The effect of a fixed submerged obstacle on an incident wave in stratified shallow water. (Mathematical aspects.)

Abstract

Previous studies of the effect of a submerged obstacle on an incident progressive wave in stratified shallow water led to secular terms in the expressions of transmitted and reflected waves. The contribution of these terms increases, monotonically, with the distance from the obstacle. A multiple scale transformation of variables is used, here, to get rid of these secular terms. The equation of Korteweg-de Vries is shown to govern the propagation of waves. A concrete application is given for certain incident barotropic and baroclinic waves. Numerical results are given for certain cases.