Nonlinear Evolution of Surface Gravity Waves over Highly Variable Depth

Details Nonlinear Evolution of Surface Gravity Waves over Highly Variable Depth Nonlinear Evolution of Surface Gravity Waves over Highly Variable Depth

Nov 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004phrvl..93w4501a&link_type=abstract

Physical Review Letters, vol. 93, Issue 23, id. 234501

Physics

7

Wave Propagation In Random Media, Nonlinear Acoustics, Acoustic Signal Processing

Scientific paper

New nonlinear evolution equations are derived that generalize those presented in a Letter by Matsuno [

Phys. Rev. Lett. 69, 609 (1992)PRLTAO0031-900710.1103/PhysRevLett.69.609

] and a terrain-following Boussinesq system recently deduced by Nachbin [

SIAM J Appl. Math.SMJMAP0036-1399 63, 905 (2003)10.1137/S0036139901397583

]. 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.

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