Nonlinear evolution of surface gravity waves over highly variable depth
Andre Nachbin | Artiles , William
dispersive waves | inhomogneous media | asymptotic theory
New nonlinear evolution equations are derived that generalize those presented in a Letter by Matsuno and a terrain-following Boussinesq system recently deduced by Nachbin. 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 (FFT) solvers.