Variable Bottom Topography

A problem in which the scattering comes from a variation in the bottom topography.

Introduction

The linear wave scattering by variable depth (or bottom topography) in the absence of a floating plate has been considered by many authors. Two approaches have been developed. The first is analytical and the solution is derived in an almost closed form (Porter95, Staziker96 and Porter and Porter 2000). However this approach is unsuitable to be generalised to the case when a thin plate is also floating on the water surface because of the complicated free surface boundary condition which the floating plate imposes. The second approach is numerical, an example of which is the method developed by Liu82, in which the boundary element method in a finite region is coupled to a separation of variables solution in the semi-infinite outer domains. This method is well suited to the inclusion of the plate as will be shown. For both the analytic and numerical approach the region of variable depth must be bounded.

Wave scattering by a Floating Elastic Plate on water of Variable Bottom Topography was treated in Wang and Meylan 2002 and is described in Floating Elastic Plate on Variable Bottom Topography