear wave equations}},
volume = {42},
year = {2004}
}
@article{Pelinovsky1992,
author = {Pelinovsky, E. N. and Mazova, R Kh.},
journal = {Nat. Hazards},
number = {3},
pages = {227--249},
publisher = {Springer Netherlands},
title = {{Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles}},
volume = {6},
year = {1992}
}
@article{Pelinovsky2013,
author = {Pelinovsky, E. N. and Shurgalina, E. G. and Sergeeva, A. and Talipova, T. and El, G. A. and Grimshaw, R. H. J.},
doi = {10.1016/j.physleta.2012.11.037},
issn = {03759601},
journal = {Phys. Lett. A},
month = {jan},
number = {3-4},
pages = {272--275},
title = {{Two-soliton interaction as an elementary act of soliton turbulence in integrable systems}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960112012169},
volume = {377},
year = {2013}
}
@article{Pelinovsky2003,
abstract = {Nearly 40 years have passed since V. I. Talanov discovered the nonlinear parabolic equation which played an important role in the nonlinear optics. It was very quickly understood that this equation could also be adapted for nonstationary wave packets of different physical nature and of any dimension. Under the later name of the nonlinear (cubic) Schr{\"{o}}dinger equation, it became a fundamental equation in the theory of weakly nonlinear wave packets in media with strong dispersion. The article is devoted to only one application of the nonlinear Schr{\"{o}}dinger equation in the theory of the so-called freak waves on the sea surface. In the last five years a great boom has occurred in the research of extreme waves on the water, for which the nonlinear parabolic equation played an important role in the understanding of physical mechanisms of the freak-wave phenomenon. More accurate, preferably numerical, models of waves on a water with more comprehensive account of the nonlinearity and dispersion come on the spot today, and many results of weakly nonlinear models are already corrected quantitatively. Nevertheless, sophisticated models do not bring new physical concepts. Hence, their description on the basis of the nonlinear parabolic equation (nonlinear Schr{\"{o}}dinger equation), performed in this paper, seems very attractive in view of their possible applications in the wave-motion physics.},
author = {Pelinovsky, E. N. and Slunyaev, A. V. and Talipova, T. and Kharif, C.},
doi = {10.1023/B:RAQE.0000019863.50302.35},
issn = {0033-8443},
journal = {Radiophysics and Quantum Electronics},
month = {jul},
number = {7},
pages = {451--463},
title = {{Nonlinear Parabolic Equation and Extreme Waves on the Sea Surface}},
url = {http://www.springerlink.com/openurl.asp?id=doi:10.1023/B:RAQE.0000019863.50302.35},
volume = {46},
year = {2003}
}
@article{Pelinovsky1999,
author = {Pelinovsky, E. N. and Troshina, E. and Golinko, V. and Osipenko, N. and Petrukhin, N.},
journal = {Phys. Chem. Earth. (B)},
number = {5},
pages = {431--436},
title = {{Runup of tsunami waves on a vertical wall in a basin of complex topography}},
volume = {24},
year = {1999}
}
@article{Pelinovsky2002,
abstract = {The problem of tsunami-risk for the French coast of the Mediterraneanis discussed. Historical data of tsunami manifestation on the French coast are described and analysed.Numerical simulation of potential tsunamis in the Ligurian Sea is done and the tsunami wave heightdistribution along the French coast is calculated. For the earthquake magnitude 6.8 (typical value forMediterranean) the tsunami phenomenon has a very local character. It is shown that the tsunami tide-gaugerecords in the vicinity of Cannes–Imperia present irregularoscillations with characteristic periodof 20–30 min and total duration of 10–20h.Tsunami propagating from the Ligurian sea to the west coastof France have significantly lesser amplitudes and they are more low-frequency (period of 40–50min).The effect of far tsunamis generated in the southern Italy and Algerian coast is studied also, thedistribution of the amplitudes along the French coast for far tsunamis is more uniform.},
author = {Pelinovsky, E. and Kharif, C. and Riabov, I. and Francius, M.},
doi = {10.1023/A:1013721313222},
journal = {Nat. Hazards},
number = {2},
pages = {135--159},
title = {{Modelling of Tsunami Propagation in the Vicinity of the French Coast of the Mediterranean}},
volume = {25},
year = {2002}
}
@article{Pelinovsky2008,
author = {Pelinovsky, E. and Kharif, C. and Talipova, T.},
doi = {10.1016/j.euromechflu.2007.08.003},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
keywords = {nonlinear shallow water equations,water waves,wave statistics},
number = {4},
pages = {409--418},
title = {{Large-amplitude long wave interaction with a vertical wall}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754607000696},
volume = {27},
year = {2008}
}
@article{Pelinovsky1996,
author = {Pelinovsky, E. and Poplavsky, A.},
issn = {00791946},
journal = {Physics and Chemistry of the Earth},
number = {12},
pages = {13--17},
title = {{Simplified model of tsunami generation by submarine landslides}},
url = {http://www.sciencedirect.com/science/article/B6V79-3VWKNBP-3/2/1637ac2e26e7a43b347e5b816e885afb},
volume = {21},
year = {1996}
}
@article{Pelinovsky2006,
abstract = {The evolution of the initially random wave field with a Gaussian spectrum shape is studied numerically within the Korteweg-de Vries (KdV) equation. The properties of the KdV random wave field are analyzed: transition to a steady state, equilibrium spectra, statistical moments of a random wave field, and the distribution functions of the wave amplitudes. Numerical simulations are performed for different Ursell parameters and spectrum width. It is shown that the wave field relaxes to the stationary state (in statistical sense) with the almost uniform energy distribution in low frequency range (Rayleigh-Jeans spectrum). The wave field statistics differs from the Gaussian one. The growing of the positive skewness and non-monotonic behavior of the kurtosis with increase of the Ursell parameter are obtained. The probability of a large amplitude wave formation differs from the Rayleigh distribution.},
author = {Pelinovsky, E. and {Sergeeva (Kokorina)}, A.},
doi = {10.1016/j.euromechflu.2005.11.001},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
keywords = {Distribution function,KdV equation,Random waves,Spectrum},
month = {jul},
number = {4},
pages = {425--434},
title = {{Numerical modeling of the KdV random wave field}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754605001007},
volume = {25},
year = {2006}
}
@article{Pelinovsky2001,
abstract = {Abstract. The problem of tsunami wave generation by variable meteo-conditions is discussed. The simpliﬁed linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation is developed to describe the resonant mechanism of the tsunami wave generation by the atmospheric disturbances moving with near-critical speed (long wave speed). Some analytical solutions of the nonlinear dispersive model are obtained. They illustrate the different regimes of soliton generation and the focusing of frequency modulated wave packets.},
author = {Pelinovsky, E. and Talipova, T. and Kurkin, A. and Kharif, C.},
doi = {10.5194/nhess-1-243-2001},
file = {:home/dds/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Pelinovsky et al. - 2001 - Nonlinear mechanism of tsunami wave generation by atmospheric disturbances(2).pdf:pdf},
issn = {16849981},
journal = {Natural Hazards And Earth System Science},
number = {4},
pages = {243--250},
title = {{Nonlinear mechanism of tsunami wave generation by atmospheric disturbances}},
url = {http://www.nat-hazards-earth-syst-sci.net/1/243/2001/},
volume = {1},
year = {2001}
}
@article{Pelinovsky2001,
abstract = {Abstract. The problem of tsunami wave generation by variable meteo-conditions is discussed. The simpliﬁed linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation is developed to describe the resonant mechanism of the tsunami wave generation by the atmospheric disturbances moving with near-critical speed (long wave speed). Some analytical solutions of the nonlinear dispersive model are obtained. They illustrate the different regimes of soliton generation and the focusing of frequency modulated wave packets.},
author = {Pelinovsky, E. and Talipova, T. and Kurkin, A. and Kharif, C.},
doi = {10.5194/nhess-1-243-2001},
file = {:home/dds/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Pelinovsky et al. - 2001 - Nonlinear mechanism of tsunami wave generation by atmospheric disturbances(2).pdf:pdf},
issn = {16849981},
journal = {Natural Hazards And Earth System Science},
number = {4},
pages = {243--250},
title = {{Nonlinear mechanism of tsunami wave generation by atmospheric disturbances}},
url = {http://www.nat-hazards-earth-syst-sci.net/1/243/2001/},
volume = {1},
year = {2001}
}
@article{PD,
author = {Pelloni, B. and Dougalis, V. A.},
journal = {Mat. Comp. Simul.},
pages = {595--606},
title = {{Numerical modelling of two-way propagation of nonlinear dispersive waves}},
volume = {55},
year = {2001}
}
@article{Peregrine1967,
author = {Peregrine, D. H.},
journal = {J. Fluid Mech.},
pages = {815--827},
title = {{Long waves on a beach}},
volume = {27},
year = {1967}
}
@article{P1967,
author = {Peregrine, D. H.},
journal = {J. Fluid Mech.},
pages = {815--827},
title = {{Long waves on beaches}},
volume = {27},
year = {1967}
}
@article{Peregrine1983,
author = {Peregrine, D. H.},
journal = {Journal of the Australian Mathematical Society Series B},
pages = {16--43},
title = {{Water waves, nonlinear Schr{\"{o}}dinger equations and their solutions}},
volume = {25},
year = {1983}
}
@inbook{Peregrine1972,
author = {Peregrine, D. H.},
chapter = {Equations},
pages = {95--121},
publisher = {Academic Press, New York},
title = {{Waves on Beaches and Resulting Sediment Transport}},
year = {1972}
}
@article{Peregrine2003,
author = {Peregrine, D. H.},
journal = {Annu. Rev. Fluid Mech.},
pages = {23--43},
title = {{Water-Wave Impact on Walls}},
volume = {35},
year = {2003}
}
@article{Peregrine1983a,
author = {Peregrine, D. H.},
journal = {J. Austral. Math. Soc. Ser. B},
number = {1},
pages = {16--43},
title = {{Water waves, nonlinear Schr{\"{o}}dinger equations and their solutions}},
volume = {25},
year = {1983}
}
@article{Peregrine1966,
abstract = {If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0.28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.},
author = {Peregrine, D. H.},
doi = {10.1017/S0022112066001678},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
number = {02},
pages = {321--330},
title = {{Calculations of the development of an undular bore}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112066001678},
volume = {25},
year = {1966}
}
@inproceedings{Bredmose3,
author = {Peregrine, D. H. and Bredmose, H. and Bullock, G. N. and Hunt, A. and Obhrai, C.},
booktitle = {Proc. 30th Int. Conf. Coast. Engng., San Diego (ed. J. M. Smith), vol. 5, ASCE},
pages = {4494--4506},
title = {{Water wave impact on walls and the role of air}},
year = {2006}
}
@inproceedings{Bredmose2,
author = {Peregrine, D. H. and Bredmose, H. and Bullock, G. N. and Obhrai, C. and Muller, G. and Wolters, G.},
booktitle = {Proceedings of the 29th International Conference on Coastal Engineering, Lisbon 2004, vol. 4, pp. 4005-4017. ASCE},
title = {{Water wave impact on walls and the role of air}},
year = {2004}
}
@inproceedings{Peregrine2004,
author = {Peregrine, D. H. and Obhrai, C. and Bullock, G. N. and Muller, G. and Wolters, G. and Bredmose, H.},
booktitle = {ICCE 2004},
title = {{Violent water wave impacts and the role of air}},
year = {2004}
}
@article{Peregrine1996,
author = {Peregrine, D. H. and Thais, L.},
journal = {J. Fluid Mech.},
pages = {377--397},
title = {{The effect of entrained air in violent water impacts}},
volume = {325},
year = {1996}
}
@article{Perla-Menzala2002,
author = {Perla-Menzala, G. and Vasconcellos, C. F. and Zuazua, E.},
journal = {Quart. Appl. Math.},
pages = {111--129},
title = {{Stabilization of the Korteweg-de Vries equation with localized damping}},
volume = {60},
year = {2002}
}
@article{Perthame2001,
abstract = {The aim of this paper is to present a numerical scheme to compute Saint-Venant equations with a source term, due to the bottom topography, in a one-dimensional framework, which satisfies the following theoretical properties: it preserves the steady state of still water, satisfies an entropy inequality, preserves the non-negativity of the height of water and remains stable with a discontinuous bottom. This is achieved by means of a kinetic approach to the system, which is the departing point of the method developed here. In this context, we use a natural description of the microscopic behavior of the system to define numerical fluxes at the interfaces of an unstructured mesh. We also use the concept of cell-centered conservative quantities (as usual in the finite volume method) and upwind interfacial sources as advocated by several authors. We show, analytically and also by means of numerical results, that the above properties are satisfied.},
author = {Perthame, B. and Simeoni, C.},
doi = {10.1007/s10092-001-8181-3},
issn = {0008-0624},
journal = {Calcolo},
month = {dec},
number = {4},
pages = {201--231},
title = {{A kinetic scheme for the Saint-Venant system with a source term}},
url = {http://link.springer.com/10.1007/s10092-001-8181-3},
volume = {38},
year = {2001}
}
@article{Peterson2003,
abstract = {Interaction of two long-crested shallow water waves is analysed in the framework of the two-soliton solution of the Kadomtsev-Petviashvili equation. The wave system is decomposed into the incoming waves and the interaction soliton that represents the particularly high wave hump in the crossing area of the waves. Shown is that extreme surface elevations up to four times exceeding the amplitude of the incoming waves typically cover a very small area but in the near-resonance case they may have considerable extension. An application of the proposed mechanism to fast ferries wash is discussed.},
author = {Peterson, P. and Soomere, T. and Engelbrecht, J. and van Groesen, E.},
journal = {Nonlin. Processes Geophys.},
pages = {503--510},
title = {{Soliton interaction as a possible model for extreme waves in shallow water}},
volume = {10},
year = {2003}
}
@article{Peterson1991,
author = {Peterson, T.},
journal = {SIAM J. Numer. Anal.},
pages = {133--140},
title = {{A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation}},
volume = {28(1)},
year = {1991}
}
@book{petr,
author = {Petrashen', G. I. and Latyshev, K. P.},
isbn = {0821818953},
publisher = {American Mathematical Society},
title = {{Asymptotic Methods and Stochastic Models in Problems of Wave Propagation}},
year = {1971}
}
@article{Petrov1964,
author = {Petrov, A. A.},
journal = {Prikl. Math. Mekh.},
pages = {917--922},
title = {{Variational statement of the problem of liquid motion in a container of finite dimensions}},
volume = {28(4)},
year = {1964}
}
@book{Petrovsky1984,
address = {Moscow},
author = {Petrovsky, I. G.},
editor = {Myshkis, A. D. and Oleinik, O. A.},
pages = {296},
publisher = {Moscow University Press},
title = {{Lectures on the theory of ordinary differential equations}},
year = {1984}
}
@article{Petviashvili1976,
author = {Petviashvili, V. I.},
journal = {Sov. J. Plasma Phys.},
pages = {469--472},
title = {{Equation of an extraordinary soliton}},
volume = {2(3)},
year = {1976}
}
@incollection{Philibert2005,
address = {Leipzig},
author = {Philibert, J.},
booktitle = {Diffusion Fundamentals},
editor = {K{\"{a}}rger, J. and Grinberg, F. and Heitjans, P.},
pages = {8--17},
publisher = {Leipzig Universt{\"{a}}tsverlag},
title = {{One and a half century of diffusion: Fick, Einstein, before and beyond}},
year = {2005}
}
@article{Phillips1960,
author = {Phillips, O. M.},
doi = {10.1017/S0022112060001043},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
pages = {193--217},
title = {{On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112060001043},
volume = {9},
year = {1960}
}
@article{Piatanesi2001,
author = {Piatanesi, A. and Tinti, S. and Pagnoni, G.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {187--194},
title = {{Tsunami waveform inversion by numerical finite-elements Green's functions}},
volume = {1},
year = {2001}
}
@article{Picozzi2014,
author = {Picozzi, A. and Garnier, J. and Hansson, T. and Suret, P. and Randoux, S. and Millot, G. and Christodoulides, D. N.},
doi = {10.1016/j.physrep.2014.03.002},
issn = {03701573},
journal = {Phys. Reports},
month = {sep},
number = {1},
pages = {1--132},
title = {{Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0370157314001203},
volume = {542},
year = {2014}
}
@article{Pires2003,
author = {Pires, C. and Miranda, P. M. A.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {341--351},
title = {{Sensitivity of the adjoint method in the inversion of tsunami source parameters}},
volume = {3},
year = {2003}
}
@article{Plafker1965,
abstract = {Alaska's Good Friday earthquake of 27 March 1964 was accompanied by vertical tectonic deformation over an area of 170,000 to 200,000 square kilometers in south-central Alaska. The deformation included two major northeast-trending zones of uplift and subsidence situated between the Aleutian Trench and the Aleutian Volcanic Arc; together they are 700 to 800 kilometers long and from 150 to 250 kilometers wide. The seaward zone is one in which uplift of as much as 10 meters on land and 15 meters on the sea floor has occurred as a result of both crustal warping and local faulting. Submarine uplift within this zone generated a train of seismic sea waves with half-wave amplitudes of more than 7 meters along the coast near the source. The adjacent zone to the northwest is one of subsidence that averages about 1 meter and attains a measured maximum of 2.3 meters. A second zone of slight uplift may exist along all or part of the Aleutian and Alaska ranges northwest of the zone of subsidence.},
author = {Plafker, G.},
doi = {10.1126/science.148.3678.1675},
issn = {0036-8075},
journal = {Science},
month = {jun},
number = {3678},
pages = {1675--1687},
pmid = {17819412},
title = {{Tectonic Deformation Associated with the 1964 Alaska Earthquake: The earthquake of 27 March 1964 resulted in observable crustal deformation of unprecedented areal extent.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/17819412},
volume = {148},
year = {1965}
}
@article{Plotnikov2001,
author = {Plotnikov, P. I. and Toland, J. F.},
journal = {Arch. Rat. Mech. Anal.},
pages = {1--83},
title = {{Nash-Moser theory for standing water waves}},
volume = {159(1)},
year = {2001}
}
@article{podyapolsk1,
author = {Podyapolsky, G. S.},
journal = {Izvestiya, Earth Physics, Akademia Nauk SSSR},
pages = {4--12},
title = {{The generation of linear gravitational waves in the ocean by seismic sources in the crust}},
volume = {1},
year = {1968}
}
@phdthesis{Pohle1950,
author = {Pohle, F. V.},
school = {New York University, USA},
title = {{The Lagragian equations of hydrodynamics: solutions which are analytic functions of time}},
year = {1950}
}
@article{Poisson1818,
author = {Poisson, S. D.},
journal = {M{\'{e}}m. Acad. R. Sci. Inst. France},
pages = {70--186},
title = {{M{\'{e}}moire sur la th{\'{e}}orie des ondes}},
volume = {1816(1)},
year = {1818}
}
@article{Pomeau2008,
abstract = {In a wide range of conditions, ocean waves break. This can be seen as the manifestation of a singularity in the dynamics of the fluid surface, moving under the effect of the fluid motion underneath. We show that, at the onset of breaking, the wave crest expands in the spanwise direction as the square root of time. This is first derived from a theoretical analysis and then compared with experimental findings. The agreement is excellent.},
author = {Pomeau, Y. and Jamin, T. and {Le Bars}, M. and {Le Gal}, P. and Audoly, B.},
doi = {10.1098/rspa.2008.0024},
issn = {1364-5021},
journal = {Proc. R. Soc. A},
month = {jul},
number = {2095},
pages = {1851--1866},
title = {{Law of spreading of the crest of a breaking wave}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2008.0024},
volume = {464},
year = {2008}
}
@inproceedings{PoncetCanada2010,
author = {Poncet, R. and Campbell, C. and Dias, F. and Locat, J. and Mosher, D.},
booktitle = {Submarine Mass Movements and Their Consequences},
editor = {et al. Mosher, D C},
pages = {755--764},
publisher = {Springer Verlag},
title = {{A study of the tsunami effects of two landslides in the St. Lawrence estuary}},
year = {2010}
}
@inproceedings{Poncet2008,
author = {Poncet, R. and Dias, F.},
booktitle = {XXII ICTAM, 25 - 29 August 2008, Adelaide, Australia},
title = {{On the inclusion of arbitrary topography and bathymetry in the nonlinear shallow-water equations}},
year = {2008}
}
@inproceedings{PoncetVasnier,
author = {Poncet, R. and Vasnier, J. C.},
title = {{Sustainable manycore parallelization of an unstructured hydrodynamic code using directive-based languages OpenMP and HMPP}},
year = {2011}
}
@book{Pontryagin1987,
abstract = {The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems. This one mathematical method can be applied in a variety of situations, including linear equations with variable coefficients, optimal processes with delay, and the jump condition. As with the three preceding volumes, all the material contained with the 42 sections of this volume is made easily accessible by way of numerous examples, both concrete and abstract in nature.},
author = {Pontryagin, L. S.},
edition = {English ed},
isbn = {978-2881240775},
pages = {360},
publisher = {CRC Press},
title = {{Mathematical Theory of Optimal Processes}},
year = {1987}
}
@book{Pope2000,
abstract = {This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.},
address = {Cambridge},
author = {Pope, S. B.},
booktitle = {Journal of Turbulence},
doi = {10.1088/1468-5248/1/1/702},
isbn = {0521598869},
issn = {1468-5248},
month = {jan},
pages = {771},
publisher = {Cambridge University Press},
title = {{Turbulent Flows}},
url = {http://www.tandfonline.com/doi/abs/10.1088/1468-5248/1/1/702},
volume = {1},
year = {2000}
}
@inproceedings{Popinet2008,
author = {Popinet, S.},
booktitle = {XXII ICTAM, 25 - 29 August 2008, Adelaide, Australia},
title = {{Adaptive direct numerical simulation of steep water waves}},
year = {2008}
}
@article{Popinet2003,
author = {Popinet, S.},
journal = {J. Comp. Phys.},
pages = {572--600},
title = {{Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries}},
volume = {190},
year = {2003}
}
@article{Popinet1999,
author = {Popinet, S. and Zaleski, S.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {775--793},
title = {{A Front-Tracking Algorithm for Accurate Representation of Surface Tension}},
volume = {30},
year = {1999}
}
@article{Porubov2006,
abstract = {Possible propagating longitudinal strain solitary waves in a plate are shown to be seriously altered when physical cubic nonlinearity is taken into account in the modeling. This also affects an amplification of the wave due to the transverse instability of plane-localized waves and due to the plane-wave interaction.},
author = {Porubov, A. V. and Maugin, G. A.},
doi = {10.1103/PhysRevE.74.046617},
journal = {Phys. Rev. E},
pages = {46617},
title = {{Propagation of localized longitudinal strain waves in a plate in the presence of cubic nonlinearity}},
url = {http://link.aps.org/doi/10.1103/PhysRevE.74.046617},
volume = {74},
year = {2006}
}
@book{Pozrikidis1992,
abstract = {This book presents a coherent introduction to boundary integral, boundary element and singularity methods for steady and unsteady flow at zero Reynolds number. The focus of the discussion is not only on the theoretical foundation, but also on the practical application and computer implementation. The text is supplemented with a number of examples and unsolved problems, many drawn from the field of particulate creeping flows. The material is selected so that the book may serve both as a reference monograph and as a textbook in a graduate course on fluid mechanics or computational fluid mechanics.},
address = {Cambridge},
author = {Pozrikidis, C.},
isbn = {978-0521405027},
pages = {272},
publisher = {Cambridge University Press},
title = {{Boundary Integral and Singularity Methods for Linearized Viscous Flow}},
year = {1992}
}
@article{press,
author = {Press, F.},
journal = {J. Geophys. Res.},
pages = {2395--2412},
title = {{Displacements, strains and tilts at tele-seismic distances}},
volume = {70},
year = {1965}
}
@inproceedings{Price2012a,
abstract = {I discuss the key features of Smoothed Particle Hydrodynamics (SPH) as a numerical method - in particular the key differences between SPH and more standard grid based approaches - that are important to the practitioner. These include the exact treatment of advection, the absence of intrinsic dissipation, exact conservation and more subtle properties that arise from its Hamiltonian formulation such as the existence of a minimum energy state for the particles. The implications of each of these are discussed, showing how they can be both advantages and disadvantages.},
address = {San Francisco},
author = {Price, D. J.},
booktitle = {Advances in computational astrophysics: methods, tools, and outcome},
editor = {Capuzzo-Dolcetta, R. and Limongi, M. and Tornamb{\`{e}}, A.},
pages = {249},
publisher = {Astronomical Society of the Pacific},
title = {{Smoothed Particle Hydrodynamics: Things I Wish My Mother Taught Me}},
year = {2012}
}
@article{Price2012b,
abstract = {Accounting for the Reynolds number is critical in numerical simulations of turbulence, particularly for subsonic flow. For smoothed particle hydrodynamics (SPH) with constant artificial viscosity coefficient $\alpha$, it is shown that the effective Reynolds number in the absence of explicit physical viscosity terms scales linearly with the Mach number – compared to mesh schemes, where the effective Reynolds number is largely independent of the flow velocity. As a result, SPH simulations with $\alpha$ = 1 will have low Reynolds numbers in the subsonic regime compared to mesh codes, which may be insufficient to resolve turbulent flow. This explains the failure of Bauer {\&} Springel to find agreement between the moving-mesh code arepo and the gadget SPH code on simulations of driven, subsonic (v∼ 0.3cs) turbulence appropriate to the intergalactic/intracluster medium, where it was alleged that SPH is somehow fundamentally incapable of producing a Kolmogorov-like turbulent cascade. We show that turbulent flow with a Kolmogorov spectrum can be easily recovered by employing standard methods for reducing $\alpha$ away from shocks.},
author = {Price, D. J.},
doi = {10.1111/j.1745-3933.2011.01187.x},
isbn = {1745-3933},
issn = {17453933},
journal = {Mon. Not. R. Astron. Soc.},
keywords = {Galaxies: clusters: intracluster medium,Hydrodynamics,Intergalactic medium,Methods: numerical,Turbulence},
number = {1},
pages = {33--37},
title = {{Resolving high reynolds numbers in smoothed particle hydrodynamics simulations of subsonic turbulence}},
volume = {420},
year = {2012}
}
@article{Price2012,
abstract = {This paper presents an overview and introduction to smoothed particle hydrodynamics and magnetohydrodynamics in theory and in practice. Firstly, we give a basic grounding in the fundamentals of SPH, showing how the equations of motion and energy can be self-consistently derived from the density estimate. We then show how to interpret these equations using the basic SPH interpolation formulae and highlight the subtle difference in approach between SPH and other particle methods. In doing so, we also critique several 'urban myths' regarding SPH, in particular the idea that one can simply increase the 'neighbour number' more slowly than the total number of particles in order to obtain convergence. We also discuss the origin of numerical instabilities such as the pairing and tensile instabilities. Finally, we give practical advice on how to resolve three of the main issues with SPMHD: removing the tensile instability, formulating dissipative terms for MHD shocks and enforcing the divergence constraint on the particles, and we give the current status of developments in this area. Accompanying the paper is the first public release of the ndspmhd SPH code, a 1, 2 and 3 dimensional code designed as a testbed for SPH/SPMHD algorithms that can be used to test many of the ideas and used to run all of the numerical examples contained in the paper. ?? 2010 Elsevier Inc..},
archivePrefix = {arXiv},
arxivId = {1012.1885},
author = {Price, D. J.},
doi = {10.1016/j.jcp.2010.12.011},
eprint = {1012.1885},
isbn = {0021-9991},
issn = {00219991},
journal = {J. Comp. Phys.},
keywords = {Astrophysics,Hydrodynamics,Magnetohydrodynamics (MHD),Particle methods,Smoothed particle hydrodynamics},
number = {3},
pages = {759--794},
title = {{Smoothed particle hydrodynamics and magnetohydrodynamics}},
volume = {231},
year = {2012}
}
@phdthesis{Primus2003,
author = {Primus, M.},
school = {Cemagref},
title = {{Mod{\'{e}}lisation physique des interactions entre avalanches de neige poudreuse et dispositifs de protection}},
type = {M�moire du stage de DEA MMGE},
year = {2003}
}
@article{Primus2004,
author = {Primus, M. and Naaim-Bouvet, F. and Naaim, M. and Faug, T.},
journal = {Cold Regions Science and Technology},
pages = {257--267},
title = {{Physical modeling of the interaction between mounds or deflecting dams and powder snow avalanches}},
volume = {39},
year = {2004}
}
@article{Prosperetti1976,
author = {Prosperetti, A.},
journal = {Phys. Fluids},
pages = {195--203},
title = {{Viscous effects on small-amplitude surface waves}},
volume = {19},
year = {1976}
}
@article{Purkiani2015,
author = {Purkiani, K. and Becherer, J. and Fl{\"{o}}ser, G. and Gr{\"{a}}we, U. and Mohrholz, V. and Schuttelaars, H. M. and Burchard, H.},
journal = {J. Geophys. Res.},
pages = {225--243},
title = {{Numerical analysis of stratification and de-stratification processes in a tidally energetic inlet with an ebb tidal delta}},
volume = {120},
year = {2015}
}
@article{Pushkarev1999,
abstract = {Numerical simulation of dynamical equations for capillary waves excited by long-scale forcing shows the presence of both Kolmogorov spectrum at high wavenumbers (with the index predicted by weak-turbulent theory) and non-monotonic spectrum at low wavenumbers. The value of the Kolmogorov constant measured in numerical experiments happens to be different from the theoretical one. We explain the difference by the coexistence of Kolmogorov and ''frozen'' turbulence with the help of maps of quasi-resonances. Observed results are believed to be generic for different physical dispersive systems and are confirmed by laboratory experiments.},
author = {Pushkarev, A. N.},
doi = {10.1016/S0997-7546(99)80032-6},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
month = {may},
number = {3},
pages = {345--351},
title = {{On the Kolmogorov and frozen turbulence in numerical simulation of capillary waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754699800326},
volume = {18},
year = {1999}
}
@article{Pushkarev2013,
author = {Pushkarev, A. N. and Zakharov, V. E.},
journal = {Phys. D},
title = {{Quasibreathers in MMT model}},
volume = {In Press},
year = {2013}
}
@book{Quiblier1997,
author = {Quiblier, J.},
publisher = {Paris: Editions Technip},
title = {{Propagation des ondes en g{\'{e}}ophysique et en g{\'{e}}otechnique. Mod{\'{e}}lisation par m{\'{e}}thodes de Fourier}},
year = {1997}
}
@article{Rabinovich1992,
author = {Rabinovich, A. B. and Leviant, A. S.},
journal = {Oceanology},
pages = {17--23},
title = {{Influence of Seiche Oscillations on the Formation of the Long-Wave Spectrum Near the Coast of the Southern Kuriles}},
volume = {32},
year = {1992}
}
@article{Rabinovich2008,
author = {Rabinovich, A. B. and Lobkovsky, L. I. and Fine, I. V. and Thomson, R. E. and Ivelskaya, T. N. and Kulikov, E. A.},
journal = {Adv. Geosci.},
pages = {105--116},
title = {{Near-source observations and modeling of the Kuril Islands tsunamis of 15 November 2006 and 13 January 2007}},
volume = {14},
year = {2008}
}
@article{Rabinovich2009,
author = {Rabinovich, A. B. and Vilibic, I. and Tinti, S.},
doi = {10.1016/j.pce.2009.10.006},
journal = {Phys. Chem. Earth. (B)},
number = {17-18},
pages = {891--893},
title = {{Meteorological tsunamis: Atmospherically induced destructive ocean waves in the tsunami frequency band}},
url = {http://www.sciencedirect.com/science/article/pii/S1474706509001260},
volume = {34},
year = {2009}
}
@article{Radder1999,
author = {Radder, A. C.},
journal = {Adv. Coast. Ocean Engng.},
pages = {21--59},
title = {{Hamiltonian dynamics of water waves}},
volume = {4},
year = {1999}
}
@article{Radder1985,
author = {Radder, A. C. and Dingemans, M. W.},
journal = {Wave Motion},
pages = {473--485},
title = {{Canonical equations for almost periodic, weakly nonlinear gravity waves}},
volume = {7},
year = {1985}
}
@phdthesis{Rafiee2012a,
author = {Rafiee, A.},
school = {University of Western Australia},
title = {{SPH modelling of multi-phase and energetic flows}},
year = {2012}
}
@article{Rafiee2012,
author = {Rafiee, A. and Cummins, S. and Rudman, M. and Thiagarajan, K.},
doi = {10.1016/j.euromechflu.2012.05.001},
issn = {09977546},
journal = {Eur. J. Mech. B/Fluids},
month = {nov},
pages = {1--16},
title = {{Comparative study on the accuracy and stability of SPH schemes in simulating energetic free-surface flows}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0997754612000714},
volume = {36},
year = {2012}
}
@inproceedings{Rafiee2013,
address = {Alaska, USA},
author = {Rafiee, A. and Repalle, N. and Dias, F.},
booktitle = {Proceedings of 23rd International Offshore and Polar Engineering Conference (ISOPE)},
title = {{Numerical simulations of 2D liquid impact benchmark problem using two-phase compressible and incompressible methods}},
year = {2013}
}
@article{Rajchenbach2002a,
author = {Rajchenbach, J.},
journal = {Phys. Rev. Lett.},
pages = {74301},
title = {{Development of Grain Avalanches}},
volume = {89},
year = {2002}
}
@article{Rajchenbach2005,
author = {Rajchenbach, J.},
journal = {J. Phys.: Condens. Matter},
pages = {S2731--S2742},
title = {{Rheology of dense granular materials: steady, uniform flow and the avalanche regime}},
volume = {17},
year = {2005}
}
@article{Rajchenbach2002,
author = {Rajchenbach, J.},
journal = {Phys. Rev. Lett.},
pages = {14301},
title = {{Dynamics of Grain Avalanches}},
volume = {88},
year = {2002}
}
@article{Rajchenbach2013,
abstract = {We report a new type of standing gravity wave of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vertically vibrating a tank. The symmetry of the star (i.e., the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. We show that a nonlinear resonant coupling between three gravity waves can be envisaged to trigger the observed symmetry breaking, although more complex interactions certainly take place in the final periodic state.},
author = {Rajchenbach, J. and Clamond, D. and Leroux, A.},
doi = {10.1103/PhysRevLett.110.094502},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {feb},
number = {9},
pages = {094502},
title = {{Observation of Star-Shaped Surface Gravity Waves}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.110.094502},
volume = {110},
year = {2013}
}
@article{Rajchenbach2011,
abstract = {By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are, respectively, of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency. The two-dimensional even pattern presents a certain similarity in the shape with the 3D axisymmetric oscillon originally recognized at the surface of a vertically vibrated layer of brass beads. The stable, 2D odd standing wave has never been observed before in any media.},
author = {Rajchenbach, J. and Leroux, A. and Clamond, D.},
doi = {10.1103/PhysRevLett.107.024502},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {jul},
number = {2},
pages = {024502},
title = {{New Standing Solitary Waves in Water}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.107.024502},
volume = {107},
year = {2011}
}
@phdthesis{Ramos2000,
author = {Ramos, D.},
school = {CMLA, Ecole Normale Sup{\'{e}}rieure de Cachan},
title = {{Quelques r{\'{e}}sultats math{\'{e}}matiques et simulations num{\'{e}}riques d'{\'{e}}coulements r{\'{e}}gis par des mod{\`{e}}les bifluides}},
year = {2000}
}
@article{Randoux2014,
author = {Randoux, S. and Walczak, P. and Onorato, M. and Suret, P.},
doi = {10.1103/PhysRevLett.113.113902},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {sep},
number = {11},
pages = {113902},
title = {{Intermittency in Integrable Turbulence}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.113.113902},
volume = {113},
year = {2014}
}
@article{Rankine1870,
author = {Rankine, W. J. M.},
doi = {10.1098/rstl.1870.0015},
issn = {0261-0523},
journal = {Phil. Trans. R. Soc. Lond},
month = {jan},
pages = {277--288},
title = {{On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance}},
url = {http://rstl.royalsocietypublishing.org/cgi/doi/10.1098/rstl.1870.0015},
volume = {160},
year = {1870}
}
@techreport{Ransom1985,
author = {Ransom, V. H.},
institution = {Idaho Engineering Laboratory},
number = {NUREG/CR-4312, EGG-23986},
title = {{RELAP5/MOD2 Code Manual}},
year = {1985}
}
@article{Ransom1988,
author = {Ransom, V. H. and Hicks, D. L.},
journal = {J. Comput. Phys.},
pages = {498--504},
title = {{Hyperbolic two-pressure models for two-phase flows revisited}},
volume = {75},
year = {1988}
}
@inbook{Rapin1995,
author = {Rapin, F.},
chapter = {French the},
editor = {Brugnot, G},
pages = {149--154},
publisher = {Editions du CEMAGREF},
title = {{Universit{\'{e}} Europ{\'{e}}enne d'{\'{e}}t{\'{e}} sur les Risques Naturels. Session 1992: Neige er avalanches}},
year = {1995}
}
@article{Rapp1990,
author = {Rapp, R. J. and Melville, W. K.},
doi = {10.1098/rsta.1990.0098},
issn = {1364-503X},
journal = {Phil. Trans. R. Soc. Lond. A},
month = {jun},
number = {1622},
pages = {735--800},
title = {{Laboratory Measurements of Deep-Water Breaking Waves}},
url = {http://rsta.royalsocietypublishing.org/cgi/doi/10.1098/rsta.1990.0098},
volume = {331},
year = {1990}
}
@article{Rastello2004,
author = {Rastello, M. and Hopfinger, E. J.},
journal = {J. Fluid. Mech.},
pages = {181--206},
title = {{Sediment-entraining suspension clouds: a model of powder-snow avalanches}},
volume = {509},
year = {2004}
}
@article{Raval2009,
author = {Raval, A. and Wen, X. and Smith, M. H.},
journal = {J. Fluid Mech},
pages = {443--473},
title = {{Numerical simulation of viscous, nonlinear and progressive water waves}},
volume = {637},
year = {2009}
}
@article{Rayleigh1883,
author = {Rayleigh, L.},
journal = {Proceedings of the London Mathematical Society},
pages = {170--177},
title = {{Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density}},
volume = {14},
year = {1883}
}
@article{Reddy1992,
author = {Reddy, S. C. and Trefethen, L. N.},
doi = {10.1007/BF01396228},
issn = {0029599X},
journal = {Numerische Mathematik},
number = {1},
pages = {235--267},
publisher = {Springer},
title = {{Stability of the method of lines}},
url = {http://www.springerlink.com/index/J6Q3HR77V3627870.pdf},
volume = {62},
year = {1992}
}
@article{Reich2000,
abstract = {We investigate the application of a cell-vertex finite volume discretization to multi-symplectic PDEs. The investigated discretization reduces to the Preissman box scheme when used on a rectangular grid. Concerning arbitrary quadrilateral grids, we show that only methods with parallelogram-like finite volume cells lead to a multi-symplectic discretization; i.e., to a method that preserves a discrete conservation law of symplecticity. One of the advantages of finite volume methods is that they can be easily adjusted to variable meshes. But, although the implementation of moving mesh finite volume methods for multi-symplectic PDEs is rather straightforward, the restriction to parallelogram-like cells implies that only meshes moving with a constant speed are multi-symplectic. To overcome this restriction, we suggest the implementation of reversible moving mesh methods based on a semi-Lagrangian approach. Numerical experiments are presented for a one dimensional dispersive shallow-water system.},
author = {Reich, S.},
doi = {10.1023/A:1022375915113},
issn = {00063835},
journal = {Bit Numerical Mathematics},
number = {3},
pages = {559--582},
publisher = {Springer Netherlands},
title = {{Finite Volume Methods for Multi-Symplectic PDES}},
url = {http://www.springerlink.com/content/h23m08h35n0t8n58/},
volume = {40},
year = {2000}
}
@article{Renouard1985,
author = {Renouard, D. P. and Seabra-Santos, F. J. and Temperville, A. M.},
journal = {Dynamics of Atmospheres and Oceans},
pages = {341--358},
title = {{Experimental study of the generation, damping, and reflexion of a solitary wave}},
volume = {9(4)},
year = {1985}
}
@article{Renzi2012a,
abstract = {A mathematical model is developed to study the behaviour of an oscillating wave energy converter in a channel. During recent laboratory tests in a wave tank, peaks in the hydrodynamic actions on the converter occurred at certain frequencies of the incident waves. This resonant mechanism is known to be generated by the transverse sloshing modes of the channel. Here the influence of the channel sloshing modes on the performance of the device is further investigated. Within the framework of a linear inviscid potential-flow theory, application of Green’s theorem yields a hypersingular integral equation for the velocity potential in the fluid domain. The solution is found in terms of a fast-converging series of Chebyshev polynomials of the second kind. The physical behaviour of the system is then analysed, showing sensitivity of the resonant sloshing modes to the geometry of the device, which concurs in increasing the maximum efficiency. Analytical results are validated with available numerical and experimental data.},
author = {Renzi, E. and Dias, F.},
doi = {10.1017/jfm.2012.194},
issn = {0022-1120},
journal = {J. Fluid Mech},
keywords = {general fluid mechanics,wave-structure interactions},
month = {may},
pages = {482--510},
title = {{Resonant behaviour of an oscillating wave energy converter in a channel}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112012001942},
volume = {701},
year = {2012}
}
@article{Renzi2012b,
abstract = {A mathematical model is developed to study the behaviour of an oscillating wave energy converter in a channel. During recent laboratory tests in a wave tank, peaks in the hydrodynamic actions on the converter occurred at certain frequencies of the incident waves. This resonant mechanism is known to be generated by the transverse sloshing modes of the channel. Here the influence of the channel sloshing modes on the performance of the device is further investigated. Within the framework of a linear inviscid potential-flow theory, application of Green’s theorem yields a hypersingular integral equation for the velocity potential in the fluid domain. The solution is found in terms of a fast-converging series of Chebyshev polynomials of the second kind. The physical behaviour of the system is then analysed, showing sensitivity of the resonant sloshing modes to the geometry of the device, which concurs in increasing the maximum efficiency. Analytical results are validated with available numerical and experimental data.},
author = {Renzi, E. and Dias, F.},
doi = {10.1017/jfm.2012.194},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {may},
pages = {482--510},
title = {{Resonant behaviour of an oscillating wave energy converter in a channel}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112012001942},
volume = {701},
year = {2012}
}
@article{Renzi2012,
author = {Renzi, E. and Sammarco, P.},
doi = {10.5194/nhess-12-1503-2012},
issn = {1684-9981},
journal = {Nat. Hazards Earth Syst. Sci.},
month = {may},
number = {5},
pages = {1503--1520},
title = {{The influence of landslide shape and continental shelf on landslide generated tsunamis along a plane beach}},
url = {http://www.nat-hazards-earth-syst-sci.net/12/1503/2012/},
volume = {12},
year = {2012}
}
@article{Renzi2010,
abstract = {An analytical forced two-horizontal-dimension model is derived to investigate landslide tsunamis propagating around a conical island lying on a flat continental platform. Separation of variables and Laplace transform are used to obtain the free-surface elevation in the whole domain and the runup at the shoreline in terms of confluent Heun functions. The main properties of these functions and their asymptotic behaviour for large parameters are investigated. Expression of the transient leading wave travelling offshore is also derived. The distinguishing physical features of landslide tsunamis propagating in a round geometry are then pointed out and compared with those of landslide tsunamis propagating along a straight coast. Analytical results satisfactorily agree with available experimental data.},
author = {Renzi, E. and Sammarco, P.},
doi = {10.1017/S0022112009993582},
issn = {0022-1120},
journal = {J. Fluid Mech},
month = {mar},
pages = {251--285},
title = {{Landslide tsunamis propagating around a conical island}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112009993582},
volume = {650},
year = {2010}
}
@phdthesis{Repalle2012,
author = {Repalle, N.},
school = {University of Western Australia},
title = {{Study of Sloshing Impact Pressures using Level Set Method}},
year = {2012}
}
@article{Reynolds1883,
author = {Reynolds, O.},
journal = {Phil. Trans. Roy. Soc.},
pages = {935--982},
title = {{An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels}},
volume = {174},
year = {1883}
}
@article{Rhie2007,
abstract = {The 26 December 2004 Great Sumatra–Andaman earthquake opened a new era for seismologists to understand the complex source process of a great earthquake. This is the first event with moment magnitude greater than 9 since the deployment of high-dynamic-range broadband seismic and Global Positioning System (GPS) sensors around the globe. This study presents an analysis of the ruptured fault- plane geometry and slip distribution using long-period teleseismic data and GPS- measured static surface displacements near the fault plane. We employ a rupture geometry with six along-strike segments with and without a steeper down-dip extension. The fault segments are further subdivided into a total of 201 ∼ 30 × 30 km fault patches. Sensitivity tests of fault-plane geometry and the variation in rupture velocity indicate that the dip and curvature of the fault plane are not well resolved from the given data set and the rupture velocity is constrained to be between 1.8 and 2.6 km/sec. Error estimations of the slip distribution using a random selection of seismic and GPS station subsets (50{\%} of all stations) illustrate that slip is well resolved along the whole rupture and the mean slip uncertainty is less than 1.5 m (about 11{\%}). Although it is possible that near-field GPS data include contributions from additional postseismic transient deformation, our preferred model suggests that the Sumatra–Andaman earthquake had a magnitude of Mw 9.20 + 0.05/−0.06.},
author = {Rhie, J. and Dreger, D. and Burgmann, R. and Romanowicz, B.},
doi = {10.1785/0120050620},
issn = {0037-1106},
journal = {Bulletin of the Seismological Society of America},
month = {jan},
number = {1A},
pages = {S115--------S127},
title = {{Slip of the 2004 Sumatra-Andaman Earthquake from Joint Inversion of Long-Period Global Seismic Waveforms and GPS Static Offsets}},
url = {http://www.bssaonline.org/cgi/doi/10.1785/0120050620},
volume = {97},
year = {2007}
}
@article{Ricchiuto2014,
author = {Ricchiuto, M. and Filippini, A. G.},
doi = {10.1016/j.jcp.2013.12.048},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {jan},
title = {{Upwind residual discretization of enhanced Boussinesq equations for wave propagation over complex bathymetries}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999113008565},
year = {2014}
}
@article{Richardson1985,
abstract = {Summary: Discusses 1) sediment transport terminology; 2) general considerations (influences on amount of material transported or deposited: A) geology {\&} topography of watershed; magnitude, intensity , duration, distribution, and season of rainfall; vegetal cover; soil condition; cultivation and grazing; surface erosion and bank cutting; B) hydraulic properties of the stream channel: fluid properties, slope, roughness, hydraulic radius, discharge, velocity, velocity distribution, turbulence, etc; 3) sources of sediment transport; 4) mode of transport; 5) total sediment discharge; 6) suspended bed sediment discharge (many equations).},
author = {Richardson, E. V.},
journal = {Transport},
pages = {46--57},
publisher = {Federal Highway Administration},
title = {{Sediment Transport}},
url = {http://www.agu.org/pubs/crossref/1977/WR013i002p00303.shtml},
year = {1985}
}
@book{Richardson1922,
address = {Cambridge},
author = {Richardson, L. F.},
pages = {262},
publisher = {Cambridge University Press},
title = {{Weather prediction by numerical process}},
year = {1922}
}
@article{Rienecker1981,
abstract = {A method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed is presented. No analytical approximations are made. A finite Fourier series, similar to Dean's stream function series, is used to give a set of nonlinear equations which can be solved using Newton's method. Application to laboratory and field situations is emphasized throughout. When compared with known results for wave speed, results from the method agree closely. Results for fluid velocities are compared with experiment and agreement found to be good, unlike results from analytical theories for high waves. The problem of shoaling waves can conveniently be studied using the present method because of its validity for all wavelengths except the solitary wave limit, using the conventional first-order approximation that on a sloping bottom the waves at any depth act as if the bed were horizontal. Wave period, energy flux and mass flux are conserved. Comparisons with experimental results show good agreement.},
author = {Rienecker, M. M. and Fenton, J. D.},
doi = {10.1017/S0022112081002851},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {apr},
pages = {119--137},
title = {{A Fourier approximation method for steady water waves}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112081002851},
volume = {104},
year = {1981}
}
@article{Ritsema1995,
author = {Ritsema, J. and Ward, S. N. and Gonz{\'{a}}lez, F. I.},
journal = {Bulletin of the Seismological Society of America},
pages = {747--754},
title = {{Inversion of deep-ocean tsunami records for 1987 to 1988 Gulf of Alaska earthquake parameters}},
volume = {85},
year = {1995}
}
@book{Roberts1991,
author = {Roberts, J. E. and Thomas, J.-M.},
publisher = {Amsterdam and New York, North-Holland},
title = {{Mixed and hybrid methods (in finite elements problems)}},
year = {1991}
}
@phdthesis{Robinson2009,
author = {Robinson, M.},
school = {Monash University},
title = {{Turbulence and Viscous Mixing using Smoothed Particle Hydrodynamics}},
year = {2009}
}
@article{Roe2005,
author = {Roe, P. L.},
doi = {10.1080/10618560600585315},
issn = {1061-8562},
journal = {International Journal of Computational Fluid Dynamics},
month = {nov},
number = {8},
pages = {581--594},
title = {{Computational fluid dynamics - retrospective and prospective}},
url = {http://www.tandfonline.com/doi/abs/10.1080/10618560600585315},
volume = {19},
year = {2005}
}
@article{Roe1981,
author = {Roe, P. L.},
journal = {J. Comput. Phys.},
pages = {357--372},
title = {{Approximate Riemann solvers, parameter vectors and difference schemes}},
volume = {43},
year = {1981}
}
@article{Roos1994,
author = {Roos, H.-G.},
doi = {10.1016/0377-0427(92)00124-R},
issn = {03770427},
journal = {J. Comp. Appl. Math.},
month = {jul},
number = {1},
pages = {43--59},
title = {{Ten ways to generate the Il'in and related schemes}},
url = {http://linkinghub.elsevier.com/retrieve/pii/037704279200124R},
volume = {53},
year = {1994}
}
@article{Rosier1997,
author = {Rosier, L.},
journal = {ESAIM Cntrol Optim. Calc. Var.},
pages = {33--55},
title = {{Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain}},
volume = {2},
year = {1997}
}
@article{Rosier2004,
author = {Rosier, L.},
journal = {ESAIM Cntrol Optim. Calc. Var.},
pages = {346--380},
title = {{Control of the surface of a fluid by a wavemaker}},
volume = {10},
year = {2004}
}
@article{Rosier2000,
author = {Rosier, L.},
doi = {10.1137/S0363012999353229},
issn = {0363-0129},
journal = {SIAM Journal on Control and Optimization},
month = {jan},
number = {2},
pages = {331--351},
title = {{Exact Boundary Controllability for the Linear Korteweg-de Vries Equation on the Half-Line}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0363012999353229},
volume = {39},
year = {2000}
}
@article{Rosier2012,
author = {Rosier, L. and Zhang, B.-Y.},
journal = {Arxiv},
pages = {35},
title = {{Unique continuation property and control for the Benjamin-Bona-Mahony equation on the torus}},
url = {http://arxiv.org/abs/1202.2667},
volume = {1202.2667},
year = {2012}
}
@article{Rossetto2011,
abstract = {The physical simulation of tsunami in the laboratory has taken a major leap forward with the construction and testing of a new wave generator, capable of recreating scaled tsunamiwaves. Numerical tools fail to reproduce tsunami nearshore and onshore processes well, and physical experiments in large scale hydraulic facilities worldwide have been limited to the generation of solitary waves as an (controversial) approximation for evolved forms of tsunami. The new concept in wave generation presented herein is born of collaboration between UCL's Earthquake and People Interaction Centre (EPICentre) and HR Wallingford. It allows for the first time the stable simulation of extremely long waves led either by a crest or a trough (depressed wave). This paper presents the working concepts behind the newwavegenerator and the first stages of testing for verifying its capacities and limitations. It is shown that the newwavegenerator can not only reproduce solitary waves and N-waves with large wavelengths, but also the 2004 Indian Ocean Tsunami as recorded off the coast of Thailand (“Mercator” trace).},
author = {Rossetto, T. and Allsop, W. and Charvet, I. and Robinson, D. I.},
doi = {10.1016/j.coastaleng.2011.01.012},
issn = {03783839},
journal = {Coastal Engineering},
keywords = {Long sine wave,N-waves,Physical modelling,Solitary waves,Tsunami,Tsunami run-up},
month = {jun},
number = {6},
pages = {517--527},
title = {{Physical modelling of tsunami using a new pneumatic wave generator}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378383911000135},
volume = {58},
year = {2011}
}
@article{Rousset2011,
abstract = {We prove the linear and nonlinear instability of the line solitary water waves with respect to transverse perturbations.},
author = {Rousset, F. and Tzvetkov, N.},
doi = {10.1007/s00222-010-0290-7},
issn = {0020-9910},
journal = {Inventiones mathematicae},
month = {may},
number = {2},
pages = {257--388},
title = {{Transverse instability of the line solitary water-waves}},
url = {http://link.springer.com/10.1007/s00222-010-0290-7},
volume = {184},
year = {2011}
}
@phdthesis{Rovarch2006,
author = {Rovarch, J.-M.},
school = {Ecole Normale Sup$\backslash$'erieure de Cachan},
title = {{Solveurs tridimensionnels pour les {\{}{\'{e}}{\}}coulements diphasiques avec transferts d'{\{}{\'{e}}{\}}nergie}},
year = {2006}
}
@phdthesis{Rovarch2006,
author = {Rovarch, J.-M.},
school = {Ecole Normale Sup$\backslash$'erieure de Cachan},
title = {{Solveurs tridimensionnels pour les {\'{e}}coulements diphasiques avec transferts d'{\'{e}}nergie}},
year = {2006}
}
@article{Rowley2005,
abstract = {Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218127405012429?journalCode=ijbc},
author = {Rowley, C. W.},
doi = {10.1142/S0218127405012429},
issn = {0218-1274},
journal = {Int. J. Bifurcation Chaos},
month = {mar},
number = {03},
pages = {997--1013},
title = {{Model reduction for fluids, using balanced proper orthogonal decomposition}},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0218127405012429},
volume = {15},
year = {2005}
}
@book{Rozhdestvenskiy1978,
address = {Moscow},
author = {Rozhdestvenskiy, B. L. and Yanenko, N. N.},
pages = {688},
publisher = {Nauka},
title = {{Systems of quasilinear equations and their application to gas dynamics}},
year = {1978}
}
@article{Ruban2012,
author = {Ruban, V. P.},
journal = {JETP},
pages = {343--353},
title = {{The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin}},
volume = {114},
year = {2012}
}
@article{Ruban2005,
author = {Ruban, V. P.},
journal = {Phys. Lett. A},
pages = {194--200},
title = {{Water waves over a time-dependent bottom: exact description for 2D potential flow}},
volume = {340},
year = {2005}
}
@article{Ruban2010,
author = {Ruban, V. P.},
doi = {10.1140/epjst/e2010-01235-x},
issn = {1951-6355},
journal = {The European Physical Journal Special Topics},
month = {aug},
number = {1},
pages = {17--33},
title = {{Conformal variables in the numerical simulations of long-crested rogue waves}},
url = {http://www.springerlink.com/index/10.1140/epjst/e2010-01235-x},
volume = {185},
year = {2010}
}
@article{Ruban2004,
author = {Ruban, V. P.},
journal = {Phys. Rev. E},
pages = {066302},
title = {{Water waves over a strongly undulanting bottom}},
volume = {70},
year = {2004}
}
@article{Ruderman2008,
abstract = {In this paper we study the propagation of nonlinear ion-acoustic waves in plasmas with negative ions. The Gardner equation governing these waves in plasmas with the negative ion concentration close to critical is derived. The weakly nonlinear theory of modulational instability based on the use of the nonlinear Schr{\"{o}}dinger equation is discussed. The investigation of the nonlinear dynamics of modulationally unstable quasi-harmonic wavepackets is carried out by the numerical solution of the Gardner equation. The results are compared with the predictions of the weakly nonlinear theory.},
author = {Ruderman, M. S. and Talipova, T. and Pelinovsky, E.},
doi = {10.1017/S0022377808007150},
issn = {0022-3778},
journal = {J. Plasma Phys.},
month = {apr},
number = {05},
pages = {639--656},
title = {{Dynamics of modulationally unstable ion-acoustic wavepackets in plasmas with negative ions}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022377808007150},
volume = {74},
year = {2008}
}
@article{Ruelle1971,
author = {Ruelle, D. and Takens, F.},
doi = {10.1007/BF01646553},
issn = {00103616},
journal = {Communications in Mathematical Physics},
number = {3},
pages = {167--192},
title = {{On the nature of turbulence}},
url = {http://www.springerlink.com/index/10.1007/BF01646553},
volume = {20},
year = {1971}
}
@article{Rusanov1962,
author = {Rusanov, V. V.},
doi = {10.1016/0041-5553(62)90062-9},
issn = {00415553},
journal = {USSR Computational Mathematics and Mathematical Physics},
number = {2},
pages = {304--320},
title = {{The calculation of the interaction of non-stationary shock waves and obstacles}},
volume = {1},
year = {1962}
}
@phdthesis{Rusche2002,
author = {Rusche, H.},
school = {University of London and Imperial College},
title = {{Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions}},
year = {2002}
}
@techreport{Russell1845,
address = {London},
author = {Russell, J. S.},
institution = {Report of the fourteenth meeting of the British Association for the Advancement of Science, York, September 1844},
pages = {311--390},
title = {{Report on Waves}},
year = {1845}
}
@article{Russell1995,
author = {Russell, L. and Zhang, B.-Y.},
journal = {J. Math. Anal. Appl.},
pages = {449--488},
title = {{Smoothing and decay properties of the Korteweg-de Vries equation on a periodic domain with point dissipation}},
volume = {190},
year = {1995}
}
@article{Russell1996,
author = {Russell, L. and Zhang, B.-Y.},
journal = {Trans. Amer. Math. Soc.},
pages = {3653--3672},
title = {{Exact Controllability and stabilizability of the Korteweg-de Vries equation}},
volume = {348},
year = {1996}
}
@article{Russell1993,
author = {Russell, L. and Zhang, B.-Y.},
journal = {SIAM Journal on Control and Optimization},
pages = {659--676},
title = {{Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain}},
volume = {31},
year = {1993}
}
@article{Ruvinsky1991,
author = {Ruvinsky, K. D. and Feldstein, F. I. and Freidman, G. I.},
journal = {J. Fluid Mech.},
pages = {339--353},
title = {{Numerical simulations of the quasistationary stage of ripple excitation by steep-capillary waves}},
volume = {230},
year = {1991}
}
@article{Ruyer-Quil2000,
abstract = {A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable Ƭ that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations.},
author = {Ruyer-Quil, C. and Manneville, P.},
doi = {10.1007/s100510050550},
issn = {1434-6028},
journal = {Eur. Phys. J. B},
number = {2},
pages = {277--292},
title = {{Improved modeling of flows down inclined planes}},
volume = {6},
year = {2000}
}
@book{Ryder1996,
abstract = {This book is a modern introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the author develops the quantum theory of scalar and spinor fields, and then of gauge fields. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of "topological" objects in field theory and, new to this edition, a chapter devoted to supersymmetry. Graduate students in particle physics and high energy physics will benefit from this book.},
address = {Cambridge},
author = {Ryder, L. H.},
edition = {2nd},
isbn = {978-0521478144},
pages = {501},
publisher = {Cambridge University Press},
title = {{Quantum Field Theory}},
year = {1996}
}
@article{Rygg1988,
abstract = {A numerical scheme for solving the nonlinear Boussinesq equations is introduced. The numerical model is used to investigate nonlinear refraction-diffraction of surface gravity waves over a semicircular shoal. Results are compared with experimental data (Whalin, 1971) and previous reported numerical results by Liu and Tsay (1984) and Liu, Yoon and Kirby (1985). The present calculations reproduce the earlier results for shallow water waves, but are superior in intermediate water depth.},
author = {Rygg, O. B.},
doi = {10.1016/0378-3839(88)90005-1},
issn = {03783839},
journal = {Coastal Engineering},
month = {sep},
number = {3},
pages = {191--211},
title = {{Nonlinear refraction-diffraction of surface waves in intermediate and shallow water}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0378383988900051},
volume = {12},
year = {1988}
}
@article{Ryzhov2010,
author = {Ryzhov, O. S.},
journal = {AIAA Journal},
number = {2},
pages = {275--286},
title = {{Solitons in Transitional Boundary Layers}},
volume = {48},
year = {2010}
}
@inbook{sabatier,
author = {Sabatier, P. C.},
chapter = {Formation},
pages = {723--759},
publisher = {Gulf Publishing Company},
title = {{Encyclopedia of fluid mechanics}},
year = {1986}
}
@article{Sadaka2012,
author = {Sadaka, G.},
doi = {10.1515/jnum-2012-0016},
issn = {1569-3953},
journal = {Journal of Numerical Mathematics},
month = {jan},
number = {3-4},
pages = {303--324},
title = {{Solution of 2D Boussinesq systems with FreeFem++: the flat bottom case}},
url = {http://www.degruyter.com/view/j/jnma.2012.20.issue-3-4/jnum-2012-0016/jnum-2012-0016.xml},
volume = {20},
year = {2012}
}
@article{Sadaka2013,
author = {Sadaka, G. and Chehab, J.-P.},
doi = {10.3934/dcdss.2013.6.1487},
issn = {1937-1632},
journal = {Discrete and Continuous Dynamical Systems - Series S},
month = {apr},
number = {6},
pages = {1487--1506},
title = {{On damping rates of dissipative KdV equations}},
url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8534},
volume = {6},
year = {2013}
}
@article{Salevik2009,
author = {Saelevik, G. and Jensen, A. and Pedersen, G.},
doi = {10.1016/j.coastaleng.2009.04.007},
issn = {03783839},
journal = {Coastal Engineering},
month = {sep},
number = {9},
pages = {897--906},
title = {{Experimental investigation of impact generated tsunami; related to a potential rock slide, Western Norway}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378383909000581},
volume = {56},
year = {2009}
}
@book{Sagaut2006,
author = {Sagaut, P.},
booktitle = {Applied Mechanics Reviews},
doi = {10.1115/1.1508154},
isbn = {3540263446},
issn = {00036900},
number = {6},
pages = {B115},
publisher = {Springer},
series = {Scientific Computation},
title = {{Large eddy simulation for incompressible flows: an introduction}},
url = {http://link.aip.org/link/AMREAD/v55/i6/pB115/s1{\&}Agg=doi},
volume = {55},
year = {2006}
}
@article{Sainflou1928,
author = {Sainflou, M.},
journal = {Annales des Ponts et Chauss{\'{e}}es},
number = {11},
pages = {5--48},
title = {{Essai sur les digues maritimes verticales}},
volume = {98},
year = {1928}
}
@article{Saito2009,
author = {Saito, T. and Furumura, T.},
journal = {Geophys. J. Int.},
pages = {877--888},
title = {{Three-dimensional tsunami generation simulation due to sea-bottom deformation and its interpretation based on the linear theory}},
volume = {178},
year = {2009}
}
@book{Sakurai1993,
abstract = {This best-selling classic sets the standard for the quantum mechanics physics market. It provides a graduate-level, non-historical, modern introduction of quantum mechanical concepts for first year graduate students. The author was a noted theorist in particle theory, and was well renowned in his area of expertise. This revised edition retains the original material, but adds topics that extend its usefulness into the 21st century. Students will still find such classic developments as neutron interferometer experiments, Feyman path integrals, correlation measurements, and Bell's inequality. Updated material includes time independent perturbation theory for The Degenerate Case which can be found in 5. New supplementary material is at the end of the text.},
author = {Sakurai, J. J.},
isbn = {978-0201539295},
pages = {500},
publisher = {Addison Wesley},
title = {{Modern Quantum Mechanics}},
year = {1993}
}
@article{Salmon1988,
author = {Salmon, R.},
journal = {Ann. Rev. Fluid Mech.},
pages = {225--256},
title = {{Hamiltonian fluid mechanics}},
volume = {20},
year = {1988}
}
@article{Salmon1983,
author = {Salmon, R.},
journal = {J. Fluid Mech},
pages = {431--444},
title = {{Practical use of Hamilton's principle}},
volume = {132},
year = {1983}
}
@article{Salupere2003,
abstract = {The paper is focused on the details of the emergence of Korteweg-de Vries (KdV) solitons from an initial harmonic excitation. Although the problem is a classical one, numerical simulations over a large range of dispersion parameters in the long run have demonstrated new features: the existence of soliton ensembles including also virtual (hidden) solitons and the periodic patterns of the wave-profile maxima.},
author = {Salupere, A. and Engelbrecht, J. and Peterson, P.},
journal = {Math. Comp. Simul.},
keywords = {kdv solitons soliton ensembles soliton interaction},
number = {1-2},
pages = {137--147},
title = {{On the long-time behaviour of soliton ensembles}},
volume = {62},
year = {2003}
}
@book{Samarskii2001,
address = {New York},
author = {Samarskii, A. A.},
isbn = {978-0824704681},
pages = {788},
publisher = {CRC Press},
title = {{The Theory of Difference Schemes}},
year = {2001}
}
@article{Sammarco2008,
abstract = {A forced two-horizontal-dimension analytical model is developed to investigate the distinguishing physical features of landslide-induced tsunamis generated and propagating on a plane beach. The analytical solution is employed to study the wave field at small times after the landslide motion starts. At larger times, the occurrence of transient edge waves travelling along the shoreline is demonstrated, showing the differences with the transient waves propagating over a bottom of constant depth. Results are satisfactorily compared with available experimental data. Finally, the validity of non-forced numerical models is discussed.},
author = {Sammarco, P. and Renzi, E.},
doi = {10.1017/S0022112007009731},
issn = {0022-1120},
journal = {J. Fluid Mech},
month = {feb},
pages = {107--119},
title = {{Landslide tsunamis propagating along a plane beach}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112007009731},
volume = {598},
year = {2008}
}
@inproceedings{Sampl1993,
address = {Grenoble},
author = {Sampl, P.},
booktitle = {Comptes Rendus International Workshop on Gravitational Mass Movements},
editor = {Buisson, L},
pages = {269--278},
title = {{Current status of the AVL avalanche simulation model - Numerical simulation of dry snow avalanches}},
year = {1993}
}
@article{Sampl2004,
author = {Sampl, P. and Zwinger, T.},
journal = {Annals of Glaciology},
pages = {393--398},
title = {{Avalanche simulation with SAMOS}},
volume = {38(1)},
year = {2004}
}
@article{Sandee1991,
author = {Sandee, J. and Hutter, K.},
doi = {10.1007/BF01175953},
journal = {Acta Mechanica},
pages = {111--152},
title = {{On the development of the theory of the solitary wave. A historical essay}},
volume = {86},
year = {1991}
}
@incollection{Sanz-Sera1997,
address = {Oxford},
author = {Sanz-Serna, J.-M.},
booktitle = {The State of the Art in Numerical Analysis},
editor = {Duff, I S and Watson, G A},
pages = {121--143},
publisher = {Clarendon Press},
title = {{Geometric integration}},
year = {1997}
}
@article{Sapoval2004,
author = {Sapoval, B. and Baldassarri, A. and Gabrielli, A.},
journal = {Phys. Rev. Lett.},
pages = {98501},
title = {{Self-Stabilized Fractality of Seacoasts through Damped Erosion}},
volume = {93},
year = {2004}
}
@article{Sarri2012,
author = {Sarri, A. and Guillas, S. and Dias, F.},
doi = {10.5194/nhess-12-2003-2012},
issn = {1684-9981},
journal = {Nat. Hazards Earth Syst. Sci.},
month = {jun},
number = {6},
pages = {2003--2018},
title = {{Statistical emulation of a tsunami model for sensitivity analysis and uncertainty quantification}},
url = {http://www.nat-hazards-earth-syst-sci.net/12/2003/2012/},
volume = {12},
year = {2012}
}
@article{Satake1995,
abstract = {Numerical computations of tsunamis are made for the 1992 Nicaragua earthquake using different governing equations, bottom frictional values and bathymetry data. The results are compared with each other as well as with the observations, both tide gauge records and runup heights. Comparison of the observed and computed tsunami waveforms indicates that the use of detailed bathymetry data with a small grid size is more effective than to include nonlinear terms in tsunami computation. Linear computation overestimates the amplitude for the later phase than the first arrival, particularly when the amplitude becomes large. The computed amplitudes along the coast from nonlinear computation are much smaller than the observed tsunami runup heights; the average ratio, or the amplification factor, is estimated to be 3 in the present case when the grid size of 1 minute is used. The factor however may depend on the grid size for the computation.},
author = {Satake, K.},
doi = {10.1007/BF00874378},
issn = {0033-4553},
journal = {Pure Appl. Geophys.},
keywords = {Nicaragua earthquake,Tsunami,finite-difference method,numerical computation},
number = {3-4},
pages = {455--470},
title = {{Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami}},
url = {http://www.springerlink.com/index/10.1007/BF00874378},
volume = {144},
year = {1995}
}
@article{sat74,
author = {Sato, R. and Matsu'ura, M.},
journal = {J. Phys. Earth},
pages = {213--221},
title = {{Strains and tilts on the surface of a semi-infinite medium}},
volume = {22},
year = {1974}
}
@article{Savage1991,
author = {Savage, S. B. and Hutter, K.},
journal = {Acta Mechanica},
pages = {201--233},
title = {{The dynamics of avalanches of granular materials from initiation to runout, I: Analysis}},
volume = {86},
year = {1991}
}
@article{Savage1989,
author = {Savage, S. B. and Hutter, K.},
journal = {J. Fluid Mech.},
pages = {177--215},
title = {{The motion of a finite mass of granular material down a rough incline}},
volume = {199},
year = {1989}
}
@article{Scardovelli1999,
author = {Scardovelli, R. and Zaleski, S.},
journal = {Annu. Rev. Fluid Mech.},
pages = {567--603},
title = {{Direct Numerical Simulation of Free-Surface and Interfacial Flow}},
volume = {31},
year = {1999}
}
@article{Schaffer2008,
author = {Sch{\"{a}}ffer, H. A.},
doi = {10.1016/j.coastaleng.2007.11.002},
issn = {03783839},
journal = {Coastal Engineering},
keywords = {Dirichlet-Neuman operator,Dispersion,Higher-order spectral method,Nonlinearity,Perturbation expansion},
month = {apr},
number = {4},
pages = {288--294},
title = {{Comparison of Dirichlet-Neumann operator expansions for nonlinear surface gravity waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378383907001275},
volume = {55},
year = {2008}
}
@article{Schamel1973,
abstract = {The dependence of the asymptotic behaviour of small ion-acoustic waves on the number of resonant electrons is investigated by assuming an electron equation of state corresponding to the observed flat-topped electron distribution functions. The result is a modified Korteweg-de Vries equation with a stronger nonlinearity.},
author = {Schamel, H.},
doi = {10.1017/S002237780000756X},
issn = {0022-3778},
journal = {J. Plasma Phys.},
month = {mar},
number = {03},
pages = {377--387},
title = {{A modified Korteweg-de Vries equation for ion acoustic wavess due to resonant electrons}},
volume = {9},
year = {1973}
}
@article{Scheffers2010,
author = {Scheffers, A. and Kelletat, D. and Haslett, S. and Scheffers, S. and Browne, T.},
journal = {Zeitschrift f{\"{u}}r Geomorphologie},
number = {3},
pages = {247--279},
title = {{Coastal boulder deposits in Galway Bay and the Aran Islands, western Ireland}},
volume = {54},
year = {2010}
}
@article{Scheffers2009,
author = {Scheffers, A. and Scheffers, S. and Kelletat, D. and Browne, T.},
journal = {Journal of Geology},
number = {5},
pages = {553--573},
title = {{Wave-Emplaced Coarse Debris and Megaclasts in Ireland and Scotland: Boulder Transport in a High-Energy Littoral Environment}},
volume = {117},
year = {2009}
}
@article{Schiesser1994,
author = {Schiesser, W. E.},
doi = {10.1016/0898-1221(94)00190-1},
issn = {08981221},
journal = {Computers Mathematics with Applications},
keywords = {kdv,mol},
number = {10-12},
pages = {147--154},
title = {{Method of lines solution of the Korteweg-de vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0898122194001901},
volume = {28},
year = {1994}
}
@book{Schlichting2000,
address = {Berlin, Heidelberg},
author = {Schlichting, H. and Gersten, K.},
isbn = {978-3-540-66270-9},
pages = {800},
publisher = {Springer-Verlag},
title = {{Boundary-Layer Theory}},
year = {2000}
}
@incollection{Schmidt2005,
address = {Boca Raton, FL},
author = {Schmidt, E. J. P. G.},
booktitle = {Control Theory of Partial Differential Equations},
editor = {Imanuvilov, O. and Leugering, G. and Triggiani, R. and Zhang, B.-Y.},
pages = {207--212},
publisher = {Chapman {\&} Hall/CRC},
title = {{On Junctions in a Network of Canals}},
year = {2005}
}
@article{Schneider-98,
author = {Schneider, G.},
journal = {SIAM Journal on Applied Mathematics},
number = {4},
pages = {1237--1245},
title = {{The Long Wave Limit for a Boussinesq Equation}},
volume = {58},
year = {1998}
}
@article{Schneider2002,
abstract = {In a previous paper we proved that long-wavelength solutions of the waterwave problem in the case of zero Surface tension split up into two wave packets. one moving to the right and one to the left. where each of these wave packets evolves independently as a solution of a Kortewg-de Vries (KdV) equation. In this paper we examine the effect of surface tension on this scenario. We find that we obtain three different physical regimes depending on the strength of the surface tension. For weak surface tension. the propagation of the wave packets is very similar to that in the zero surface tension case. For strong nsurface tension, the evolution is again governed by a pair of KdV equations, but the coefficients in these equations have changed in such a way that the KdV soliton now represents a wave of depression on the fluid surface. Finally, at a special, intermediate value of the surface tension (where the Bond number equals (1)/(3)) the KdV description breaks down and it is necessary to introduce a new approximating$\backslash$nequation, the Kawahara equation. which is a fifth order. nonlinear$\backslash$npartial differential equation. In each of these regimes we give rigorous$\backslash$nestimates of the difference between the solution of the appropriate$\backslash$nmodulation equation and the Solution of the true water-wave problem.},
author = {Schneider, G. and Wayne, C. E.},
doi = {10.1007/s002050200190},
isbn = {0020502001},
issn = {00039527},
journal = {Arch. Rat. Mech. Anal.},
number = {3},
pages = {247--285},
title = {{The rigorous approximation of long-wavelength capillary-gravity waves}},
volume = {162},
year = {2002}
}
@article{Schober2008,
abstract = {Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space–time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge–Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the MS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of MS integrators in the nonlinear regime.},
author = {Schober, C. M. and Wlodarczyk, T. H.},
doi = {10.1016/j.jcp.2008.01.026},
issn = {00219991},
journal = {J. Comput. Phys},
keywords = {Box schemes,Dispersion relation,Double-pole soliton,Leapfrog method,Multisymplectic methods,Sine-Gordon equation},
month = {may},
number = {10},
pages = {5090--5104},
title = {{Dispersive properties of multisymplectic integrators}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999108000600},
volume = {227},
year = {2008}
}
@article{Scho,
author = {Schonbek, M. E.},
journal = {J. Diff. Eqns.},
pages = {325--352},
title = {{Existence of solutions for the Boussinesq system of equations}},
volume = {42},
year = {1981}
}
@book{Schultz1973,
abstract = {This book presents a unified and mathematically rigorous approach to the finite element method for solving continuous or indefinite-dimensional problems. It is designed for the reader with a background in calculus and linear algebra. The book contains sufficient practical and theoretical detail to enable one to implement the method intelligently.},
author = {Schultz, M. H.},
edition = {First},
isbn = {978-0138354053},
pages = {192},
publisher = {Prentice Hall},
title = {{Spline Analysis}},
year = {1973}
}
@article{Schumacher2003,
author = {Schumacher, J. and Sreenivasan, K. R.},
journal = {Phys. Rev. Lett.},
pages = {174501},
title = {{Geometric features of the mixing of passive scalars at high Schmidt numbers}},
volume = {91},
year = {2003}
}
@article{Scolan2010,
author = {Scolan, Y.-M.},
doi = {10.1016/j.jfluidstructs.2010.06.002},
issn = {08899746},
journal = {J. Fluids and Struct.},
month = {aug},
number = {6},
pages = {918--953},
title = {{Some aspects of the flip-through phenomenon: A numerical study based on the desingularized technique}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S088997461000071X},
volume = {26},
year = {2010}
}
@book{Scott2004,
address = {New-York},
author = {Scott, A.},
isbn = {1-579-58385-7},
pages = {850},
publisher = {Routledge},
title = {{Encyclopedia of Nonlinear Science}},
year = {2004}
}
@book{Scott2003,
abstract = {Much mathematical modeling has involved the assumption that physical systems are approximately linear, leading to the construction of equations which although relatively easy to solve, are unrealistic and overlook significant phenomena. Models assuming nonlinear systems however lead to the emergence of new structures that reflect reality much more closely. This second edition of Nonlinear Science places a strong emphasis on applications to realistic problems. It includes numerous new topics such as empirical results in molecular dynamics, solid-state physics, neuroscience, fluid dynamics, and biophysics; numerous new exercises and solutions; updated sections on nerve impulse dynamics, quantum theory of pump-probe measures, and local modes on lattices. With over 350 problems, including hints and solutions, this is an invaluable resource for graduate students and researchers in the applied sciences, mathematics, biology, physics and engineering.},
author = {Scott, A.},
edition = {2nd},
isbn = {978-0198528524},
pages = {504},
publisher = {Oxford University Press},
title = {{Nonlinear Science: Emergence and Dynamics of Coherent Structures}},
year = {2003}
}
@phdthesis{Seabra-Santos1985,
author = {Seabra-Santos, F. J.},
school = {Institut National Polytechnique de Grenoble},
title = {{Contribution {\`{a}} l'{\'{e}}tude des ondes de gravit{\'{e}} bidimensionnelles en eau peu profonde}},
year = {1985}
}
@article{Seabra-Santos1987,
author = {Seabra-Santos, F. J. and Renouard, D. P. and Temperville, A. M.},
journal = {J. Fluid Mech},
pages = {117--134},
title = {{Numerical and Experimental study of the transformation of a Solitary Wave over a Shelf or Isolated Obstacle}},
volume = {176},
year = {1987}
}
@article{Seabra-Santos1989,
author = {Seabra-Santos, F. J. and Temperville, A. M. and Renouard, D. P.},
journal = {Eur. J. Mech. B/Fluids},
number = {2},
pages = {103--115},
title = {{On the weak interaction of two solitary waves}},
volume = {8},
year = {1989}
}
@article{Sedletsky2003,
abstract = {The method of multiple scales is used to derive the fourth-order nonlinear Schr{\"{o}}dinger equation (NSEIV) that describes the amplitude modulations of the fundamental harmonic of Stokes waves on the surface of a medium-and large-depth (compared to the wavelength) fluid layer. The new terms of this equation describe the third-order linear dispersion effect and the nonlinearity dispersion effects. As the nonlinearity and the dispersion decrease, the equation uniformly transforms into the nonlinear Schr{\"{o}}dinger equation for Stokes waves on the surface of a finite-depth fluid that was first derived by Hasimoto and Ono. The coefficients of the derived equation are given in an explicit form as functions of kh (h is the fluid depth, and k is the wave number). As kh tends to infinity, these coefficients transform into the coefficients of the NSEIV that was first derived by Dysthe for an infinite depth.},
author = {Sedletsky, Yu. V.},
doi = {10.1134/1.1600810},
issn = {1063-7761},
journal = {JETP Lett.},
month = {jul},
number = {1},
pages = {180--193},
title = {{The fourth-order nonlinear Schr{\"{o}}dinger equation for the envelope of Stokes waves on the surface of a finite-depth fluid}},
url = {http://link.springer.com/10.1134/1.1600810},
volume = {97},
year = {2003}
}
@article{Seguin2012,
author = {Seguin, N. and Andreianov, B.},
doi = {10.3934/dcds.2012.32.1939},
issn = {1078-0947},
journal = {Discrete Contin. Dynam. Syst. Ser. A},
month = {feb},
number = {6},
pages = {1939--1964},
title = {{Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes}},
url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=6983},
volume = {32},
year = {2012}
}
@article{Segur1973,
abstract = {The method of solution of the Korteweg–de Vries equation outlined by Gardner et al. (1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.},
author = {Segur, H.},
doi = {10.1017/S0022112073001813},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
pages = {721--736},
title = {{The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112073001813},
volume = {59},
year = {1973}
}
@incollection{Segur2007a,
author = {Segur, H.},
booktitle = {Tsunami and Nonlinear waves},
editor = {Kundu, A.},
pages = {3--29},
publisher = {Springer},
title = {{Waves in shallow water, with emphasis on the tsunami of 2004}},
year = {2007}
}
@incollection{Segur2007,
address = {New York},
author = {Segur, H.},
booktitle = {Tsunamis and Nonlinear waves},
editor = {Kundu, A.},
pages = {3--29},
publisher = {Springer},
title = {{Waves in shallow water, with emphasis on the tsunami of 2004}},
year = {2007}
}
@article{Segur2005,
author = {Segur, H. and Henderson, D. and Carter, J. D. and Hammack, J. and Li, C. and Pheiff, D. and Socha, K.},
journal = {J. Fluid Mech.},
pages = {229--271},
title = {{Stabilizing the Benjamin-Feir instability}},
volume = {539},
year = {2005}
}
@article{Seliger1968,
author = {Seliger, R. L. and Whitham, G. B.},
journal = {Proc. R. Soc. Lond. A},
pages = {1--25},
title = {{Variational principle in continuous mechanics}},
volume = {305},
year = {1968}
}
@article{Sen1978,
author = {Sen, A. and Karney, C. F. F. and Johnston, G. L. and Bers, A.},
doi = {10.1088/0029-5515/18/2/002},
issn = {0029-5515},
journal = {Nuclear Fusion},
month = {feb},
number = {2},
pages = {171--179},
title = {{Three-dimensional effects in the non-linear propagation of lower-hybrid waves}},
url = {http://stacks.iop.org/0029-5515/18/i=2/a=002?key=crossref.1640b4db84ee67ed153371fa49902c9f},
volume = {18},
year = {1978}
}
@book{Senechal1995,
abstract = {Quasicrystals and Geometry brings together for the first time the many strands of contemporary research in quasicrystal geometry and weaves them into a coherent whole. The author describes the historical and scientific context of this work, and carefully explains what has been proved and what is conjectured. This, together with a bibliography of over 250 references, provides a solid background for further study. The discovery in 1984 of crystals with 'forbidden' symmetry posed fascinating and challenging problems in many fields of mathematics, as well as in the solid state sciences. Increasingly, mathematicians and physicists are becoming intrigued by the quasicrystal phenomenon, and the result has been an exponential growth in the literature on the geometry of diffraction patterns, the behaviour of the Fibonacci and other nonperiodic sequences, and the fascinating properties of the Penrose tilings and their many relatives.},
address = {Cambridge},
author = {Senechal, M.},
isbn = {978-0521575416},
pages = {286},
publisher = {Cambridge University Press},
title = {{Quasicrystals and geometry}},
year = {1995}
}
@article{Seo2013,
author = {Seo, S.-N. and Liu, P. L.-F.},
doi = {10.1016/j.coastaleng.2012.10.008},
issn = {03783839},
journal = {Coastal Engineering},
month = {mar},
pages = {133--150},
title = {{Edge waves generated by the landslide on a sloping beach}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0378383912001652},
volume = {73},
year = {2013}
}
@article{Sergeeva2011,
abstract = {The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.},
author = {Sergeeva, A. and Pelinovsky, E. and Talipova, T.},
doi = {10.5194/nhess-11-323-2011},
issn = {1684-9981},
journal = {Nat. Hazards Earth Syst. Sci.},
month = {feb},
number = {2},
pages = {323--330},
title = {{Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework}},
url = {http://www.nat-hazards-earth-syst-sci.net/11/323/2011/},
volume = {11},
year = {2011}
}
@article{Serre1991,
author = {Serre, D.},
journal = {Phys. D},
number = {1},
pages = {113--128},
title = {{Variations de grande amplitude pour la densit{\'{e}} d'un fluide visqueux compressible}},
volume = {48},
year = {1991}
}
@article{Serre1953a,
author = {Serre, F.},
journal = {La Houille blanche},
pages = {830--872},
title = {{Contribution {\`{a}} l'{\'{e}}tude des {\'{e}}coulements permanents et variables dans les canaux}},
volume = {8},
year = {1953}
}
@article{Serre1953,
author = {Serre, F.},
journal = {La Houille blanche},
pages = {374--388},
title = {{Contribution {\`{a}} l'{\'{e}}tude des {\'{e}}coulements permanents et variables dans les canaux}},
volume = {8},
year = {1953}
}
@article{Serre1956,
author = {Serre, F.},
journal = {La Houille blanche},
pages = {375--390},
title = {{Contribution to the study of long irrotational waves}},
volume = {3},
year = {1956}
}
@techreport{Shabat2005,
abstract = {This is a preliminary version of the Chapter 1 of a book "Computable Integrability"},
address = {Linz},
author = {Shabat, A. B. and Kartashova, E.},
institution = {RISC, JKU Linz},
pages = {24},
title = {{Computable Integrability. Chapter 1: General notions and ideas}},
year = {2005}
}
@article{Shampine1994,
author = {Shampine, L. F.},
doi = {10.1002/num.1690100608},
issn = {0749159X},
journal = {Numerical Methods for Partial Differential Equations},
number = {6},
pages = {739--755},
title = {{ODE solvers and the method of lines}},
url = {http://doi.wiley.com/10.1002/num.1690100608},
volume = {10},
year = {1994}
}
@article{Shampine1997,
author = {Shampine, L. F. and Reichelt, M. W.},
journal = {SIAM Journal on Scientific Computing},
pages = {1--22},
title = {{The MATLAB ODE Suite}},
volume = {18},
year = {1997}
}
@article{Shao2003,
author = {Shao, S. and Lo, E. Y. M.},
journal = {Advances in Water Resources},
pages = {787--800},
title = {{Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface}},
volume = {26},
year = {2003}
}
@article{Shemer2013,
abstract = {Experiments on extremely steep deterministic waves generated in a large wave tank by focusing of a broad-banded wave train serve as a motivation for the theoretical analysis of the conditions leading to wave breaking. Particular attention is given to the crest of the steepest wave where both the horizontal velocity and the vertical acceleration attain their maxima. Analysis is carried out up to the third order in wave steepness. The apparent, Eulerian and Lagrangian accelerations are computed for wave parameters observed in experiments. It is demonstrated that for a wave group with a wide spectrum, the crest propagation velocity differs significantly from both the phase and the group velocities of the peak wave. Conclusions are drawn regarding the applicability of various criteria for wave breaking.},
author = {Shemer, L.},
doi = {10.5194/nhess-13-2101-2013},
issn = {1684-9981},
journal = {Nat. Hazards Earth Syst. Sci.},
month = {aug},
number = {8},
pages = {2101--2107},
title = {{On kinematics of very steep waves}},
url = {http://www.nat-hazards-earth-syst-sci.net/13/2101/2013/},
volume = {13},
year = {2013}
}
@article{Shemer2014,
author = {Shemer, L. and Liberzon, D.},
doi = {10.1063/1.4860235},
issn = {1070-6631},
journal = {Phys. Fluids},
month = {jan},
number = {1},
pages = {016601},
title = {{Lagrangian kinematics of steep waves up to the inception of a spilling breaker}},
url = {http://scitation.aip.org/content/aip/journal/pof2/26/1/10.1063/1.4860235},
volume = {26},
year = {2014}
}
@article{Shemer2009,
author = {Shemer, L. and Sergeeva, A.},
doi = {10.1029/2008JC005077},
issn = {0148-0227},
journal = {J. Geophys. Res.},
month = {jan},
number = {C1},
pages = {C01015},
title = {{An experimental study of spatial evolution of statistical parameters in a unidirectional narrow-banded random wavefield}},
url = {http://doi.wiley.com/10.1029/2008JC005077},
volume = {114},
year = {2009}
}
@article{Shemer2010a,
author = {Shemer, L. and Sergeeva, A. and Liberzon, D.},
doi = {10.1029/2010JC006326},
issn = {0148-0227},
journal = {J. Geophys. Res.},
month = {dec},
number = {C12},
pages = {C12039},
title = {{Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves}},
volume = {115},
year = {2010}
}
@article{Shemer2010,
author = {Shemer, L. and Sergeeva, A. and Slunyaev, A.},
journal = {Phys. Fluids},
number = {1},
pages = {016601},
title = {{Applicability of envelope model equations for simulation of narrow-spectrum unidirectional random wave field evolution: Experimental validation}},
volume = {22},
year = {2010}
}
@inproceedings{Shepard1968,
abstract = {In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface. These irregularly-spaced locations, hence referred to as “data points,” may have diverse meanings: in meterology, weather observation stations; in geography, surveyed locations; in city and regional planning, centers of data-collection zones; in biology, observation locations. It is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point. In order to display these data in some type of contour map or perspective view, to compare them with data for the same region based on other data points, or to analyze them for extremes, gradients, or other purposes, it is extremely useful, if not essential, to define a continuous function fitting the given values exactly. Interpolated values over a fine grid may then be evaluated. In using such a function it is assumed that the original data are without error, or that compensation for error will be made after interpolation.},
author = {Shepard, D.},
booktitle = {23rd ACM national conference},
doi = {10.1145/800186.810616},
isbn = {1-59593-161-9},
pages = {517--524},
title = {{A two-dimensional interpolation function for irregularly-spaced data}},
year = {1968}
}
@article{Shepherd1990,
author = {Shepherd, T. G.},
journal = {Adv. Geophys},
pages = {287--338},
title = {{Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics}},
volume = {32},
year = {1990}
}
@article{Shi2012,
author = {Shi, F. and Kirby, J. T. and Harris, J. C. and Geiman, J. D. and Grilli, S. T.},
doi = {10.1016/j.ocemod.2011.12.004},
journal = {Ocean Modelling},
pages = {36--51},
title = {{A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation}},
url = {http://www.sciencedirect.com/science/article/pii/S1463500311002010},
volume = {43-44},
year = {2012}
}
@article{Shi2011,
author = {Shi, H. and Xie, G.},
doi = {10.1155/2011/735248},
issn = {1024-123X},
journal = {Math. Prob. Eng.},
pages = {1--13},
title = {{Collective Dynamics of Swarms with a New Attraction/Repulsion Function}},
url = {http://www.hindawi.com/journals/mpe/2011/735248/},
year = {2011}
}
@article{SMi,
author = {Shiach, J. B. and Mingham, C. G.},
journal = {Coastal Engineering},
pages = {32--45},
title = {{A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations}},
volume = {56},
year = {2009}
}
@article{Shin2004,
author = {Shin, J. O. and Dalziel, S. B. and Linden, P. F.},
journal = {J. Fluid Mech.},
pages = {1--34},
title = {{Gravity currents produced by lock exchange}},
volume = {521},
year = {2004}
}
@article{Shkadov1970,
author = {Shkadov, V. Ya.},
doi = {10.1007/BF01024797},
issn = {0015-4628},
journal = {Fluid Dynamics},
number = {1},
pages = {29--34},
title = {{Wave flow regimes of a thin layer of viscous fluid subject to gravity}},
url = {http://link.springer.com/10.1007/BF01024797},
volume = {2},
year = {1970}
}
@article{Shkadov1971,
author = {Shkadov, V. Ya.},
doi = {10.1007/BF01013543},
issn = {0015-4628},
journal = {Fluid Dynamics},
number = {2},
pages = {12--15},
title = {{Wave-flow theory for a thin viscous liquid layer}},
url = {http://link.springer.com/10.1007/BF01013543},
volume = {3},
year = {1971}
}
@article{Shokin2007,
author = {Shokin, Yu. I. and Fedotova, Z. I. and Khakimzyanov, G. S. and Chubarov, L. B. and Beisel, S. A.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {1},
pages = {63--85},
title = {{Modelling surface waves generated by a moving landslide with allowance for vertical flow structure}},
volume = {22},
year = {2007}
}
@article{Shokin2006,
abstract = {In this paper we consider an explicit difference predictor-corrector scheme of the second order of approximation for solving one-dimensional nonlinear shallow water equations, which yields nonoscillating profiles of discontinuous solutions with the proposed choice of the approximation viscosity of the scheme. For linearized shallow water equations the proposed scheme retains the Riemann invariants monotonicity. The choice of approximation viscosity is based on the study of the dispersion of the differential approximation of the scheme for a one-dimensional scalar equation. We give the generalization of the scheme to the case of movable grids. The proposed scheme has properties similar to those of the known TVD schemes with minmod-type limiters [3].},
author = {Shokin, Yu. I. and Sergeeva, Yu. V. and Khakimzyanov, G. S.},
doi = {10.1515/156939806779801957},
issn = {0927-6467},
journal = {Russ. J. Numer. Anal. Math. Modelling},
month = {jan},
number = {5},
pages = {459--479},
title = {{Predictor-corrector scheme for the solution of shallow water equations}},
volume = {21},
year = {2006}
}
@article{Shokin2005,
author = {Shokin, Yu. I. and Sergeeva, Yu. V. and Khakimzyanov, G. S.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {5},
pages = {463--481},
title = {{Construction of monotonic schemes by the differential approximation method}},
volume = {20},
year = {2005}
}
@article{Shu1988,
author = {Shu, C.-W.},
journal = {SIAM J. Sci. Statist. Comput.},
pages = {1073--1084},
title = {{Total-variation-diminishing time discretizations}},
volume = {9},
year = {1988}
}
@inproceedings{shu,
author = {Shu, C.-W.},
booktitle = {Advanced Numerical Approximation of Nonlinear Hyperbolic Equations},
pages = {325--432},
publisher = {Springer Berlin / Heidelberg},
title = {{Essentially non-oscillatory and weighted Essentially non-oscillatory schemes for hyperbolic conservation laws}},
year = {1997}
}
@article{Shu1988a,
author = {Shu, C.-W. and Osher, S.},
journal = {J. Comput. Phys.},
pages = {439--471},
title = {{Efficient implementation of essentially non-oscillatory shock-capturing schemes}},
volume = {77},
year = {1988}
}
@article{Shukla2006,
author = {Shukla, P. K. and Kourakis, I. and Eliasson, B. and Marklund, M. and Stenflo, L.},
journal = {Phys. Rev. Lett.},
pages = {094501},
title = {{Instability and evolution of nonlinearly interacting water waves}},
volume = {97},
year = {2006}
}
@book{Shurgalina2012,
address = {Saarbrucken},
author = {Shurgalina, E. G. and Pelinovsky, E. N.},
pages = {110},
publisher = {LAP LAMBERT Academic Publishing},
title = {{Dynamics of random ensembles of free surface gravity waves}},
year = {2012}
}
@article{Shyue1998,
author = {Shyue, K. M.},
journal = {J. Comput. Phys.},
pages = {208--242},
title = {{An efficient shock-capturing algorithm for compressible multicomponent problems}},
volume = {142},
year = {1998}
}
@book{Silin1971,
address = {Moscow},
author = {Silin, V. P.},
edition = {1},
publisher = {Nauka},
title = {{Introduction to the kinetic theory of gases}},
year = {1971}
}
@article{Simarro2013,
author = {Simarro, G.},
doi = {10.1016/j.ocemod.2013.08.004},
issn = {14635003},
journal = {Ocean Modelling},
month = {dec},
pages = {74--79},
title = {{Energy balance, wave shoaling and group celerity in Boussinesq-type wave propagation models}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S146350031300142X},
volume = {72},
year = {2013}
}
@article{Simmen1985,
author = {Simmen, J. A. and Saffman, P. G.},
journal = {Stud. Appl. Math.},
pages = {35--57},
title = {{Steady deep-water waves on a linear shear current}},
volume = {73},
year = {1985}
}
@article{Simon1981,
author = {Simon, M. J.},
journal = {Journal of Fluid Mechanics},
pages = {159--187},
title = {{Wave-energy extraction by a submerged cylindrical resonant duct}},
volume = {104},
year = {1981}
}
@book{Singh1996,
author = {Singh, V. P.},
publisher = {Kluwer Academic Publishers, Dordrecht},
title = {{Dam Breach Modelling Technology}},
year = {1996}
}
@article{Sirovich1987,
author = {Sirovich, L.},
journal = {Quarterly of Applied Mathematics},
pages = {561--590},
title = {{Turbulence and the dynamics of coherent structures: Parts I-III}},
volume = {45},
year = {1987}
}
@article{Skandrani,
author = {Skandrani, C. and Kharif, C. and Poitevin, J.},
journal = {Contemp. Math.},
pages = {157--171},
title = {{Nonlinear evolution of water surface waves: the frequency down-shift phenomenon}},
volume = {200},
year = {1996}
}
@article{Slunyaev2010,
author = {Slunyaev, A.},
journal = {Eur. Phys. J. Special Topics},
pages = {67--80},
title = {{Freak wave events and the wave phase coherence}},
volume = {185},
year = {2010}
}
@article{Slunyaev2005,
author = {Slunyaev, A. V.},
journal = {JETP Lett.},
number = {5},
pages = {926--941},
title = {{A high-order nonlinear envelope equation for gravity waves in finite-depth water}},
volume = {101},
year = {2005}
}
@article{Slunyaev2011,
abstract = {In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for sailing and sea use. A number of huge wave accidents, resulting in damages, ship losses and people injuries and deaths, are known. Now marine researchers do believe that these waves belong to a specific kind of sea wave, not taken into account by conventional models for sea wind waves. This paper addresses the nature of the rogue wave problem from a general viewpoint based on wave process ideas. We start by introducing some primitive elements of sea wave physics with the purpose of paving the way for further discussion. We discuss linear physical mechanisms which are responsible for high wave formation, at first. Then, we proceed with a description of different sea conditions, starting from the open deep sea, and approaching the sea coast. Nonlinear effects which are able to cause rogue waves are emphasised. In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear optics.},
author = {Slunyaev, A. and Didenkulova, I. and Pelinovsky, E.},
journal = {Contemporary Physics},
number = {6},
pages = {571--590},
title = {{Rogue waters}},
volume = {52},
year = {2011}
}
@article{Slunyaev2002,
abstract = {The problem of freak wave formation on water of finite depth is discussed. Dispersive focusing in a nonlinear medium is suggested as a possible mechanism of giant wave generation. This effect is considered within the framework of the nonlinear Schr{\"{o}}dinger equation and the DaveyStewartson system, describing 2+1-dimensional surfacewave groups onwater of finite depth. In the 2 +1-dimensional case, the dispersive grouping is accompanied with a geometrical focusing. Necessary wave conditions for the occurrence of such a phenomenon are discussed. Influence of non-optimal phase modulation and presence of strong random wave component are found to be weak: they do not cancel the mechanism of wave amplification. The mechanism of dispersive focusing is compared with the wave enhancement due to the BenjaminFeir instability, which is found to be extremely sensitive with respect to weak random perturbations.},
author = {Slunyaev, A. and Kharif, C. and Pelinovsky, E. and Talipova, T.},
doi = {10.1016/S0167-2789(02)00662-0},
issn = {01672789},
journal = {Physica D: Nonlinear Phenomena},
keywords = {davey,dispersive focusing,freak waves,modulational instability,nonlinear focusing,rogue waves,stewartson equations},
number = {1-2},
pages = {77--96},
title = {{Nonlinear wave focusing on water of finite depth}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0167278902006620},
volume = {173},
year = {2002}
}
@article{Slunyaev2011a,
author = {Slunyaev, A. and Sergeeva, A.},
journal = {JETP Lett.},
number = {10},
pages = {843--851},
title = {{Stochastic simulations of unidirectional intense waves in deep water applied to turbulence}},
volume = {94},
year = {2011}
}
@article{Smith1982,
author = {Smith, F. T. and Bodonyi, R. J.},
doi = {10.1098/rspa.1982.0168},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {dec},
number = {1787},
pages = {463--489},
title = {{Amplitude-Dependent Neutral Modes in the Hagen-Poiseuille Flow Through a Circular Pipe}},
volume = {384},
year = {1982}
}
@article{Smith1990,
author = {Smith, F. T. and Doorly, D. J. and Rothmayer, A. P.},
doi = {10.1098/rspa.1990.0034},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {apr},
number = {1875},
pages = {255--281},
title = {{On Displacement-Thickness, Wall-Layer and Mid-Flow Scales in Turbulent Boundary Layers, and Slugs of Vorticity in Channel and Pipe Flows}},
volume = {428},
year = {1990}
}
@book{Smoller1994,
abstract = {The purpose of this book is to make easily available the basics of the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley. It presents the modern ideas in these fields in a way that is accessible to a wider audience than just mathematicians. The book is divided into four main parts: linear theory, reaction-diffusion equations, shock-wave theory, and the Conley index. For the second edition numerous typographical errors and other mistakes have been corrected and a new chapter on recent results has been added. The new chapter contains discussions of the stability of traveling waves, symmetry-breaking bifurcations, compensated compactness, viscous profiles for shock waves, and general notions for construction traveling-wave solutions for systems of nonlinear equations.},
author = {Smoller, J.},
edition = {2nd},
publisher = {Springer, Berlin},
title = {{Shock waves and Reaction-Diffusion Equations}},
year = {1994}
}
@article{smylie,
author = {Smylie, D. E. and Mansinha, L.},
journal = {Geophys. J.R. Astr. Soc.},
pages = {329--354},
title = {{The elasticity theory of dislocations in real earth models and changes in the rotation of the earth}},
volume = {23},
year = {1971}
}
@article{Socquet-Juglard2005,
author = {Socquet-Juglard, H. and Dysthe, K. B. and Trulsen, K. and Krogstad, H. E. and Liu, J.},
journal = {J. Fluid Mech.},
pages = {195--216},
title = {{Probability distributions of surface gravity waves during spectral changes}},
volume = {542},
year = {2005}
}
@article{Sod1978,
author = {Sod, G. A.},
journal = {J. Comput. Phys.},
pages = {1--31},
title = {{A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws}},
volume = {43},
year = {1978}
}
@article{Soderlind2003,
author = {S{\"{o}}derlind, G.},
journal = {ACM Trans. Math. Software},
pages = {1--26},
title = {{Digital filters in adaptive time-stepping}},
volume = {29},
year = {2003}
}
@article{Soderlind2006,
author = {S{\"{o}}derlind, G. and Wang, L.},
journal = {J. Comp. Appl. Math.},
pages = {225--243},
title = {{Adaptive time-stepping and computational stability}},
volume = {185(2)},
year = {2006}
}
@book{sokol,
author = {Sokolnikoff, I. S. and Specht, R. D.},
publisher = {McGraw-Hill, New York},
title = {{Mathematical theory of elasticity}},
year = {1946}
}
@article{Solli2007,
author = {Solli, D. R. and Ropers, C. and Koonath, P. and Jalali, B.},
journal = {Nature},
pages = {1054--1058},
title = {{Optical rogue waves}},
volume = {450},
year = {2007}
}
@article{Song2008,
author = {Song, Y. T. and Fu, L.-L. and Zlotnicki, V. and Ji, C. and Hjorleifsdottir, V. and Shum, C. K. and Yi, Y.},
journal = {Ocean Modelling},
pages = {362--379},
title = {{The role of horizontal impulses of the faulting continental slope in generating the 26 December 2004 tsunami}},
volume = {20},
year = {2008}
}
@article{Song2006,
abstract = {Two physical parameters are introduced into the basic ocean equations to generalize numerical ocean models for various vertical coordinate systems and their hybrid features. The two parameters are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara [Kasahara, A., 1974. Various vertical coordinate systems used for numerical weather prediction. Mon. Weather Rev. 102, 509 522], the Jacobian pressure gradient formulation of Song [Song, Y.T., 1998. A general pressure gradient formation for ocean models. Part I: Scheme design and diagnostic analysis. Mon. Weather Rev. 126 (12), 3213 3230], and a newly introduced parametric function that permits both Boussinesq (volume-conserving) and non-Boussinesq (mass-conserving) conditions. Based on this new formulation, a generalized modeling approach is proposed. Several representative oceanographic problems with different scales and characteristics coastal canyon, seamount topography, non-Boussinesq Pacific Ocean with nested eastern Tropics, and a global ocean model have been used to demonstrate the model’s capabilities for multiscale applications. The inclusion of non-Boussinesq physics in the topography-following ocean model does not incur computational expense, but more faithfully represents satellite-observed ocean-bottom-pressure data. Such a generalized modeling approach is expected to benefit oceanographers in solving multiscale ocean-related problems by using various coordinate systems on the same numerical platform.},
author = {Song, Y. T. and Hou, T. Y.},
doi = {10.1016/j.ocemod.2005.01.001},
issn = {14635003},
journal = {Ocean Modelling},
month = {jan},
number = {3-4},
pages = {298--332},
title = {{Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1463500305000107},
volume = {11},
year = {2006}
}
@book{Sorensen1997,
author = {Sorensen, R. M.},
publisher = {Springer},
title = {{Basic coastal engineering}},
year = {1997}
}
@book{Souriau1997,
address = {New York},
author = {Souriau, J.-M.},
pages = {406},
publisher = {Springer},
title = {{Structure of Dynamical Systems: a Symplectic View of Physics}},
year = {1997}
}
@article{Spiteri2002,
author = {Spiteri, R. J. and Ruuth, S. J.},
journal = {SIAM Journal on Numerical Analysis},
pages = {469--491},
title = {{A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods}},
volume = {40},
year = {2002}
}
@article{SVBM2002,
author = {Spivak, B. and Vanden-Broeck, J.-M. and Miloh, T.},
journal = {European Journal of Mechanics B-Fluids},
pages = {207--224},
title = {{Free-surface wave damping due to viscosity and surfactants}},
volume = {21},
year = {2002}
}
@book{Spivak1971,
address = {Princeton},
author = {Spivak, M.},
isbn = {978-0805390216},
pages = {160},
publisher = {Westview Press},
title = {{Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus}},
year = {1971}
}
@article{Sreenivasan1999,
abstract = {Nonlinear fluid simulations are developed by us to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a very dense Fermi (quantum) plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations (EPO) is determined critically by a ratio of the energy density of the EPOs and the electron kinetic energy density of quantum plasmas. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory.},
author = {Sreenivasan, K. R.},
doi = {10.1103/RevModPhys.71.S383},
issn = {00346861},
journal = {Reviews of Modern Physics},
number = {2},
pages = {S383--------S395},
pmid = {17930512},
publisher = {American Physical Society},
title = {{Fluid turbulence}},
url = {http://link.aps.org/doi/10.1103/RevModPhys.71.S383},
volume = {71},
year = {1999}
}
@book{Sretenskii1977,
author = {Sretenskii, L. N.},
publisher = {Moscow, Izdatel'stvo Nauka},
title = {{Theory of wave motions in a fluid}},
year = {1977}
}
@article{Staedtke2005,
author = {Staedtke, H. and Franchello, G. and Worth, B. and Graf, U. and Romstedt, P. and Kumbaro, A. and Garcia-Cascales, J. and Paill{\`{e}}re, H. and Deconinck, H. and Ricchiuto, M. and Smith, B. and {De Cachard}, F. and Toro, E. F. and Romesnki, E. and Mimouni, S.},
journal = {Nuclear Engineering and Design},
pages = {379--400},
title = {{Advanced three-dimensional two-phase flow simulation tools for application to reactor safety (ASTAR)}},
volume = {235},
year = {2005}
}
@article{Stansby1998,
abstract = {Experiments have been undertaken to investigate dam-break flows where a thin plate separating water at different levels is withdrawn impulsively in a vertically upwards direction. Depth ratios of 0, 0.1 and 0.45 were investigated for two larger depth values of 10 cm and 36 cm. The resulting sequence of surface profiles is shown to satisfy approximately Froude scaling. For the dry-bed case a horizontal jet forms at small times and for the other cases a vertical, mushroom-like jet occurs, none of which have been observed previously. We analyse the initial-release problem in which the plate is instantaneously removed or dissolved. Although this shows singular behaviour, jet-like formations are predicted. Artificially smoothing out the singularity enables a fully nonlinear, potential-flow computation to follow the jet formation for small times. There is qualitative agreement between theory and experiment. In the experiments, after a bore has developed downstream as a result of highly complex flow interactions, the surface profiles agree remarkably well with exact solutions of the shallow-water equations which assume hydrostatic pressure and uniform velocity over depth.},
author = {Stansby, P. K. and Chegini, A. and Barnes, T. C. D.},
journal = {J. Fluid Mech.},
pages = {407--424},
title = {{The initial stages of dam-break flow}},
volume = {374},
year = {1998}
}
@article{Starr1947,
author = {Starr, V. P.},
journal = {J. Mar. Res.},
pages = {175--193},
title = {{Momentum and energy integrals for gravity waves of finite height}},
volume = {6},
year = {1947}
}
@article{Stefanakis2011,
abstract = {Until now, the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the nonlinear shallow water equations are used to investigate the boundary value problem for plane and nontrivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the boundary value problem. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced run-up of nonleading waves. The evolution of energy reveals the existence of a quasiperiodic state for the case of sinusoidal waves. Dispersion is found to slightly reduce the value of maximum run-up but not to change the overall picture. Run-up amplification occurs for both leading elevation and depression waves.},
author = {Stefanakis, T. and Dias, F. and Dutykh, D.},
doi = {10.1103/PhysRevLett.107.124502},
journal = {Phys. Rev. Lett.},
pages = {124502},
title = {{Local Runup Amplification by Resonant Wave Interactions}},
volume = {107},
year = {2011}
}
@inproceedings{Stefanakis2012,
address = {Rhodes, Greece},
author = {Stefanakis, T. and Dias, F. and Dutykh, D.},
booktitle = {Proceedings of the Twenty-second International Offshore and Polar Engineering Conference},
title = {{Resonant Long-Wave Run-Up On A Plane Beach}},
year = {2012}
}
@article{Stefanakis2013,
abstract = {The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier {\&} Greenspan, 1958). Then, using numerical simulations, we build on the work of Stefanakis et al. (2011) for an infinite sloping beach and we find that resonant run-up amplification of monochromatic waves is robust to spectral perturbations of the incoming wave and resonant regimes do exist for certain values of the frequency. In the setting of a finite beach attached to a constant depth region, resonance can only be observed when the incoming wavelength is larger than the distance from the undisturbed shoreline to the seaward boundary. Wavefront steepness is also found to play a role in wave run-up, with steeper waves reaching higher run-up values.},
archivePrefix = {arXiv},
arxivId = {1212.5689},
author = {Stefanakis, T. and Xu, S. and Dutykh, D. and Dias, F.},
eprint = {1212.5689},
journal = {Submitted},
title = {{Run-up amplification of transient long waves}},
url = {http://arxiv.org/abs/1212.5689},
year = {2013}
}
@article{stek2,
author = {Steketee, J. A.},
journal = {Can. J. Phys.},
pages = {192--205},
title = {{On Volterra's dislocation in a semi-infinite elastic medium}},
volume = {36},
year = {1958}
}
@phdthesis{Stephan2010,
author = {Stephan, L.},
school = {Universit{\'{e}} de Savoie},
title = {{Mod{\'{e}}lisation de la ventilation naturelle pour l'optimisation du rafra{\^{\i}}chissement passif des b{\^{a}}timents}},
year = {2010}
}
@article{Stevenson2005,
author = {Stevenson, D. J.},
journal = {Physics Today},
pages = {10--11},
title = {{Tsunamis and Earthquakes: What Physics is interesting?}},
volume = {June},
year = {2005}
}
@article{Stewart1984,
author = {Stewart, H. B. and Wendroff, B.},
journal = {J. Comput. Phys},
pages = {363--409},
title = {{Two-phase flows: models and methods}},
volume = {56},
year = {1984}
}
@article{Stiassnie1984a,
abstract = {It is shown that Zakharov's integral equation yields the modified Schr{\"{o}}dinger equation for the particular case of a narrow spectrum.},
author = {Stiassnie, M.},
doi = {10.1016/0165-2125(84)90043-X},
issn = {01652125},
journal = {Wave Motion},
month = {jul},
number = {4},
pages = {431--433},
title = {{Note on the modified nonlinear Schr{\"{o}}dinger equation for deep water waves}},
url = {http://linkinghub.elsevier.com/retrieve/pii/016521258490043X},
volume = {6},
year = {1984}
}
@article{Stiassnie2009,
author = {Stiassnie, M. and Gramstad, O.},
journal = {J. Fluid Mech.},
pages = {433--442},
title = {{On Zakharov's kernel and the interaction of non-collinear wavetrains in finite water depth}},
volume = {639},
year = {2009}
}
@article{Stiassnie1984,
author = {Stiassnie, M. and Shemer, L.},
journal = {J. Fluid Mech},
pages = {47--67},
title = {{On modifications of the Zakharov equation for surface gravity waves}},
volume = {143},
year = {1984}
}
@article{Stiassnie2005,
abstract = {The mathematical and statistical properties of the evolution of a system of four interacting surface gravity waves are investigated in detail. Any deterministic quartet of waves is shown to evolve recurrently, but the ensemble averages taken over many realizations with random initial conditions reach constant asymptotic values. The characteristic time-scale for which such asymptotic values are approached is extremely large when randomness is introduced through the initial phases. The characteristic time-scale becomes of an order comparable to that of the recurrence periods when beside the random initial phases, the initial amplitudes are taken to be Rayleigh-distributed. The ensemble-averaged results in the second case resemble, to a certain extent, those derived from the kinetic equation.},
author = {Stiassnie, M. and Shemer, L.},
doi = {10.1016/j.wavemoti.2004.07.002},
issn = {01652125},
journal = {Wave Motion},
keywords = {Kinetic equation,Nonlinear interactions,Water waves},
month = {apr},
number = {4},
pages = {307--328},
title = {{On the interaction of four water-waves}},
volume = {41},
year = {2005}
}
@book{Stoker1957,
address = {New York},
author = {Stoker, J. J.},
publisher = {Interscience},
title = {{Water Waves: The mathematical theory with applications}},
year = {1957}
}
@book{Stoker1958b,
address = {Hoboken, NJ, USA},
author = {Stoker, J. J.},
doi = {10.1002/9781118033159},
isbn = {9781118033159},
month = {jan},
pages = {600},
publisher = {John Wiley {\&} Sons, Inc.},
title = {{Water Waves: The Mathematical Theory with Applications}},
year = {1992}
}
@book{Stoker1958,
author = {Stoker, J. J.},
publisher = {Wiley},
title = {{Water waves, the mathematical theory with applications}},
year = {1958}
}
@article{Stokes1847,
author = {Stokes, G. G.},
journal = {Trans. Camb. Phil. Soc.},
pages = {441--455},
title = {{On the theory of oscillatory waves}},
volume = {8},
year = {1847}
}
@article{Stokes1880,
author = {Stokes, G. G.},
doi = {10.1017/CBO9780511702242.016},
journal = {Mathematical and Physical Papers},
pages = {314--326},
title = {{Supplement to a paper on the theory of oscillatory waves}},
volume = {1},
year = {1880}
}
@article{Strang1983,
author = {Strang, G. and Iserles, A.},
doi = {10.1137/0720096},
issn = {0036-1429},
journal = {SIAM J. Numer. Anal.},
month = {dec},
number = {6},
pages = {1251--1257},
title = {{Barriers to Stability}},
url = {http://epubs.siam.org/doi/abs/10.1137/0720096},
volume = {20},
year = {1983}
}
@article{Su1969,
author = {Su, C. H. and Gardner, C. S.},
journal = {J. Math. Phys.},
pages = {536--539},
title = {{Korteweg-de Vries equation and generalizations. III. Derivation of the Korteweg-de Vries equation and Burgers equation.}},
volume = {10},
year = {1969}
}
@article{SG1969,
author = {Su, C. H. and Gardner, C. S.},
journal = {J. Math. Phys.},
pages = {536--539},
title = {{KdV equation and generalizations. Part III. Derivation of Korteweg-de Vries equation and Burgers equation}},
volume = {10},
year = {1969}
}
@article{Su1980,
author = {Su, C. H. and Mirie, R. M.},
journal = {J. Fluid Mech.},
pages = {509--525},
title = {{On head-on collisions between two solitary waves}},
volume = {98},
year = {1980}
}
@article{Sudobicher1968,
author = {Sudobicher, V. G. and Shugrin, S. M.},
journal = {Izv. Akad. Nauk SSSR},
number = {3},
pages = {116--122},
title = {{Flow along a dry channel}},
volume = {13},
year = {1968}
}
@article{Sugimoto1991,
author = {Sugimoto, N.},
journal = {J. Fluid Mech.},
pages = {631--653},
title = {{Burgers equation with a fractional derivative; hereditary effects on nonlinear acoustic waves}},
volume = {225},
year = {1991}
}
@inproceedings{Sugimoto1990,
author = {Sugimoto, N.},
booktitle = {Frontiers of Nonlinear Acoustics, 12th Intl Symp. on Nonlinear Acoustics},
editor = {Hamilton, M F and Blackstock, D T},
title = {{Evolution of nonlinear acoustic waves in a gas-filled pipe}},
year = {1990}
}
@inbook{Sugimoto1989,
author = {Sugimoto, N.},
chapter = {'Generaliz},
editor = {Jeffrey, A},
pages = {162--179},
publisher = {Longman Scientific {\&} Technical},
title = {{Nonlinear wave motion}},
year = {1989}
}
@book{Sulem1999,
author = {Sulem, C. and Sulem, P.-L.},
publisher = {Springer-Verlag, New York},
title = {{The Nonlinear Schr{\"{o}}dinger Equation. Self-Focusing and Wave Collapse}},
year = {1999}
}
@article{Sun1991,
author = {Sun, S.M.},
doi = {10.1016/0022-247X(91)90410-2},
issn = {0022247X},
journal = {Journal of Mathematical Analysis and Applications},
month = {apr},
number = {2},
pages = {471--504},
title = {{Existence of a generalized solitary wave solution for water with positive bond number less than}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0022247X91904102},
volume = {156},
year = {1991}
}
@article{Sun1993,
author = {Sun, S.M. and Shen, M.C.},
doi = {10.1006/jmaa.1993.1042},
issn = {0022247X},
journal = {Journal of Mathematical Analysis and Applications},
month = {jan},
number = {2},
pages = {533--566},
title = {{Exponentially Small Estimate for the Amplitude of Capillary Ripples of a Generalized Solitary Wave}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022247X83710425},
volume = {172},
year = {1993}
}
@book{Sutradhar2008,
address = {Berlin, Heidelberg},
author = {Sutradhar, A. and Paulino, G. H. and Gray, L. J.},
pages = {276},
publisher = {Springer-Verlag Berlin Heidelberg},
title = {{Symmetric Galerkin Boundary Element Method}},
year = {2008}
}
@article{Sweby1984,
author = {Sweby, P. K.},
journal = {SIAM J. Numer. Anal.},
pages = {995--1011},
title = {{High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws}},
volume = {21(5)},
year = {1984}
}
@article{Swegle1995,
author = {Swegle, J. W. and Hicks, D. L. and Attaway, S. W.},
doi = {10.1006/jcph.1995.1010},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {jan},
number = {1},
pages = {123--134},
title = {{Smoothed Particle Hydrodynamics Stability Analysis}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999185710108},
volume = {116},
year = {1995}
}
@article{Sy2005,
author = {Sy, M.},
journal = {Applied Mathematics Letters},
pages = {1351--1358},
title = {{A remark on the Kazhikhov-Smagulov type model: the vanishing initial density}},
volume = {18},
year = {2005}
}
@article{Synolakis2005,
author = {Synolakis, C. E.},
journal = {Nature},
pages = {17--18},
title = {{India must cooperate on tsunami warning system}},
volume = {434},
year = {2005}
}
@article{Synolakis1987,
author = {Synolakis, C. E.},
journal = {J. Fluid Mech.},
pages = {523--545},
title = {{The runup of solitary waves}},
volume = {185},
year = {1987}
}
@phdthesis{Synolakis1986,
author = {Synolakis, C. E.},
school = {California Institute of Technology},
title = {{The runup of long waves}},
year = {1986}
}
@article{Synolakis1991,
abstract = {This is a study of the application of linear theory for the estimation of the maximum runup height of long waves on plane beaches. The linear theory is reviewed and a method is presented for calculating the maximum runup. This method involves the calculation of the maximum value of an integral, now known as the runup integral. Laboratory and numerical results are presented to support this method. The implications of the theory are used to reevaluate many existing empirical runup correlations. It is shown that linear theory predicts the maximum runup satisfactorily. This study demonstrates that it is now possible to match complex offshore wave-evolution algorithms with linear theory runup solutions for the purpose of obtaining realistic tsunami inundation estimates.},
author = {Synolakis, C. E.},
doi = {10.1007/BF00162789},
issn = {0921-030X},
journal = {Nat. Hazards},
number = {2-3},
pages = {221--234},
title = {{Tsunami runup on steep slopes: How good linear theory really is}},
url = {http://link.springer.com/10.1007/BF00162789},
volume = {4},
year = {1991}
}
@article{Synolakis2002,
abstract = {The origin of the Papua New Guinea tsunami that killed over 2100 people on 17 July 1998 has remained controversial, as dislocation sources based on the parent earthquake fail to model its extreme run–up amplitude. The generation of tsunamis by submarine mass failure had been considered a rare phenomenon which had aroused virtually no attention in terms of tsunami hazard mitigation. We report on recently acquired high–resolution seismic reflection data which yield new images of a large underwater slump, coincident with photographic and bathymetric evidence of the same feature, suspected of having generated the tsunami. T–phase records from an unblocked hydrophone at Wake Island provide new evidence for the timing of the slump. By merging geological data with hydrodynamic modelling, we reproduce the observed tsunami amplitude and timing in a manner consistent with eyewitness accounts. Submarine mass failure is predicted based on fundamental geological and geotechnical information.},
author = {Synolakis, C. E. and Bardet, J.-P. and Borrero, J. C. and Davies, H. L. and Okal, E. A. and Silver, E. A. and Sweet, S. and Tappin, D. R.},
doi = {10.1098/rspa.2001.0915},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
keywords = {Papua New Guinea,hydroacoustics,hydrodynamic simulation,slumps,tsunamis},
month = {apr},
number = {2020},
pages = {763--789},
title = {{The slump origin of the 1998 Papua New Guinea Tsunami}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.2001.0915},
volume = {458},
year = {2002}
}
@article{Syno2006,
author = {Synolakis, C. E. and Bernard, E. N.},
journal = {Phil. Trans. R. Soc. A},
pages = {2231--2265},
title = {{Tsunami science before and beyond Boxing Day 2004}},
volume = {364},
year = {2006}
}
@techreport{noaa_report,
author = {Synolakis, C. E. and Bernard, E. N. and Titov, V. V. and Kanoglu, U. and Gonzalez, F. I.},
institution = {NOAA/Pacific Marine Environmental Laboratory},
title = {{Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models}},
year = {2007}
}
@article{Synolakis2008,
author = {Synolakis, C. E. and Bernard, E. N. and Titov, V. V. and K{\^{a}}noglu, U. and Gonz{\'{a}}lez, F. I.},
journal = {Pure Appl. Geophys.},
pages = {2197--2228},
title = {{Validation and Verification of Tsunami Numerical Models}},
volume = {165},
year = {2008}
}
@article{Synolakis2006,
author = {Synolakis, C. E. and Kong, L.},
journal = {Earthquake Spectra},
pages = {67--91},
title = {{Runup measurements of the December 2004 Indian ocean tsunami}},
volume = {22},
year = {2006}
}
@article{SLCY1997,
author = {Synolakis, C. E. and Liu, P. L.-F. and Carrier, G. F. and Yeh, H.},
journal = {Science},
pages = {598--600},
title = {{Tsunamigenic seafloor deformations}},
volume = {278},
year = {1997}
}
@article{Synolakis1993,
author = {Synolakis, C. E. and Skjelbreia, J. E.},
doi = {10.1061/(ASCE)0733-950X(1993)119:3(323)},
issn = {0733-950X},
journal = {J. Waterway, Port, Coastal and Ocean Engineering},
month = {may},
number = {3},
pages = {323--342},
title = {{Evolution of Maximum Amplitude of Solitary Waves on Plane Beaches}},
url = {http://ascelibrary.org/doi/abs/10.1061/(ASCE)0733-950X(1993)119:3(323)},
volume = {119},
year = {1993}
}
@article{Tadepalli1996,
author = {Tadepalli, S. and Synolakis, C. E.},
journal = {Phys. Rev. Lett.},
pages = {2141--2144},
title = {{Model for the leading waves of tsunamis}},
volume = {77},
year = {1996}
}
@article{TS94,
author = {Tadepalli, S. and Synolakis, C. E.},
journal = {Proc. R. Soc. Lond. A},
pages = {99--112},
title = {{The run-up of N-waves on sloping beaches}},
volume = {445},
year = {1994}
}
@article{Taha1984,
abstract = {Various numerical methods are used in order to approximate the Korteweg-de Vries equation, namely: (i) Zabusky-Kruskal scheme, (ii) hopscotch method, (iii) a scheme due to Goda, (iv) a proposed local scheme, (v) a proposed global scheme, (vi) a scheme suggested by Kruskal, (vii) split step Fourier method by Tappert, (viii) an improved split step Fourier method, and (ix) pseudospectral method by Fornberg and Whitham. Comparisons between our proposed scheme, which is developed using notions of the inverse scattering transform, and the other utilized schemes are obtained.},
author = {Taha, T. R. and Ablowitz, M. J.},
doi = {10.1016/0021-9991(84)90004-4},
issn = {00219991},
journal = {J. Comput. Phys},
number = {2},
pages = {231--253},
publisher = {Elsevier},
title = {{Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/0021999184900044},
volume = {55},
year = {1984}
}
@techreport{Tajchman1998,
author = {Tajchman, M. and Freydier, P.},
institution = {Note EDF HT-33/98/033/A},
title = {{Sch{\'{e}}ma VFFC : application {\`{a}} l'{\'{e}}tude d'un cas test d'{\'{e}}bullition en tuyau droit repr{\'{e}}sentant le fonctionnement en bouillotte d'un coeur REP}},
year = {1998}
}
@article{Takhtadzhyan1974,
author = {Takhtadzhyan, L. A. and Faddeev, L. D.},
doi = {10.1007/BF01036500},
issn = {00405779},
journal = {Theor. Math. Phys.},
number = {2},
pages = {1046--1057},
title = {{Essentially nonlinear one-dimensional model of classical field theory}},
volume = {21},
year = {1974}
}
@article{Tamura2009,
author = {Tamura, H. and Waseda, T. and Miyazawa, Y.},
doi = {10.1029/2008GL036280},
issn = {0094-8276},
journal = {Geophys. Res. Lett.},
month = {jan},
number = {1},
pages = {L01607},
title = {{Freakish sea state and swell-windsea coupling: Numerical study of the Suwa - Maru incident}},
url = {http://www.agu.org/pubs/crossref/2009/2008GL036280.shtml},
volume = {36},
year = {2009}
}
@article{Tanaka1986,
author = {Tanaka, M.},
journal = {Phys. Fluids},
pages = {650--655},
title = {{The stability of solitary waves}},
volume = {29(3)},
year = {1986}
}
@article{Tang2003,
abstract = {We develop efficient moving mesh algorithms for one- and two-dimensional hyperbolic systems of conservation laws. The algorithms are formed by two independent parts: PDE evolution and mesh-redistribution. The first part can be any appropriate high-resolution scheme, and the second part is based on an iterative procedure. In each iteration, meshes are first redistributed by an equidistribution principle, and then on the resulting new grids the underlying numerical solutions are updated by a conservative-interpolation formula proposed in this work. The iteration for the mesh-redistribution at a given time step is complete when the meshes governed by a nonlinear equationreach the equilibrium state. The main idea of the proposed method is to keep the mass-conservation of the underlying numerical solution at each redistribution step. In one dimension, we can show that the underlying numerical approximation obtained in the mesh-redistribution part satisfies the desired TVD property, which guarantees that the numerical solution at any time level is TVD, provided that the PDE solver in the first part satisfies such a property. Several test problems in one and two dimensions are computed using the proposed moving mesh algorithm. The computations demonstrate that our methods are efficient for solving problems with shock discontinuities, obtaining the same resolution with a much smaller number of grid points than the uniform mesh approach.},
author = {Tang, H. and Tang, T.},
doi = {10.1137/S003614290138437X},
issn = {0036-1429},
journal = {SIAM J. Numer. Anal.},
month = {jan},
number = {2},
pages = {487--515},
title = {{Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws}},
url = {http://epubs.siam.org/doi/abs/10.1137/S003614290138437X},
volume = {41},
year = {2003}
}
@article{Tanioka1996,
author = {Tanioka, Y. and Satake, K.},
journal = {Geophysical Research Letters},
pages = {861--864},
title = {{Tsunami generation by horizontal displacement of ocean bottom}},
volume = {23},
year = {1996}
}
@article{Tao2007,
author = {Tao, T.},
doi = {10.1016/j.jde.2006.07.019},
issn = {00220396},
journal = {J. Diff. Eqns.},
month = {jan},
number = {2},
pages = {623--651},
title = {{Scattering for the quartic generalised Korteweg-de Vries equation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0022039606002804},
volume = {232},
year = {2007}
}
@article{Tappin2008,
abstract = {The Papua New Guinea (PNG) tsunami of July 1998 was a seminal event because it demonstrated that relatively small and relatively deepwater Submarine Mass Failures (SMFs) can cause devastating local tsunamis that strike without warning. There is a comprehensive data set that proves this event was caused by a submarine slump. Yet, the source of the tsunami has remained controversial. This controversy is attributed to several causes. Before the PNG event, it was questionable as to whether SMFs could cause devastating tsunamis. As a result, only limited modelling of SMFs as tsunami sources had been undertaken, and these excluded slumps. The results of these models were that SMFs in general were not considered to be a potential source of catastrophic tsunamis. To effectively model a SMF requires fairly detailed geological data, and these too had been lacking. In addition, qualitative data, such as evidence from survivors, tended to be disregarded in assessing alternative tsunami sources. The use of marine geological data to identify areas of recent submarine failure was not widely applied. The disastrous loss of life caused by the PNG tsunami resulted in a major investigation into the area offshore of the devastated coastline, with five marine expeditions taking place. This was the first time that a focussed, large-scale, international programme of marine surveying had taken place so soon after a major tsunami. It was also the first time that such a comprehensive data set became the basis for tsunami simulations. The use of marine mapping subsequently led to a larger involvement of marine geologists in the study of tsunamis, expanding the knowledge base of those studying the threat from SMF hazards. This paper provides an overview of the PNG tsunami and its impact on tsunami science. It presents revised interpretations of the slump architecture based on new seabed relief images and, using these, the most comprehensive tsunami simulation of the PNG event to date. Simulation results explain the measured runups to a high degree. The PNG tsunami has made a major impact on tsunami science. It is one of the most studied SMF tsunamis, yet it remains the only one known of its type: a slump.},
author = {Tappin, D. R. and Watts, P. and Grilli, S. T.},
journal = {Nat. Hazards Earth Syst. Sci.},
pages = {243--266},
title = {{The Papua New Guinea tsunami of 17 July 1998: anatomy of a catastrophic event}},
volume = {8},
year = {2008}
}
@inbook{Tatehata1997,
author = {Tatehata, H.},
chapter = {The New Ts},
editor = {Hebenstreit, Gerald T},
pages = {175--188},
publisher = {Springer},
title = {{Perspectives on Tsunami Hazard Reduction: Observations, Theory and Planning}},
year = {1997}
}
@article{Tayfun1980,
author = {Tayfun, M. A.},
journal = {J. Geophys. Res.},
pages = {1548--1552},
title = {{Narrow-band nonlinear sea waves}},
volume = {85},
year = {1980}
}
@article{Tayfun2007,
author = {Tayfun, M. A. and Fedele, F.},
doi = {10.1016/j.oceaneng.2006.11.006},
issn = {00298018},
journal = {Ocean Engineering},
month = {aug},
number = {11-12},
pages = {1631--1649},
title = {{Wave-height distributions and nonlinear effects}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0029801807000431},
volume = {34},
year = {2007}
}
@article{Taylor1953,
author = {Taylor, G. I.},
journal = {Proc. R. Soc. Lond. A},
pages = {44--59},
title = {{An experimental study of standing waves}},
volume = {218},
year = {1953}
}
@article{Taylor1950,
author = {Taylor, G. I.},
journal = {Proc. R. Soc. Lond. A},
pages = {192--196},
title = {{The instability of liquid surfaces when accelerated in a direction perpendicular to their planes}},
volume = {201},
year = {1950}
}
@article{Taylor1965,
author = {Taylor, G. I. and McEwan, A. D.},
doi = {10.1017/S0022112065000538},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {mar},
pages = {1--15},
title = {{The stability of a horizontal fluid interface in a vertical electric field}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112065000538},
volume = {22},
year = {1965}
}
@book{taylor,
author = {Taylor, M.},
isbn = {0387946543},
publisher = {Springer},
title = {{Partial Differential Equations}},
year = {1996}
}
@article{Temple2004,
author = {Temple, B. and Hong, J.},
doi = {10.1137/S0036139902405249},
issn = {0036-1399},
journal = {SIAM J. Appl. Math},
month = {jan},
number = {3},
pages = {819--857},
title = {{A Bound on the Total Variation of the Conserved Quantities for Solutions of a General Resonant Nonlinear Balance Law}},
url = {http://epubs.siam.org/doi/abs/10.1137/S0036139902405249},
volume = {64},
year = {2004}
}
@article{Thelwell2006,
abstract = {The two-dimensional cubic nonlinear Schr{\"{o}}dinger equation admits a large family of one-dimensional bounded travelling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant phase have been well studied previously. Some of these solutions were found to be stable with respect to one-dimensional perturbations. No such solutions are stable with respect to two-dimensional perturbations. We consider stability of the larger class of solutions whose phase is dependent on the spatial dimension of the one-dimensional wave form. We study the spectral stability of such nontrivial-phase solutions numerically, using Hill's method. We present evidence which suggests that all such nontrivial-phase solutions are unstable with respect to both one- and two-dimensional perturbations. Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear Schr{\"{o}}dinger equations, and in the focusing and defocusing cases.},
author = {Thelwell, R. J. and Carter, J. D. and Deconinck, B.},
doi = {10.1088/0305-4470/39/1/006},
issn = {0305-4470},
journal = {J. Phys. A: Math. Gen},
month = {jan},
number = {1},
pages = {73--84},
title = {{Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schr{\"{o}}dinger equation}},
url = {http://stacks.iop.org/0305-4470/39/i=1/a=006?key=crossref.bf25c5a76a680adccdd234e10a051782},
volume = {39},
year = {2006}
}
@article{Thomas1988,
author = {Thomas, M. D. and Craik, A. D. D.},
journal = {J. Fluids Structures},
pages = {323--338},
title = {{Three-wave resonance for free-surface flows over flexible boundaries}},
volume = {2},
year = {1988}
}
@article{Thomas1979,
author = {Thomas, P. D. and Lombart, C. K.},
journal = {AIAA Journal},
number = {10},
pages = {1030--1037},
title = {{Geometric conservation law and its application to flow computations on moving grid}},
volume = {17},
year = {1979}
}
@article{Thornber2008,
author = {Thornber, B. J. R. and Drikakis, D.},
journal = {Int. J. Numer. Meth. Fluids},
pages = {1535--1541},
title = {{Numerical dissipation of upwind schemes in low Mach flow}},
volume = {56},
year = {2008}
}
@article{Thornber2007,
author = {Thornber, B. and Mosedale, A. and Drikakis, D.},
journal = {J. Comput. Phys.},
pages = {1902--1929},
title = {{On the implicit large eddy simulations of homogeneous decaying turbulence}},
volume = {226},
year = {2007}
}
@book{Thorpe2005,
author = {Thorpe, S. A.},
publisher = {Cambridge University Press},
title = {{The Turbulent Ocean}},
year = {2005}
}
@article{Tian2010,
author = {Tian, Z. and Perlin, M. and Choi, W.},
journal = {J. Fluid Mech},
pages = {217--257},
title = {{Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model}},
volume = {655},
year = {2010}
}
@article{Tikhonov1962,
abstract = {Non-uniform nets are widely used in the solution of various differential equations by difference methods. However, little has been done to study the convergence of the difference schemes. The simplest examples show that the most frequently used criteria for judging the quality of difference schemes, a uniform estimate or a mean estimate of the approximation error of the scheme, are unsound for non-uniform nets and can give an untrue idea of the order of accuracy of the scheme.},
author = {Tikhonov, A. N. and Samarskii, A. A.},
journal = {Zh. vych. mat.},
number = {5},
pages = {812--832},
title = {{Homogeneous difference schemes on non-uniform nets}},
volume = {2},
year = {1962}
}
@article{Tikhonov1961,
abstract = {Homogeneous difference schemes, suitable for transforming differential equations whose coefficients belong to certain classes of function into difference equations, are defined and discussed. The main points which arise are, first, whether the solution of the resulting difference equation converges to that of the original differential equation in the given class of coefficients, and of what order the convergence is, if it exists; and, secondly, how the “best” scheme, giving a high degree of accuracy in the widest class of coefficients and stability with respect to computing errors, can be selected. A basic lemma concerning the necessary condition for convergence is proved. Examples are given of a difference scheme for Sturm-Liouville type operators in the class of sufficiently smooth coefficients, of a scheme for the first boundary problem in the class of smooth coefficients and in the class of discontinuous coefficients, as well as in the class of piece-wise continuous coefficients. The latter is the basic class of coefficients which is discussed in the article. Green's function for the difference operator is constructed, and bounds are found for it and for its first difference ratios.},
author = {Tikhonov, A. N. and Samarskii, A. A.},
journal = {Zh. vych. mat.},
number = {1},
pages = {5--63},
title = {{Homogeneous difference schemes}},
volume = {1},
year = {1961}
}
@article{Tinti2000,
author = {Tinti, S. and Bortolucci, E.},
journal = {Pure Appl. Geophys.},
pages = {281--318},
title = {{Energy of Water Waves Induced by Submarine Landslides}},
volume = {157},
year = {2000}
}
@article{Tinti1999,
author = {Tinti, S. and Bortolucci, E. and Armigliato, A.},
doi = {10.1007/s004450050267},
issn = {02588900},
journal = {Bulletin of Volcanology},
keywords = {7,7 lagrangian,aeolian islands 7 landslide,approach 7 numerical simulations,tsunami 7 finite element technique,vulcano},
number = {1-2},
pages = {121--137},
title = {{Numerical simulation of the landslide-induced tsunami of 1988 on Vulcano Island, Italy}},
url = {http://www.springerlink.com/openurl.asp?genre=article{\&}id=doi:10.1007/s004450050267},
volume = {61},
year = {1999}
}
@article{Tinti2001,
author = {Tinti, S. and Bortolucci, E. and Chiavettieri, C.},
journal = {Pure appl. geophys.},
pages = {759--797},
title = {{Tsunami Excitation by Submarine Slides in Shallow-water Approximation}},
volume = {158},
year = {2001}
}
@article{Tinti2000a,
abstract = {Stromboli is an island volcano of the Aeolian Volcanic Arc, characterised by persistent activity. The cone rises about 2500–3000 m from its submarine base with very steep slopes; its summit at 924 m above the sea level. The subaerial growth of Stromboli, occurred in the last 100 ka, has been marked by repeated episodes of large gravitational collapses especially affecting the NW flank of the island in the last 13 ka. The last one occurred less than 5000 years ago forming the deep depression on the NW seaward flank, named Sciara del Fuoco (SdF), and it produced very likely large water waves. This paper envisages a scenario where a huge mass of volcanic material collapses into the sea in the same sector in which the SdF collapse took place in Holocenic times and it computes possible tsunami evolutions assuming the present-day bathymetry. Numerical simulations are performed by means of two distinct models; one for the mass collapse and one for the tsunami. Slope failure dynamics are calculated with the aid of a Lagrangian model: the landslide is subdivided into blocks, and the motion of each constituent block is calculated by applying the basic principle of mechanical momentum conservation, with block–block and block–ambient interactions being taken into account. Water waves are computed by solving a system of shallow-water equations including a forcing term dependent on the sliding mass motion. The finite-element (FE) technique is employed since it permits the use of non-uniform grids, which are adequate to account for marine basins with irregular coastlines. In addition to the sensitivity analysis concerning the main parameters governing the slide motion, two main cases are explored, differing in the slide path followed by the mass. The resulting tsunami is very large, with giant waves as high as several meters (tens of meters in the worst cases) impinging the coast. Due to the strong wave refraction induced by bathymetry, waves travel around the island, affecting even the island coast opposite the source.},
author = {Tinti, S. and Bortolucci, E. and Romagnoli, C.},
doi = {10.1016/S0377-0273(99)00138-9},
issn = {03770273},
journal = {Journal of Volcanology and Geothermal Research},
keywords = {Stromboli,debris avalanche,numerical model,sectorcollapse,tsunami},
month = {feb},
number = {1-2},
pages = {103--128},
title = {{Computer simulations of tsunamis due to sector collapse at Stromboli, Italy}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0377027399001389},
volume = {96},
year = {2000}
}
@article{Tinti2005,
abstract = {On the 30th of December 2002 two tsunamis were generated only 7 min apart in Stromboli, southern Tyrrhenian Sea, Italy. They represented the peak of a volcanic crisis that started 2 days before with a large emission of lava flows from a lateral vent that opened some hundreds of meters below the summit craters. Both tsunamis were produced by landslides that detached from the Sciara del Fuoco. This is a morphological scar and is the result of the last collapse of the northwestern flank of the volcanic edifice, that occurred less than 5 ka B.P. The first tsunami was due to a submarine mass movement that started very close to the coastline and that involved about 20106 m3 of material. The second tsunami was engendered by a subaerial landslide that detached at about 500 m above sea level and that involved a volume estimated at 49106 m3. The latter landslide can be seen as the retrogressive continuation of the first failure. The tsunamis were not perceived as distinct events by most people. They attacked all the coasts of Stromboli within a few minutes and arrived at the neighbouring island of Panarea, 20 km SSW of Stromboli, in less than 5 min. The tsunamis caused severe damage at Stromboli. In this work, the two tsunamis are studied by means of numerical simulations that use two distinct models, one for the landslides and one for the water waves. The motion of the sliding bodies is computed by means of a Lagrangian approach that partitions the mass into a set of blocks: we use both one-dimensional and two-dimensional schemes. The landslide model calculates the instantaneous rate of the vertical displacement of the sea surface caused by the motion of the underwater slide. This is included in the governing equations of the tsunami, which are solved by means of a finite-element (FE) technique. The tsunami is computed on two different grids formed by triangular elements, one covering the near-field around Stromboli and the other also including the island of Panarea. The simulations show that the main tsunamigenic potential of the slides is restricted to the first tens of seconds of their motion when they interact with the shallow-water coastal area, and that it diminishes drastically in deep water. The simulations explain how the tsunamis that are generated in the Sciara del Fuoco area, are able to attack the entire coastline of Stromboli with larger effects on the northern coast than on the southern. Strong refraction and bending of the tsunami fronts is due to the large near-shore bathymetric gradient, which is also responsible for the trapping of the waves and for the persistence of the oscillations. Further, the first tsunami produces large waves and runup heights comparable with the observations. The simulated second tsunami is only slightly smaller, though it was induced by a mass that is approximately one third of the first. The arrival of the first tsunami is negative, in accordance with most eyewitness reports. Conversely, the leading wave of the second tsunami is positive.},
author = {Tinti, S. and Pagnoni, G. and Zaniboni, F.},
doi = {10.1007/s00445-005-0022-9},
issn = {02588900},
journal = {Bulletin of Volcanology},
keywords = {december 2002 stromboli eruption,landslide induced tsunami,landslide model,stromboli,tsunami runup,tsunami simulation},
number = {5},
pages = {462--479},
title = {{The landslides and tsunamis of the 30th of December 2002 in Stromboli analysed through numerical simulations}},
url = {http://www.springerlink.com/index/10.1007/s00445-005-0022-9},
volume = {68},
year = {2006}
}
@article{Tinti2005,
abstract = {On the 30th of December 2002 two tsunamis were generated only 7 min apart in Stromboli, southern Tyrrhenian Sea, Italy. They represented the peak of a volcanic crisis that started 2 days before with a large emission of lava flows from a lateral vent that opened some hundreds of meters below the summit craters. Both tsunamis were produced by landslides that detached from the Sciara del Fuoco. This is a morphological scar and is the result of the last collapse of the northwestern flank of the volcanic edifice, that occurred less than 5 ka B.P. The first tsunami was due to a submarine mass movement that started very close to the coastline and that involved about 20106 m3 of material. The second tsunami was engendered by a subaerial landslide that detached at about 500 m above sea level and that involved a volume estimated at 49106 m3. The latter landslide can be seen as the retrogressive continuation of the first failure. The tsunamis were not perceived as distinct events by most people. They attacked all the coasts of Stromboli within a few minutes and arrived at the neighbouring island of Panarea, 20 km SSW of Stromboli, in less than 5 min. The tsunamis caused severe damage at Stromboli. In this work, the two tsunamis are studied by means of numerical simulations that use two distinct models, one for the landslides and one for the water waves. The motion of the sliding bodies is computed by means of a Lagrangian approach that partitions the mass into a set of blocks: we use both one-dimensional and two-dimensional schemes. The landslide model calculates the instantaneous rate of the vertical displacement of the sea surface caused by the motion of the underwater slide. This is included in the governing equations of the tsunami, which are solved by means of a finite-element (FE) technique. The tsunami is computed on two different grids formed by triangular elements, one covering the near-field around Stromboli and the other also including the island of Panarea. The simulations show that the main tsunamigenic potential of the slides is restricted to the first tens of seconds of their motion when they interact with the shallow-water coastal area, and that it diminishes drastically in deep water. The simulations explain how the tsunamis that are generated in the Sciara del Fuoco area, are able to attack the entire coastline of Stromboli with larger effects on the northern coast than on the southern. Strong refraction and bending of the tsunami fronts is due to the large near-shore bathymetric gradient, which is also responsible for the trapping of the waves and for the persistence of the oscillations. Further, the first tsunami produces large waves and runup heights comparable with the observations. The simulated second tsunami is only slightly smaller, though it was induced by a mass that is approximately one third of the first. The arrival of the first tsunami is negative, in accordance with most eyewitness reports. Conversely, the leading wave of the second tsunami is positive.},
author = {Tinti, S. and Pagnoni, G. and Zaniboni, F.},
doi = {10.1007/s00445-005-0022-9},
issn = {02588900},
journal = {Bulletin of Volcanology},
keywords = {december 2002 stromboli eruption,landslide induced tsunami,landslide model,stromboli,tsunami runup,tsunami simulation},
number = {5},
pages = {462--479},
title = {{The landslides and tsunamis of the 30th of December 2002 in Stromboli analysed through numerical simulations}},
url = {http://www.springerlink.com/index/10.1007/s00445-005-0022-9},
volume = {68},
year = {2005}
}
@article{Tinti05,
author = {Tinti, S. and Tonini, R.},
journal = {J. Fluid Mech.},
pages = {33--64},
title = {{Analytical evolution of tsunamis induced by near-shore earthquakes on a constant-slope ocean}},
volume = {535},
year = {2005}
}
@article{Tissier2012,
author = {Tissier, M. and Bonneton, P. and Marche, F. and Chazel, F. and Lannes, D.},
journal = {Coastal Engineering},
pages = {54--66},
title = {{A new approach to handle wave breaking in fully non-linear Boussinesq models}},
volume = {67},
year = {2012}
}
@article{Tissier2011,
author = {Tissier, M. and Bonneton, P. and Marche, F. and Chazel, F. and Lannes, D.},
journal = {Journal of Coastal Research},
pages = {603--607},
title = {{Nearshore Dynamics of Tsunami-like Undular Bores using a Fully Nonlinear Boussinesq Model}},
volume = {64},
year = {2011}
}
@book{Titchmarsh1976,
author = {Titchmarsh, E. C.},
edition = {2nd},
editor = {Titchmarsh, E. C.},
isbn = {978-0198533498},
pages = {464},
publisher = {Oxford University Press},
title = {{The Theory of Functions}},
year = {1976}
}
@techreport{Titov1997,
author = {Titov, V. V. and Gonz{\'{a}}lez, F. I.},
institution = {Pacific Marine Environmental Laboratory, NOAA},
number = {ERL PMEL-112},
title = {{Implementation and testing of the method of splitting tsunami (MOST) model}},
year = {1997}
}
@article{Titov2005,
abstract = {A new method for real-time tsunami forecasting will provide NOAA Tsunami Warning Centers with forecast guidance tools during an actual tsunami event. PMEL has developed the methodology of combining real-time data from tsunameters with numerical model estimates to provide site- and event-specific forecasts for tsunamis in real time. An overview of the technique and testing of this methodology is presented.},
author = {Titov, V. V. and Gonzalez, F. I. and Bernard, E. N. and Eble, M. C. and Mofjeld, H. O. and Newman, J. C. and Venturato, A. J.},
journal = {Natural Hazards},
keywords = {tsunami - real-time forecast - tsunami measurement},
pages = {41--58},
title = {{Real-Time Tsunami Forecasting: Challenges and Solutions}},
volume = {35},
year = {2005}
}
@article{Titov,
author = {Titov, V. V. and Rabinovich, A. B. and Mofjeld, H. O. and Thomson, R. E. and Gonz{\'{a}}lez, F. I.},
journal = {Science},
pages = {2045--2048},
title = {{The global reach of the 26 December 2004 Sumatra tsunami}},
volume = {309},
year = {2005}
}
@article{TS,
author = {Titov, V. V. and Synolakis, C. E.},
journal = {J. Waterway, Port, Coastal, and Ocean Engineering},
pages = {157--171},
title = {{Numerical modeling of tidal wave runup}},
volume = {124},
year = {1998}
}
@article{Tkalich2007a,
author = {Tkalich, P. and Dao, M. H. and Soon, C. E.},
journal = {Journal of Earthquake and Tsunami},
pages = {87--98},
title = {{Tsunami propagation modeling and forecasting for early warning system}},
volume = {1(1)},
year = {2007}
}
@article{Kartashova2014,
author = {Tobisch, E.},
journal = {JETP},
number = {2},
pages = {359--365},
title = {{Energy spectrum of ensemble of weakly nonlinear gravity-capillary waves on a fluid surface}},
volume = {119},
year = {2014}
}
@inproceedings{Tochon-Danguy1975,
author = {Tochon-Danguy, J.-C. and Hopfinger, E. J.},
booktitle = {Actes du colloque de Grindelwald},
title = {{Simulation of the dynamics of powder avalanches}},
year = {1975}
}
@article{todo2,
author = {Todorovska, M. I. and Hayir, A. and Trifunac, M. D.},
journal = {Soil Dynamics and Earthquake Engineering},
pages = {129--141},
title = {{A note on tsunami amplitudes above submarine slides and slumps}},
volume = {22},
year = {2002}
}
@article{Todo,
author = {Todorovska, M. I. and Trifunac, M. D.},
journal = {Soil Dynamics and Earthquake Engineering},
pages = {151--167},
title = {{Generation of tsunamis by a slowly spreading uplift of the seafloor}},
volume = {21},
year = {2001}
}
@article{Toepffer1997,
author = {Toepffer, C. and Cercignani, C.},
doi = {10.1002/ctpp.2150370217},
issn = {08631042},
journal = {Contributions to Plasma Physics},
number = {2-3},
pages = {279--291},
title = {{Analytical Results for the Boltzmann Equation}},
url = {http://doi.wiley.com/10.1002/ctpp.2150370217},
volume = {37},
year = {1997}
}
@article{Toffoli2009,
author = {Toffoli, A. and Benoit, M. and Onorato, M. and Bitner-Gregersen, E. M.},
journal = {Nonlin. Processes Geophys.},
pages = {131--139},
title = {{The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth}},
volume = {16},
year = {2009}
}
@article{Toffoli2011,
author = {Toffoli, A. and Bitner-Gregersen, E. M.},
journal = {Open Ocean Eng. J.},
pages = {24--33},
title = {{Extreme and rogue waves in directional wave fields}},
volume = {4},
year = {2011}
}
@inproceedings{Tomita2003,
address = {Honolulu, Hawaii, USA},
author = {Tomita, T. and Shimosako, K. and Takano, T.},
booktitle = {Proceedings of The 13th International Offshore and Polar Engineering Conference},
pages = {639--646},
title = {{Wave Forces Acting on Flap-type Storm Surge Barrier and Waves Transmitted on It}},
year = {2003}
}
@article{TP,
author = {Tonelli, M. and Petti, M.},
journal = {Coastal Engineering},
pages = {609--620},
title = {{Hybrid finite-volume finite-difference scheme for 2DH improved Boussinesq equations}},
volume = {56},
year = {2009}
}
@article{Toro1992,
author = {Toro, E. F.},
journal = {Philosophical Transactions: Physical Sciences and Engineering},
pages = {43--68},
title = {{Riemann Problems and the WAF Method for Solving the Two-Dimensional Shallow Water Equations}},
volume = {338},
year = {1992}
}
@book{Toro2009,
abstract = {High resolution upwind and centred methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Direct applicability of the methods include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. For this third edition the book was thoroughly revised and contains substantially more, and new material both in its fundamental as well as in its applied parts.},
address = {Berlin, Heidelberg},
author = {Toro, E. F.},
doi = {10.1007/b79761},
isbn = {978-3-540-25202-3},
pages = {724},
publisher = {Springer},
title = {{Riemann Solvers and Numerical Methods for Fluid Dynamics}},
url = {http://link.springer.com/10.1007/b79761},
year = {2009}
}
@article{Toro1994,
author = {Toro, E. F. and Spruce, M. and Speares, W.},
journal = {Shock Waves},
pages = {25--34},
title = {{Restoration of the contact surface in the HLL Riemann solver}},
volume = {4},
year = {1994}
}
@article{Torsvik2007,
author = {Torsvik, T. and Liu, P. L.-F.},
journal = {Coastal Engineering},
pages = {263--269},
title = {{An efficient method for the numerical calculation of viscous effects on transient long-waves}},
volume = {54},
year = {2007}
}
@article{Touboul2012,
abstract = {In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the solution into an open subdomain and at a given time, when the right hand side source term is known. The mapping that associates this trace to the shape of the domain is nonlinear. We show (i) an approximate controllability property for the linearized parabolic problem and (ii) an exact local controllability property for the linearized and the nonlinear equations in the hyperbolic case. We then address the same questions in the context of a finite difference spatial semi-discretization in both the parabolic and hyperbolic problems. In this discretized case again we prove a local controllability result for the parabolic problem, and an exact controllability for the hyperbolic case, applying a local surjectivity theorem together with a unique continuation property of the underlying adjoint discrete system.},
author = {Touboul, J.},
doi = {10.3934/mcrf.2012.2.429},
issn = {2156-8472},
journal = {Mathematical Control and Related Fields},
keywords = {Heat equation,controllability,semi-discrete controllability,shape of the domain,wave equation},
month = {oct},
number = {4},
pages = {429--455},
title = {{Controllability of the heat and wave equations and their finite difference approximations by the shape of the domain}},
url = {http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=7856},
volume = {2},
year = {2012}
}
@article{Touboul2006,
author = {Touboul, J. and Giovanangeli, J. P. and Kharif, C. and Pelinovsky, E.},
journal = {Eur. J. Mech. B/Fluids},
pages = {662--676},
title = {{Freak waves under the action of wind: experiments and simulations}},
volume = {25(5)},
year = {2006}
}
@article{Toumi1996,
author = {Toumi, I. and Kumbaro, A.},
journal = {J. Comput. Physics},
pages = {286--300},
title = {{An Approximate Linearized Riemann Solver for a Two-Fluid Model}},
volume = {124},
year = {1996}
}
@techreport{Toumi1999,
author = {Toumi, I. and Kumbaro, A. and Paill{\`{e}}re, H.},
institution = {CEA Saclay},
title = {{Approximate Riemann Solvers and Flux Vector Splitting Schemes for Two-Phase Flow}},
year = {1999}
}
@book{Townsend1980,
abstract = {Turbulent flow is a most important branch of fluid dynamics yet its complexity has tended to make it one of the least understood. Empirical data have been appearing rapidly for more than twenty years but a consistent theory of turbulent flow based on the results has been lacking. The original edition of Dr Townsend's book was the first to attempt a systematic and comprehensive discussion of all kinds of turbulent motion and to provide a reliable analysis of the processes which occur. The theory and associated concepts are applied to the description of a variety of flows: free turbulent flows such as wakes and jets, wall flows in pipes and boundary layers, flows affected by buoyancy forces such as heat plumes and the atmospheric boundary layer and flows with curved streamlines. This monograph will appeal to practitioners and researchers in engineering, meteorology, oceanography, physics and applied mathematics. This paperback edition was first issued in hard covers in 1976 as a complete revision, taking into account developments since 1955, of the first edition. It will be useful as an advanced text in applied mathematics, and the other disciplines mentioned above.},
author = {Townsend, A. A. R.},
edition = {2},
isbn = {0521298199},
issn = {978-0521298193},
pages = {444},
publisher = {Cambridge University Press},
title = {{The Structure of Turbulent Shear Flow}},
year = {1980}
}
@book{Trefethen2000,
abstract = {This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web. This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature.},
author = {Trefethen, L. N.},
editor = {Trefethen, L. N.},
isbn = {978-0898714654},
pages = {184},
publisher = {Society for Industrial and Applied Mathematics, Philadelphia, PA, USA},
title = {{Spectral methods in MatLab}},
url = {http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/spectral.html},
year = {2000}
}
@book{Trefethen1997,
address = {Philadelphia},
author = {Trefethen, L. N. and Bau, D.},
editor = {Trefethen, L. N. and Bau, D.},
pages = {369},
publisher = {SIAM},
title = {{Numerical linear algebra}},
year = {1997}
}
@inproceedings{Trefftz1926,
address = {Z{\"{u}}rich},
author = {Trefftz, E.},
booktitle = {Proc. 2nd Int. Cong. Appl. Mech.},
pages = {131--137},
title = {{Gegenst{\"{u}}ck zum ritzschen Verfahren}},
year = {1926}
}
@book{Truesdell1954,
address = {Bloomington},
author = {Truesdell, C.},
pages = {?},
publisher = {Indiana University Press},
title = {{The Kinematics of Vorticity}},
year = {1954}
}
@article{Trulsen1996,
author = {Trulsen, K. and Dysthe, K. B.},
journal = {Wave Motion},
pages = {281--289},
title = {{A modified nonlinear Schr{\"{o}}dinger equation for broader bandwidth gravity waves on deep water}},
volume = {24},
year = {1996}
}
@article{Trulsen1997,
author = {Trulsen, K. and Dysthe, K. B.},
journal = {J. Fluid Mech.},
pages = {359--373},
title = {{Frequency downshift in three-dimensional wave trains in a deep basin}},
volume = {352},
year = {1997}
}
@article{Trulsen2000,
author = {Trulsen, K. and Kliakhandler, I. and Dysthe, K. B. and Velarde, M. G.},
journal = {Phys. Fluids},
pages = {2432--2437},
title = {{On weakly nonlinear modulation of waves on deep water}},
volume = {12},
year = {2000}
}
@article{Trulsen2012,
author = {Trulsen, K. and Zeng, H. and Gramstad, O.},
doi = {10.1063/1.4748346},
issn = {10706631},
journal = {Phys. Fluids},
number = {9},
pages = {097101},
title = {{Laboratory evidence of freak waves provoked by non-uniform bathymetry}},
volume = {24},
year = {2012}
}
@article{Tsai1996,
author = {Tsai, W. and Yue, D. K. P.},
doi = {10.1146/annurev.fl.28.010196.001341},
journal = {Ann. Rev. Fluid Mech.},
pages = {249--278},
title = {{Computation of Nonlinear Free-Surface Flows}},
volume = {28},
year = {1996}
}
@article{Tsarev1992,
author = {Tsarev, V. A.},
doi = {10.3367/UFNr.0162.199210b.0063},
issn = {0042-1294},
journal = {Sov. Phys. Usp.},
number = {10},
pages = {842--856},
title = {{Anomalous nuclear effects in solids ('cold fusion'): questions still remain}},
url = {http://ufn.ru/ru/articles/1992/10/b/},
volume = {35},
year = {1992}
}
@article{Tseluiko2009,
abstract = {The steady, gravity-driven flow of a liquid film over a topographically structured substrate is investigated. The analysis is based on a model nonlinear equation for the film thickness derived on the basis of long-wave asymptotics. The free-surface shape is expanded in a regular asymptotic expansion in powers of the topography amplitude, and solutions are obtained up to second order. Solutions are constructed for downward steps, upward steps, and rectangular trenches, and the results are compared favorably with numerical solutions of the nonlinear model equation. The results indicate that all of the salient features previously found for film flows over steps and into trenches are captured by the small-step asymptotics, including the capillary ridge formed just above a downward step and oscillations upstream of an upward step. We derive analytical expressions for the period and amplitude of these oscillations. The effect of a normal electric on the film surface shape is also investigated on the assumption that both the film and the medium above the film behave as perfect dielectrics. Again, the small-amplitude asymptotics describe the essential characteristics of the free surface, including oscillations downstream of a downwards step with a quantifiable period and amplitude. It is established analytically and numerically that the amplitude of interfacial oscillations just upstream of a step decreases with an increase of the electric field strength in the case of perfect conductors, but increases to a limiting value for perfect dielectrics. It is found that nonlinear solutions are in excellent agreement with the small-amplitude theory even for relatively large topography amplitudes},
author = {Tseluiko, D. and Blyth, M. G. and Papageorgiou, D. T. and Vanden-Broeck, J.-M.},
doi = {10.1137/080721674},
issn = {0036-1399},
journal = {SIAM J. Appl. Math},
keywords = {electrohydrodynamics,film flows,flow over topography},
month = {jan},
number = {3},
pages = {845--865},
title = {{Viscous Electrified Film Flow over Step Topography}},
url = {http://epubs.siam.org/doi/abs/10.1137/080721674},
volume = {70},
year = {2009}
}
@article{Tseluiko2008,
author = {Tseluiko, D. and Blyth, M. G. and Papageorgiou, D. T. and Vanden-Broeck, J.-M.},
doi = {10.1017/S002211200700986X},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {feb},
pages = {449--475},
title = {{Electrified viscous thin film flow over topography}},
url = {http://www.journals.cambridge.org/abstract{\_}S002211200700986X},
volume = {597},
year = {2008}
}
@article{Tseluiko2007,
abstract = {We study a nonlinear nonlocal evolution equation describing the hydrodynamics of thin films in the presence of normal electric fields. The liquid film is assumed to be perfectly conducting and to completely wet the upper or lower surface of a horizontal flat plate. The flat plate is held at constant voltage, and a vertical electric field is generated by a second parallel electrode kept at a different constant voltage and placed at a large vertical distance from the bottom plate. The fluid is viscous, and gravity and surface tension act. The equation is derived using lubrication theory and contains an additional nonlinear nonlocal term representing the electric field. The electric field is linearly destabilizing and is particularly important in producing nontrivial dynamics in the case when the film rests on the upper side of the plate. We give rigorous results on the global boundedness of positive periodic smooth solutions, using an appropriate energy functional. We also implement a fully implicit numerical scheme and perform extensive numerical experiments. Through a combination of analysis and numerical experiments we present evidence for the global existence of positive smooth solutions. This means, in turn, that the film does not touch the wall in finite time but asymptotically at infinite time. Numerical solutions are presented to support such phenomena, which are also observed in hanging films when electric fields are absent.},
author = {Tseluiko, D. and Papageorgiou, D. T.},
doi = {10.1137/060663532},
issn = {0036-1399},
journal = {SIAM J. Appl. Math},
keywords = {electrohydrodynamics,nonlocal evolution equation,thin film},
month = {jan},
number = {5},
pages = {1310--1329},
title = {{Nonlinear Dynamics of Electrified Thin Liquid Films}},
url = {http://epubs.siam.org/doi/abs/10.1137/060663532},
volume = {67},
year = {2007}
}
@article{Tseluiko2006,
author = {Tseluiko, D. and Papageorgiou, D. T.},
doi = {10.1017/S0022112006009712},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {may},
pages = {361--386},
title = {{Wave evolution on electrified falling films}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112006009712},
volume = {556},
year = {2006}
}
@article{Tseng1999,
author = {Tseng, M.-H.},
journal = {Int. J. Num. Meth. Fluids},
pages = {831--843},
title = {{Explicit finite volume non-oscillatory schemes for 2D transient free-surface flows}},
volume = {30},
year = {1999}
}
@book{Tsinober2009,
address = {Dordrecht},
author = {Tsinober, A.},
doi = {10.1007/978-90-481-3174-7},
edition = {Second},
isbn = {978-90-481-3173-0},
pages = {464},
publisher = {Springer Netherlands},
title = {{An Informal Conceptual Introduction to Turbulence}},
year = {2009}
}
@article{Tsuji1995,
abstract = {A field survey of the June 3, 1994 East Java earthquake tsunami was conducted within three weeks, and the distributions of the seismic intensities, tsunami heights, and human and house damages were surveyed. The seismic intensities on the south coasts of Java and Bali Islands were small for an earthquake with magnitudeM 7.6. The earthquake caused no land damage. About 40 minutes after the main shock, a huge tsunami attacked the coasts, several villages in East Java Province were damaged severely, and 223 persons perished. At Pancer Village about 70 percent of the houses were swept away and 121 persons were killed by the tsunami. The relationship between tsunami heights and distances from the source shows that the Hatori''s tsunami magnitude wasm=3, which seems to be larger for the earthquake magnitude. But we should not consider this an extraordinary event because it was pointed out byHatori (1994) that the magnitudes of tsunamis in the Indonesia-Philippine region generally exceed 1�2 grade larger than those of other regions.},
author = {Tsuji, Y. and Imamura, F. and Matsutomi, H. and Synolakis, C. E. and Nanang, P. T. and Jumadi and Harada, S. and Han, S. S. and Arai, K. and Cook, B.},
journal = {Pure Appl. Geophys.},
keywords = {1994 East Java Tsunami - aftershock area - large t},
pages = {839--854},
title = {{Field survey of the East Java earthquake and tsunami of June 3, 1994}},
volume = {144},
year = {1995}
}
@article{Tuck,
author = {Tuck, E. O.},
journal = {J. Ship Research},
pages = {265--271},
title = {{The effect of a surface layer of viscous fluid on the wave resistance of a thin ship}},
volume = {18},
year = {1974}
}
@conference{Ernie,
author = {Tuck, E. O.},
booktitle = {NSF Workshop on Tsunamis, California},
editor = {Hwang, L S and {Y.K. Lee}, Tetra Tech Inc.},
pages = {43--109},
title = {{Models for predicting tsunami propagation}},
year = {1979}
}
@article{Tuck1972,
abstract = {A general solution of the linear long-wave equation is obtained for arbitrary ground motion on a uniformly sloping beach. Numerical results are presented for specific shapes and time histories of ground motion. Near-shore large amplitude waves are also investigated using non-linear theory.},
author = {Tuck, E. O. and Hwang, L.-S.},
doi = {10.1017/S0022112072002289},
issn = {0022-1120},
journal = {J. Fluid Mech},
month = {mar},
number = {03},
pages = {449--461},
title = {{Long wave generation on a sloping beach}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112072002289},
volume = {51},
year = {1972}
}
@techreport{Tuck2007,
author = {Tuck, E. O. and Scullen, D. C. and Lazauskas, L.},
institution = {The University of Adelaide},
title = {{Sea wave pattern evaluation}},
year = {2007}
}
@article{Tulin1999,
author = {Tulin, M. P. and Waseda, T.},
doi = {10.1017/S0022112098003255},
issn = {00221120},
journal = {J. Fluid Mech.},
month = {jan},
pages = {197--232},
title = {{Laboratory observations of wave group evolution, including breaking effects}},
url = {http://www.journals.cambridge.org/abstract{\_}S0022112098003255},
volume = {378},
year = {1999}
}
@article{Turitsyna2013,
abstract = {Studying the transition from a linearly stable coherent laminar state to a highly disordered state of turbulence is conceptually and technically challenging, and of great interest because all pipe and channel flows are of that type. In optics, understanding how a system loses coherence, as spatial size or the strength of excitation increases, is a fundamental problem of practical importance. Here, we report our studies of a fibre laser that operates in both laminar and turbulent regimes. We show that the laminar phase is analogous to a one-dimensional coherent condensate and the onset of turbulence is due to the loss of spatial coherence. Our investigations suggest that the laminar–turbulent transition in the laser is due to condensate destruction by clustering dark and grey solitons. This finding could prove valuable for the design of coherent optical devices as well as systems operating far from thermodynamic equilibrium.},
author = {Turitsyna, E. G. and Smirnov, S. V. and Sugavanam, S. and Tarasov, N. and Shu, X. and Babin, S. A. and Podivilov, E. V. and Churkin, D. V. and Falkovich, G. and Turitsyn, S. K.},
doi = {10.1038/nphoton.2013.246},
issn = {1749-4885},
journal = {Nature Photonics},
month = {sep},
number = {10},
pages = {783--786},
title = {{The laminar-turbulent transition in a fibre laser}},
url = {http://www.nature.com/doifinder/10.1038/nphoton.2013.246},
volume = {7},
year = {2013}
}
@article{Turkel1999,
author = {Turkel, E.},
journal = {Ann. Rev. Fluid Mech.},
pages = {385--416},
title = {{Preconditioning techniques in CFD}},
volume = {31},
year = {1999}
}
@article{Turnbull2007a,
author = {Turnbull, B. and McElwaine, J. N.},
doi = {10.3189/172756507781833938},
journal = {Journal of Glaciology},
pages = {30--40},
title = {{A comparison of powder-snow avalanches at Vall{\'{e}}e de la Sionne, Switzerland, with plume theories}},
volume = {53(180)},
year = {2007}
}
@article{Turnbull2008,
author = {Turnbull, B. and McElwaine, J. N.},
doi = {10.1029/2007JF000753},
journal = {J. Geophys. Res.},
pages = {F01003},
title = {{Experiments on the non-Boussinesq flow of self-igniting suspension currents on a steep open slope}},
volume = {113},
year = {2008}
}
@article{Turnbull2007,
author = {Turnbull, B. and McElwaine, J. N. and Ancey, C.},
doi = {10.1029/2006JF000489},
journal = {J. Geophys. Res.},
pages = {F01004},
title = {{Kulikovskiy-Sveshnikova-Beghin model of powder snow avalanches: Development and application}},
volume = {112},
year = {2007}
}
@book{Turner1973,
abstract = {The phenomena treated in this book all depend on the action of gravity on small density differences in a non-rotating fluid. The author gives a connected account of the various motions which can be driven or influenced by buoyancy forces in a stratified fluid, including internal waves, turbulent shear flows and buoyant convection. This excellent introduction to a rapidly developing field, first published in 1973, can be used as the basis of graduate courses in university departments of meteorology, oceanography and various branches of engineering. This edition is reprinted with corrections, and extra references have been added to allow readers to bring themselves up to date on specific topics. Professor Turner is a physicist with a special interest in laboratory modelling of small-scale geophysical processes. An important feature is the superb illustration of the text with many fine photographs of laboratory experiments and natural phenomena.},
author = {Turner, J. S.},
isbn = {0521297265},
issn = {978-0521297264},
pages = {412},
publisher = {Cambridge University Press},
title = {{Buoyancy Effects in Fluids}},
year = {1973}
}
@article{Umlauf2003,
author = {Umlauf, L. and Burchard, H.},
journal = {J. Mar. Res.},
number = {2},
pages = {235--265},
title = {{A generic length-scale equation for geophysical turbulence models}},
volume = {61},
year = {2003}
}
@article{Umlauf2005,
author = {Umlauf, L. and Burchard, H.},
journal = {Cont. Shelf Res.},
pages = {795--827},
title = {{Second-order turbulence closure models for geophysical boundary layers. A review of recent work}},
volume = {25},
year = {2005}
}
@article{Ursell1953,
author = {Ursell, F.},
journal = {Proc. Camb. Phil. Soc.},
pages = {685--694},
title = {{The long-wave paradox in the theory of gravity waves}},
volume = {49},
year = {1953}
}
@article{Vakhitov1973,
author = {Vakhitov, N. G. and Kolokolov, A. A.},
doi = {10.1007/BF01031343},
issn = {0033-8443},
journal = {Radiophysics and Quantum Electronics},
month = {jul},
number = {7},
pages = {783--789},
title = {{Stationary solutions of the wave equation in a medium with nonlinearity saturation}},
url = {http://www.springerlink.com/index/10.1007/BF01031343},
volume = {16},
year = {1973}
}
@article{Vallet2004,
author = {Vallet, J. and Turnbull, B. and Joly, S. and Dufour, F.},
journal = {Cold Regions Science and Technology},
number = {2--3},
pages = {153--159},
title = {{Observations on powder snow avalanches using videogrammetry}},
volume = {39},
year = {2004}
}
@article{Albada1982,
author = {van Albada, G. D. and van Leer, B. and Roberts, W. W.},
journal = {Astron. Astrophysics},
pages = {76},
title = {{A comparative study of computational methods in cosmic gas dynamics}},
volume = {108},
year = {1982}
}
@article{driess,
author = {van den Driessche, P. and Braddock, R. D.},
journal = {J. Mar. Res.},
pages = {217--226},
title = {{On the elliptic generating region of a tsunami}},
volume = {30},
year = {1972}
}
@article{VanGroesen2006,
abstract = {Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schr{\"{o}}dinger equation we will introduce a transformation to displaced phase-amplitude variables with respect to a background of monochromatic waves. The potential energy in the Hamiltonian then depends essentially on the phase. Looking as a special case to phases that are time independent, the oscillator equation for the signal at each position becomes autonomous, with the change of phase with position as only driving force for a spatial evolution towards extreme waves. This is observed to be the governing process of wave amplification in classes of already known solutions of NLS, namely the Akhmediev-, Ma- and Peregrine-solitons. We investigate the case of the soliton on finite background in detail in this Letter as the solution that descibes the complete spatial evolution of modulational instability from background to extreme waves.},
author = {van Groesen, E. and Karjanto, N.},
doi = {10.1016/j.physleta.2006.02.037},
issn = {03759601},
journal = {Phys. Lett. A},
month = {jun},
number = {4},
pages = {312--319},
title = {{Displaced phase-amplitude variables for waves on finite background}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0375960106003021},
volume = {354},
year = {2006}
}
@article{Leer2006,
author = {van Leer, B.},
journal = {Commun. Comput. Phys.},
pages = {192--206},
title = {{Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual-Distribution Schemes}},
volume = {1},
year = {2006}
}
@article{Leer1979,
author = {van Leer, B.},
journal = {J. Comput. Phys.},
pages = {101--136},
title = {{Towards the ultimate conservative difference scheme V: a second order sequel to Godunov' method}},
volume = {32},
year = {1979}
}
@incollection{Vanden-Broeck2007,
author = {Vanden-Broeck, J.-M.},
booktitle = {Solitary waves in fluids},
pages = {55--84},
title = {{Solitary waves in water: numerical methods and results}},
year = {2007}
}
@book{Vanden-Broeck2010,
abstract = {Free surface problems occur in many aspects of science and of everyday life such as the waves on a beach, bubbles rising in a glass of champagne, melting ice, pouring flows from a container and sails billowing in the wind. Consequently, the effect of surface tension on gravity-capillary flows continues to be a fertile field of research in applied mathematics and engineering. Concentrating on applications arising from fluid dynamics, Vanden-Broeck draws upon his years of experience in the field to address the many challenges involved in attempting to describe such flows mathematically. Whilst careful numerical techniques are implemented to solve the basic equations, an emphasis is placed upon the reader developing a deep understanding of the structure of the resulting solutions. The author also reviews relevant concepts in fluid mechanics to help readers from other scientific fields who are interested in free boundary problems.},
address = {Cambridge},
author = {Vanden-Broeck, J.-M.},
isbn = {978-0521811903},
pages = {330},
publisher = {Cambridge University Press},
title = {{Gravity-Capillary Free-Surface Flows}},
year = {2010}
}
@article{Vantorre2004,
author = {Vantorre, M. and Banasiak, R. and Verhoeven, R.},
journal = {Applied Ocean Research},
pages = {61--72},
title = {{Modelling of hydraulic performance and wave energy extraction by a point absorber in heave}},
volume = {26},
year = {2004}
}
@article{Vasseur1999,
author = {Vasseur, A.},
doi = {10.1080/03605309908821491},
issn = {0360-5302},
journal = {Comm. Partial Diff. Eqns.},
month = {jan},
number = {11-12},
pages = {1987--1997},
title = {{Time regularity for the system of isentropic gas dynamics with $\gamma$ = 3}},
url = {http://www.tandfonline.com/doi/abs/10.1080/03605309908821491},
volume = {24},
year = {1999}
}
@article{Vassilevskii2011,
author = {Vassilevskii, Yu. and Simakov, S. and Salamatova, V. and Ivanov, Yu. and Dobroserdova, T.},
journal = {Russ. J. Numer. Anal. Math. Modelling},
number = {6},
pages = {605--622},
title = {{Numerical issues of modelling blood flow in networks of vessels with pathologies}},
volume = {26},
year = {2011}
}
@article{Vazquez-Cendon1999,
author = {Vazquez-Cendon, M. E.},
journal = {Journal of Computational Physics},
pages = {497--526},
title = {{Improved Treatment of Source Terms in Upwind Schemes for the Shallow Water Equations in Channels with Irregular Geometry}},
volume = {148},
year = {1999}
}
@article{Velichko2002,
author = {Velichko, A. S. and Dotsenko, S. F. and Potetyunko, E. N.},
journal = {Phys. Oceanogr.},
pages = {308--322},
title = {{Amplitude-energy characteristics of tsunami waves for various types of seismic sources generating them}},
volume = {12(6)},
year = {2002}
}
@article{Ven1,
author = {Venakides, S.},
journal = {AMS Transactions},
pages = {189--226},
title = {{The zero dispersion limit of the Korteweg-de Vries equation with periodic initial data}},
volume = {301},
year = {1987}
}
@article{Venkataraman2004,
author = {Venkataraman, A. and Kanamori, H.},
journal = {J. Geophys. Res.},
pages = {B05302},
title = {{Observational constraints on the fracture energy of subduction zone earthquakes}},
volume = {109},
year = {2004}
}
@book{Vennard1982,
author = {Vennard, J. K. and Street, R. L.},
edition = {Sixth},
pages = {689},
publisher = {Springer},
title = {{Elementary fluid mechanics}},
year = {1982}
}
@article{Verner1978,
author = {Verner, J. H.},
journal = {SIAM J. Num. Anal.},
pages = {772--790},
title = {{Explicit Runge-Kutta methods with estimates of the local truncation error}},
volume = {15(4)},
year = {1978}
}
@article{Vertesi1990,
author = {V{\'{e}}rtesi, P.},
journal = {SIAM J. Numer. Anal.},
pages = {1322--1331},
title = {{Optimal Lebesgue constant for Lagrange interpolation}},
volume = {27},
year = {1990}
}
@article{Vignoli2008,
author = {Vignoli, G. and Titarev, V. A. and Toro, E. F.},
doi = {10.1016/j.jcp.2007.11.006},
issn = {00219991},
journal = {J. Comp. Phys.},
month = {feb},
number = {4},
pages = {2463--2480},
title = {{ADER schemes for the shallow water equations in channel with irregular bottom elevation}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999107004779},
volume = {227},
year = {2008}
}
@incollection{Vila2005,
author = {Vila, J. P.},
booktitle = {Meshfree Methods for Partial Differential Equations II},
title = {{SPH Renormalized Hybrid Methods for Conservation Laws: Applications to Free Surface Flows}},
year = {2005}
}
@article{Vila1999,
author = {Vila, J. P.},
doi = {10.1142/S0218202599000117},
issn = {0218-2025},
journal = {Mathematical Models and Methods in Applied Sciences},
month = {mar},
number = {02},
pages = {161--209},
title = {{On particle weighted methods and smooth particle hydrodynamics}},
url = {http://www.worldscientific.com/doi/abs/10.1142/S0218202599000117},
volume = {09},
year = {1999}
}
@phdthesis{Vila1986,
author = {Vila, J. P.},
school = {University Paris VI},
title = {{Sur la th{\'{e}}orie et l'approximation num{\'{e}}rique des probl{\`{e}}mes hyperboliques non lin{\'{e}}aires, application aux {\'{e}}quations de Saint-Venant et {\`{a}} la mod{\'{e}}lisation des avalanches denses}},
type = {Ph.D. Thesis},
year = {1986}
}
@article{Savage,
author = {Villeneuve, M. and Savage, S. B.},
journal = {J. Hydraulic Res.},
pages = {249--266},
title = {{Nonlinear, dispersive, shallow-water waves developed by a moving bed}},
volume = {31},
year = {1993}
}
@article{Viotti2013a,
author = {Viotti, C. and Dutykh, D. and Dias, F.},
journal = {Procedia IUTAM},
pages = {1--9},
title = {{The conformal-mapping method for surface gravity waves in the presence of variable bathymetry and mean current}},
volume = {Submitted},
year = {2013}
}
@article{Viotti2014,
author = {Viotti, C. and Dutykh, D. and Dias, F.},
doi = {10.1016/j.piutam.2014.01.053},
issn = {22109838},
journal = {Procedia IUTAM},
pages = {110--118},
title = {{The Conformal-mapping Method for Surface Gravity Waves in the Presence of Variable Bathymetry and Mean Current}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S2210983814000546},
volume = {11},
year = {2014}
}
@article{Viotti2013,
abstract = {Extreme surface waves in a deep-water long-crested sea are often interpreted as a manifestation in the real world of the so-called breathing solitons of the focusing nonlinear Schr{\"{o}}dinger equation. While the spontaneous emergence of such coherent structures from nonlinear wave dynamics was demonstrated to take place in fiber-optics systems, the same point remains far more controversial in the hydrodynamic case. With the aim to shed further light on this matter, the emergence of breatherlike coherent wave groups in a long-crested random sea is investigated here by means of high-resolution spectral simulations of the fully nonlinear two-dimensional Euler equations. The primary focus of our study is to parametrize the structure of random wave fields with respect to the Benjamin-Feir index, which is a nondimensional measure of the energy localization in Fourier space. This choice is motivated by previous results, showing that extreme-wave activity in a long-crested sea is highly sensitive to such a parameter, which is varied here by changing both the characteristic spectral bandwidth and the average wave steepness. It is found that coherent wave groups, closely matching realizations of Kuznetsov-Ma breathers in Euler dynamics, develop within wave fields characterized by sufficiently narrow-banded spectra. The characteristic spatial and temporal scales of wave group dynamics, and the corresponding occurrence of extreme events, are quantified and discussed by means of space-time autocorrelations of the surface elevation envelope and extreme-event statistics.},
author = {Viotti, C. and Dutykh, D. and Dudley, J. M. and Dias, F.},
doi = {10.1103/PhysRevE.87.063001},
issn = {1539-3755},
journal = {Phys. Rev. E},
month = {jun},
number = {6},
pages = {063001},
title = {{Emergence of coherent wave groups in deep-water random sea}},
volume = {87},
year = {2013}
}
@article{Voellmy1955,
author = {Voellmy, A.},
journal = {Schweizerische Bauzeitung},
pages = {159--162,212--217,246--249,280--285},
title = {{{\"{U}}ber die Zerst{\"{o}}rungskraft von Lawinen}},
volume = {73},
year = {1955}
}
@article{volt,
author = {Volterra, V.},
journal = {Annales Scientifiques de l'Ecole Normale Sup{\'{e}}rieure},
number = {3},
pages = {401--517},
title = {{Sur l'{\'{e}}quilibre des corps {\'{e}}lastiques multiplement connexes}},
volume = {24},
year = {1907}
}
@book{Voltsinger1989,
address = {Leningrad},
author = {Voltsinger, N. E. and Pelinovsky, E. N. and Klevannyi, K. A.},
pages = {272},
publisher = {Gidrometeoizdat},
title = {{Long wave dynamics of coastal regions}},
year = {1989}
}
@article{Gerstner1804,
author = {von Gerstner, F. J.},
journal = {Abhandlungen der K{\"{o}}nigl. B{\"{o}}hmischen Gesellschaft der Wissenschaften. Prague.},
pages = {1--65},
title = {{Theorie der Wellen sammit einer daraus abgeleiteten Theorie der Deichprofile}},
volume = {1},
year = {1804}
}
@article{Vuillon2003,
author = {Vuillon, L.},
journal = {Bulletin of the Belgian Mathematical Society-Simon Stevin},
number = {5},
pages = {787--805},
title = {{Balanced words}},
volume = {10},
year = {2003}
}
@misc{Vuillon2014,
author = {Vuillon, L. and Dutykh, D. and Fedele, F.},
booktitle = {http://youtu.be/hIhLlsV69OQ},
pages = {http://youtu.be/hIhLlsV69OQ},
title = {{Animation of a perturbed pattern dynamics under the hyperbolic NLS equation: $\backslash$url{\{}http://youtu.be/hIhLlsV69OQ{\}}}},
url = {http://youtu.be/hIhLlsV69OQ},
year = {2014}
}
@article{Walczak2015,
author = {Walczak, P. and Randoux, S. and Suret, P.},
doi = {10.1103/PhysRevLett.114.143903},
issn = {0031-9007},
journal = {Phys. Rev. Lett.},
month = {apr},
number = {14},
pages = {143903},
title = {{Optical Rogue Waves in Integrable Turbulence}},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.114.143903},
volume = {114},
year = {2015}
}
@article{Waleffe1995,
author = {Waleffe, F.},
doi = {10.1063/1.868682},
issn = {10706631},
journal = {Phys. Fluids},
number = {12},
pages = {3060},
title = {{Transition in shear flows. Nonlinear normality versus non-normal linearity}},
volume = {7},
year = {1995}
}
@article{Waleffe1997,
abstract = {A self-sustaining process conjectured to be generic for wall-bounded shear flows is investigated. The self-sustaining process consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls. The process is analyzed and shown to be remarkably insensitive to whether there is no-slip or free-slip at the walls. A low-order model of the process is derived from the Navier-Stokes equations for a sinusoidal shear flow. The model has two unstable steady solutions above a critical Reynolds number, in addition to the stable laminar flow. For some parameter values, there is a second critical Reynolds number at which a homoclinic bifurcation gives rise to a stable periodic solution. This suggests a direct link between unstable steady solutions and almost periodic solutions that have been computed in plane Couette flow. It is argued that this self-sustaining process is responsible for the bifurcation of shear flows at low Reynolds numbers and perhaps also for controlling the near-wall region of turbulent shear flows at higher Reynolds numbers.},
author = {Waleffe, F.},
doi = {10.1063/1.869185},
issn = {10706631},
journal = {Phys. Fluids},
number = {4},
pages = {883},
title = {{On a self-sustaining process in shear flows}},
volume = {9},
year = {1997}
}
@article{Waleffe1995a,
author = {Waleffe, F.},
journal = {Stud. Appl. Math.},
number = {95},
pages = {319--343},
title = {{Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process}},
volume = {95},
year = {1995}
}
@article{Walker2005,
author = {Walker, K. T. and Ishii, M. and Shrearer, P. M.},
journal = {Geophysical Research Letters},
pages = {24303},
title = {{Rupture details of the 28 March 2005 Sumatra Mw 8.6 earthquake imaged with teleseismic P waves}},
volume = {32},
year = {2005}
}
@article{Walton2011,
abstract = {The high-Reynolds-number stability of unsteady pipe flow to axisymmetric disturbances is studied using asymptotic analysis. It is shown that as the disturbance amplitude is increased, nonlinear effects first become significant within the critical layer, which moves away from the pipe wall as a result. It is found that the flow stabilizes once the basic profile has become sufficiently fully developed. By tracing the nonlinear neutral curve back to earlier times, it is found that in addition to the wall mode, which arises from a classical upper branch linear stability analysis, there also exists a nonlinear neutral centre mode, governed primarily by inviscid dynamics. The centre mode problem is solved numerically and the results show the existence of a concentrated region of vorticity centred on or close to the pipe axis and propagating downstream at almost the maximum fluid velocity. The connection between this structure and the puffs and slugs of vorticity observed in experiments is discussed.},
author = {Walton, A. G.},
doi = {10.1017/jfm.2011.302},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {sep},
pages = {284--315},
title = {{The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes}},
volume = {684},
year = {2011}
}
@article{Walton2005,
author = {Walton, A. G.},
doi = {10.1098/rspa.2004.1428},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {mar},
number = {2055},
pages = {813--824},
title = {{The stability of nonlinear neutral modes in Hagen-Poiseuille flow}},
volume = {461},
year = {2005}
}
@article{Wang2006,
author = {Wang, X. and Liu, P. L.-F.},
journal = {J. Hydr. Res.},
pages = {147--154},
title = {{An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian Ocean tsunami}},
volume = {44(2)},
year = {2006}
}
@article{Wang2003,
abstract = {We analyze the multisymplectic Preissman scheme for the KdV equation with the periodic boundary condition and show that the unconvergence of the widely-used iterative methods to solve the resulting nonlinear algebra system of the Preissman scheme is due to the introduced potential function. A artificial numerical condition is added to the periodic boundary condition. The added boundary condition makes the numerical implementation of the multisymplectic Preissman scheme practical and is proved not to change the numerical solutions of the KdV equation. Based on our analysis, we derive some new schemes which are not restricted by the artificial boundary condition and more efficient than the Preissman scheme because of less computing cost and less computer storages. By eliminating the auxiliary variables, we also derive two schemes for the KdV equation, one is a 12-point scheme and the other is an 8-point scheme. As the byproducts, we present two new explicit schemes which are not multisymplectic but still have remarkable numerical stable property.},
author = {Wang, Y. and Wang, B. and Qin, M. Z.},
journal = {Appl. Math. Comput.},
keywords = {integrators geometry equation pdes},
number = {2},
pages = {299--326},
title = {{Numerical Implementation of the Multisymplectic Preissman Scheme and Its Equivalent Schemes}},
url = {http://arxiv.org/abs/math-ph/0303028},
volume = {149},
year = {2003}
}
@article{Ward80,
author = {Ward, S. N.},
journal = {J. Phys. Earth},
pages = {441--474},
title = {{Relationship of tsunami generation and an earthquake source}},
volume = {28},
year = {1980}
}
@article{Ward,
author = {Ward, S. N.},
journal = {J. Geophysical Res.},
pages = {11201--11215},
title = {{Landslide tsunami}},
volume = {106},
year = {2001}
}
@article{Ward2003,
author = {Ward, S. N. and Day, S. J.},
doi = {10.1046/j.1365-246X.2003.02016.x},
issn = {0956540X},
journal = {Geophysical Journal International},
month = {sep},
number = {3},
pages = {891--902},
title = {{Ritter Island Volcano - lateral collapse and the tsunami of 1888}},
url = {http://doi.wiley.com/10.1046/j.1365-246X.2003.02016.x},
volume = {154},
year = {2003}
}
@article{Ward2001,
abstract = {Geological evidence suggests that during a future eruption, Cumbre Vieja Volcano on the Island of La Palma may experience a catastrophic failure of its west flank, dropping 150 to 500 km³ of rock into the sea. Using a geologically reasonable estimate of landslide motion, we model tsunami waves produced by such a collapse. Waves generated by the run‐out of a 500 km³ (150 km³) slide block at 100 m/s could transit the entire Atlantic Basin and arrive on the coasts of the Americas with 10-25 m (3-8 m) height.},
author = {Ward, S. N. and Day, S. J.},
doi = {10.1029/2001GL013110},
issn = {0094-8276},
journal = {Geophysical Research Letters},
number = {17},
pages = {3397},
title = {{Cumbre Vieja Volcano - Potential collapse and tsunami at La Palma, Canary Islands}},
url = {http://www.agu.org/pubs/crossref/2001/2001GL013110.shtml},
volume = {28},
year = {2001}
}
@article{Watts1998,
author = {Watts, P.},
journal = {ASCE J of Waterways Port Coastal and Oc Eng},
pages = {127--137},
title = {{Wavemaker curves for tsunamis generated by underwater landslides}},
volume = {124},
year = {1998}
}
@article{Watts2003,
abstract = {Case studies of landslide tsunamis require integration of marine geology data and interpretations into numerical simulations of tsunami attack. Many landslide tsunami generation and propagation models have been proposed in recent time, further motivated by the 1998 Papua New Guinea event. However, few of these models have proven capable of integrating the best available marine geology data and interpretations into successful case studies that reproduce all available tsunami observations and records. We show that nonlinear and dispersive tsunami propagation models may be necessary for many landslide tsunami case studies. GEOWAVE is a comprehensive tsunami simulation model formed in part by combining the Tsunami Open and Progressive Initial Conditions System (TOPICS) with the fully nonlinear Boussinesq water wave model FUNWAVE. TOPICS uses curve fits of numerical results from a fully nonlinear potential flow model to provide approximate landslide tsunami sources for tsunami propagation models, based on marine geology data and interpretations. In this work, we validate GEOWAVE with successful case studies of the 1946 Unimak, Alaska, the 1994 Skagway, Alaska, and the 1998 Papua New Guinea events. GEOWAVE simulates accurate runup and inundation at the same time, with no additional user interference or effort, using a slot technique. Wave breaking, if it occurs during shoaling or runup, is also accounted for with a dissipative breaking model acting on the wave front. The success of our case studies depends on the combination of accurate tsunami sources and an advanced tsunami propagation and inundation model.},
author = {Watts, P. and Grilli, S. T. and Kirby, J. T. and Fryer, G. J. and Tappin, D. R.},
doi = {10.5194/nhess-3-391-2003},
issn = {16849981},
journal = {Natural Hazards And Earth System Science},
number = {5},
pages = {391--402},
publisher = {Citeseer},
title = {{Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model}},
url = {http://www.nat-hazards-earth-syst-sci.net/3/391/2003/},
volume = {3},
year = {2003}
}
@article{Watts2005,
abstract = {Based on numerical simulations presented in Part I, we derive predictive empirical equations describing tsunami generation by submarine mass failure (SMF) that are only valid in the vicinity of the tsunami sources. We give equations for slides and slumps, along with some cautions about their appropriate use. We further discuss results obtained here and in Part I and their practical application to case studies. We show that initial acceleration is the primary parameter describing SMF center of mass motion during tsunami generation. We explain an apparent paradox, raised in Part I, in slump center of mass motion, whereby the distance traveled is proportional to shear strength along the failure plane. We stress that the usefulness of predictive equations depends on the quality of the parameters they rely on. Parameter ranges are discussed in the paper, and we propose a method to estimate slump motion and shear strength and discuss SMF thickness to length values, for case studies. We derive the analytical tools needed to characterize SMF tsunami sources in propagation models. Specifically, we quantify three-dimensional (3D) effects on tsunami characteristic amplitude, and we propose an analytical method to specify initial 3D tsunami elevations, shortly after tsunami generation, in long wave tsunami propagation models. This corresponds to treating SMF tsunami sources like coseismic displacement tsunami sources. We conduct four case studies of SMF tsunamis and show that our predictive equations can provide rapid rough estimates of overall tsunami observations that might be useful in crisis situations, when time is too short to run propagation models. Thus, for each case, we show that the characteristic tsunami amplitude is a reasonable predictor of maximum runup in actual 3D geometry. We refer to the latter observation as the correspondence principle, which we propose to apply for rapid tsunami hazard assessment, in combination with the predictive tsunami amplitude equations.},
author = {Watts, P. and Grilli, S. T. and Tappin, D. R. and Fryer, G. J.},
doi = {10.1061/(ASCE)0733-950X(2005)131:6(298)},
issn = {0733950X},
journal = {Journal of Waterway Port Coastal and Ocean Engineering},
number = {6},
pages = {298},
title = {{Tsunami generation by submarine mass failure. II: Predictive equations and case studies}},
url = {http://link.aip.org/link/JWPED5/v131/i6/p298/s1{\&}Agg=doi},
volume = {131},
year = {2005}
}
@article{Watts2000,
author = {Watts, P. and Imamura, F. and Grilli, S. T.},
journal = {Science of Tsunami Hazards},
number = {2},
pages = {107--123},
publisher = {Citeseer},
title = {{Comparing model simulations of three benchmark tsunami generation cases}},
url = {http://scholar.google.com/scholar?hl=en{\&}btnG=Search{\&}q=intitle:Comparing+model+simulations+of+three+Benchmark+tsunami+generation+cases{\#}0},
volume = {18},
year = {2000}
}
@article{Wayne2002,
abstract = {In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for a Boussinesq equation. The equations governing the corrections to the KdV approximation are explicitly solvable and we prove estimates showing that they do indeed give a significantly better approximation than the KdV equation alone. We also present the results of numerical experiments which show that the error estimates we derive are essentially optimal.},
author = {Wayne, C. E. and Wright, J. D.},
doi = {10.1137/S1111111102411298},
issn = {1536-0040},
journal = {SIAM J. Appl. Dyn. Sys.},
month = {jan},
number = {2},
pages = {271--302},
title = {{Higher Order Modulation Equations for a Boussinesq Equation}},
url = {http://epubs.siam.org/doi/abs/10.1137/S1111111102411298},
volume = {1},
year = {2002}
}
@article{Wedin2004,
author = {Wedin, H. and Kerswell, R. R.},
doi = {10.1017/S0022112004009346},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {jun},
pages = {333--371},
title = {{Exact coherent structures in pipe flow: travelling wave solutions}},
volume = {508},
year = {2004}
}
@article{Wehausen1960,
author = {Wehausen, J. V. and Laitone, E. V.},
journal = {Handbuch der Physik},
pages = {446--778},
title = {{Surface waves}},
volume = {9},
year = {1960}
}
@article{Wei1995,
author = {Wei, G. and Kirby, J. T. and Grilli, S. T. and Subramanya, R.},
journal = {J. Fluid Mech.},
pages = {71--92},
title = {{A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves}},
volume = {294},
year = {1995}
}
@article{Wei2006,
author = {Wei, Y. and Mao, X.-Z. and Cheung, K. F.},
journal = {Journal of Waterwave, Port, Coastal and Ocean Engineering},
pages = {114--124},
title = {{Well-Balanced Finite-Volume Model for Long-Wave Runup}},
volume = {132},
year = {2006}
}
@article{Weinan1992,
abstract = {The homogenization of a scalar conservation law with a highly oscillatory forcing term is studied. Effective equations are derived for the local averages of the oscillatory solutions, together with approximations that correctly represent the phase and the amplitude of the oscillations. A random choice method is also designed, which, as demonstrated by our numerical results, gives the correct local averages without necessarily resolving the small scales. Finally, the homogenization problem with an additional small viscosity term is studied.},
author = {Weinan, E.},
doi = {10.1137/0152055},
issn = {0036-1399},
journal = {SIAM J. Appl. Math.},
month = {aug},
number = {4},
pages = {959--972},
title = {{Homogenization of Scalar Conservation Laws with Oscillatory Forcing Terms}},
url = {http://epubs.siam.org/doi/abs/10.1137/0152055},
volume = {52},
year = {1992}
}
@article{Weinberger1975,
author = {Weinberger, H.},
journal = {Rend. Mat. Univ. Roma},
pages = {295--310},
title = {{Invariant sets for weakly coupled parabolic and elliptic systems}},
volume = {8},
year = {1975}
}
@article{Weinkauf2012,
author = {Weinkauf, T. and Theisel, H.},
doi = {10.1109/MCSE.2012.97},
journal = {Comp. Sci. Eng.},
pages = {78--84},
title = {{Flow Visualization and Analysis Using Streak and Time Lines}},
volume = {14},
year = {2012}
}
@article{Weinstein1983,
author = {Weinstein, A.},
journal = {J. Diff. Geom.},
pages = {523--557},
title = {{The local structure of Poisson manifolds}},
volume = {18},
year = {1983}
}
@article{Weinstein2008,
author = {Weinstein, S. A. and Lundgren, P. R.},
journal = {Pure Appl. Geophys.},
pages = {451--474},
title = {{Finite Fault Modeling in a Tsunami Warning Center Context}},
volume = {165},
year = {2008}
}
@article{Wessel2009,
author = {Wessel, P.},
doi = {10.1007/s00024-008-0437-2},
issn = {0033-4553},
journal = {Pure Appl. Geophys.},
month = {feb},
number = {1-2},
pages = {301--324},
title = {{Analysis of Observed and Predicted Tsunami Travel Times for the Pacific and Indian Oceans}},
url = {http://www.springerlink.com/index/10.1007/s00024-008-0437-2},
volume = {166},
year = {2009}
}
@article{West1987a,
abstract = {We present a new numerical method for studying the evolution of free and bound waves on the nonlinear ocean surface. The technique, based on a representation due to Watson and West (1975), uses a slope expansion of the velocity potential at the free surface and not an expansion about a reference surface. The numerical scheme is applied to a number of wave and wave train configurations including longwave-shortwave interactions and the three-dimensional instability of waves with finite slope. The results are consistent with those obtained in other studies. One strength of the technique is that it can be applied to a variety of wave train and spectral configurations without modifying the code.},
author = {West, B. J. and Brueckner, K. A. and Janda, R. S. and Milder, D. M. and Milton, R. L.},
doi = {10.1029/JC092iC11p11803},
issn = {0148-0227},
journal = {J. Geophys. Res.},
number = {C11},
pages = {11803},
title = {{A new numerical method for surface hydrodynamics}},
url = {http://doi.wiley.com/10.1029/JC092iC11p11803},
volume = {92},
year = {1987}
}
@article{West1987,
abstract = {We present a new numerical method for studying the evolution of free and bound waves on the nonlinear ocean surface. The technique, based on a representation due to Watson and West (1975), uses a slope expansion of the velocity potential at the free surface and not an expansion about a reference surface. The numerical scheme is applied to a number of wave and wave train configurations including longwave-shortwave interactions and the three-dimensional instability of waves with finite slope. The results are consistent with those obtained in other studies. One strength of the technique is that it can be applied to a variety of wave train and spectral configurations without modifying the code.},
author = {West, B. J. and Brueckner, K. A. and Janda, R. S. and Milder, D. M. and Milton, R. L.},
doi = {10.1029/JC092iC11p11803},
issn = {0148-0227},
journal = {J. Geophys. Res.},
number = {C11},
pages = {11803--11824},
title = {{A New Numerical Method for Surface Hydrodynamics}},
url = {http://www.agu.org/pubs/crossref/1987/JC092iC11p11803.shtml},
volume = {92},
year = {1987}
}
@article{wester,
author = {Westergaard, H. M.},
journal = {Bull. Amer. Math. Soc.},
pages = {695},
title = {{General solution of the problem of elastostatics of an n-dimensional homogeneous isotropic solid in an n-dimensional space}},
volume = {41},
year = {1935}
}
@article{Whitham1967a,
abstract = {This paper reviews various uses of variational methods in the theory of nonlinear dispersive waves, with details presented for water waves. The appropriate variational principle for water waves is discussed first, and used to derive the long-wave approximations of Boussinesq and Korteweg {\&} de Vries. The resonant near-linear interaction theory is presented briefly in terms of the Lagrangian function of the variational principle. Then the author's theory of slowly varying wavetrains and its application to Stokes's waves are reviewed. Luke's perturbation theory for slowly varying wavetrains is also given. Finally, it is shown how more general dispersive relations can be formulated by means of integro-differential equations; an important application of this, developed with some success, is towards resolving longstanding difficulties in understanding the breaking of water waves.},
author = {Whitham, G. B.},
doi = {10.1098/rspa.1967.0119},
issn = {1364-5021},
journal = {Proc. R. Soc. Lond. A},
month = {jun},
number = {1456},
pages = {6--25},
title = {{Variational Methods and Applications to Water Waves}},
url = {http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1967.0119},
volume = {299},
year = {1967}
}
@article{Whitham1965,
author = {Whitham, G. B.},
journal = {J. Fluid Mech.},
pages = {273--283},
title = {{A general approach to linear and non-linear dispersive waves using a Lagrangian}},
volume = {22},
year = {1965}
}
@book{Whitham1999,
address = {New York},
author = {Whitham, G. B.},
isbn = {978-0471940906},
pages = {656},
publisher = {John Wiley {\&} Sons Inc.},
title = {{Linear and nonlinear waves}},
year = {1999}
}
@article{Whitham1967,
author = {Whitham, G. B.},
journal = {J. Fluid Mech.},
pages = {399--412},
title = {{Non-linear dispersion of water waves}},
volume = {27},
year = {1967}
}
@article{Whitmore2009,
author = {Whitmore, P. and Brink, U. and Caropolo, M. and Huerfano-Mureno, V. and Knight, W. and Sammler, W. and Sandrik, A.},
journal = {Science of Tsunami Hazards},
pages = {86--107},
title = {{NOAA/West coast and Alaska tsunami warning center Atlantic Ocean response criteria}},
volume = {28(2)},
year = {2009}
}
@book{Widder1946,
author = {Widder, D. V.},
publisher = {Princeton Univ. Press},
series = {Princeton Mathematical series, 6},
title = {{The Laplace transform}},
year = {1946}
}
@article{Wigner1960,
author = {Wigner, E.},
journal = {Communications in Pure and Applied Mathematics},
month = {feb},
number = {1},
title = {{The Unreasonable Effectiveness of Mathematics in the Natural Sciences}},
volume = {13},
year = {1960}
}
@article{Williams2010,
author = {Williams, D. M.},
journal = {Irish Journal of Earth Sciences},
pages = {13--23},
title = {{Mechanisms of wave transport of megaclasts on elevated cliff-top platforms: examples from western Ireland relevant to the storm-wave versus tsunami controversy}},
volume = {28},
year = {2010}
}
@article{Williams1981,
author = {Williams, J. M.},
doi = {10.1098/rsta.1981.0159},
issn = {1364-503X},
journal = {Phil. Trans. R. Soc. Lond. A},
month = {aug},
number = {1466},
pages = {139--188},
title = {{Limiting Gravity Waves in Water of Finite Depth}},
url = {http://rsta.royalsocietypublishing.org/cgi/doi/10.1098/rsta.1981.0159},
volume = {302},
year = {1981}
}
@article{Willis2009,
author = {Willis, A. P. and Kerswell, R. R.},
doi = {10.1017/S0022112008004618},
issn = {0022-1120},
journal = {J. Fluid Mech.},
month = {dec},
pages = {213--233},
title = {{Turbulent dynamics of pipe flow captured in a reduced model: puff relaminarization and localized 'edge' states}},
volume = {619},
year = {2009}
}
@article{Willis2008a,
abstract = {The recent discovery of unstable traveling waves (TWs) in pipe flow has been hailed as a significant breakthrough with the hope that they populate the turbulent attractor. We confirm the existence of coherent states with inter