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Nonlinear Evolution of Surface Gravity Waves over Highly Variable Depth
Nonlinear Evolution of Surface Gravity Waves over Highly Variable Depth
Nov 2004
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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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