An operator expansion formalism for nonlinear surface waves over variable depth

RALPH A. SMITH

doi:10.1017/S0022112098001219

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The Hamiltonian formalism for surface waves associated with the method of Watson & West (1975) is extended to handle the case of spatially varying bottom depth. This description models moderately nonlinear waves over a wider range of scales than Boussinesq-type approximations. A pseudospectral simulation code has been developed using this formalism in two horizontal dimensions. Computations using the model compare well with measurements of waves over a bar, diffractive focusing by topography, and shoaling of solitary waves. Waveforms are computed accurately until near the point of breaking.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Nicholls, David P. and Reitich, Fernando 2001. Stability of High-Order Perturbative Methods for the Computation of Dirichlet–Neumann Operators. Journal of Computational Physics, Vol. 170, Issue. 1, p. 276.

Willemsen, Jorge F. 2001. Deterministic modelling of driving and dissipation for ocean surface gravity waves. Journal of Geophysical Research: Oceans, Vol. 106, Issue. C11, p. 27187.

Willemsen, Jorge F. 2002. Deterministic modeling of driving and dissipation for ocean surface gravity waves in two horizontal dimensions. Journal of Geophysical Research: Oceans, Vol. 107, Issue. C8,

Reitich, Fernando 2003. Free Boundary Problems. p. 265.

Galiev, Sh. U. 2003. The theory of non-linear transresonant wave phenomena and an examination of Charles Darwin's earthquake reports. Geophysical Journal International, Vol. 154, Issue. 2, p. 300.

Nicholls, David P. and Reitich, Fernando 2004. Shape deformations in rough-surface scattering: cancellations, conditioning, and convergence. Journal of the Optical Society of America A, Vol. 21, Issue. 4, p. 590.

Guyenne, Philippe and Nicholls, David P. 2005. Numerical simulation of solitary waves on plane slopes. Mathematics and Computers in Simulation, Vol. 69, Issue. 3-4, p. 269.

Craig, Walter Guyenne, Philippe Nicholls, David P. and Sulem, Catherine 2005. Hamiltonian long–wave expansions for water waves over a rough bottom. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 461, Issue. 2055, p. 839.

Galiev, Sh.U. 2005. Strongly nonlinear two-speed wave equations for coastal waves and their application. Physica D: Nonlinear Phenomena, Vol. 208, Issue. 3-4, p. 147.

Bingham, Harry B. and Agnon, Yehuda 2005. A Fourier–Boussinesq method for nonlinear water waves. European Journal of Mechanics - B/Fluids, Vol. 24, Issue. 2, p. 255.

Fructus, Dorian and Grue, John 2007. An explicit method for the nonlinear interaction between water waves and variable and moving bottom topography. Journal of Computational Physics, Vol. 222, Issue. 2, p. 720.

Nicholls, David P. 2007. Boundary Perturbation Methods for Water Waves. GAMM-Mitteilungen, Vol. 30, Issue. 1, p. 44.

Guyenne, Philippe and Nicholls, David P. 2008. A High-Order Spectral Method for Nonlinear Water Waves over Moving Bottom Topography. SIAM Journal on Scientific Computing, Vol. 30, Issue. 1, p. 81.

Li, Bin 2008. Wave Equations for Regular and Irregular Water Wave Propagation. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 134, Issue. 2, p. 121.

Chazel, F. Benoit, M. Ern, A. and Piperno, S. 2009. A double-layer Boussinesq-type model for highly nonlinear and dispersive waves. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 465, Issue. 2108, p. 2319.

Schäffer, Hemming A. 2009. A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH. Coastal Engineering, Vol. 56, Issue. 5-6, p. 517.

Lannes, David and Bonneton, Philippe 2009. Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation. Physics of Fluids, Vol. 21, Issue. 1,

Nicholls, David P. and Taber, Mark 2009. Detection of ocean bathymetry from surface wave measurements. European Journal of Mechanics - B/Fluids, Vol. 28, Issue. 2, p. 224.

Ruban, V. P. 2009. Water wave collapses over quasi-one-dimensional nonuniformly periodic bed profiles. Physical Review E, Vol. 80, Issue. 6,

Li, Bin 2010. A mathematical model for weakly nonlinear water wave propagation. Wave Motion, Vol. 47, Issue. 5, p. 265.

Download full list

Article contents

An operator expansion formalism for nonlinear surface waves over variable depth

Abstract

Information

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

An operator expansion formalism for nonlinear surface waves over variable depth

Abstract

Information

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests