An operator expansion formalism for nonlinear surface waves over variable depth

Abstract

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.