Gravity waves on water of variable depth

Abstract

This is a study of the propagation of gravity waves over a basin in which the propagation distance is large compared with the scale of the bottom topography, which, in turn, is large compared with the depth. Special emphasis is given to the low-frequency part of the spectrum and to geometries containing a beach (see figure 1) because of their importance in tidal wave phenomena. Both reflexion phenomena and the dispersive character of the propagation are accounted for and the non-linear aspects of the large amplification associated with the beach climbing are also included. However, the analysis of problems in which the waves break is valid only up to the inception of breaking; post-breaking phenomena are not treated.