Boundary integral method applied to the propagation of non-linear gravity waves generated by a moving bottom

Abstract

A numerical procedure is applied for the solution of the non-linear problem of propagation of waves generated in a homogeneous fluid, occupying an infinite channel, by the bounded motion of the bottom. For the sake of comparison, the analytical solution of the corresponding linearized problem is also given. The obtained results show that for sufficiently small amplitude of the bottom’s motion, the predictions of the linear theory are in good agreement with those of the nonlinear theory only in some starting time interval, this interval being longer for smaller amplitudes. In the course of time, a growing oscillatory divergence is found to exist between the two theories. This divergence increases significantly with the increase of the amplitude of the bottom’s motion. Numerical results are presented and discussed. Unlike results of other publications, the numerical scheme given here proves numerical stability for the considered cases.