Wave forces on steeply-sloping sea walls

Abstract

The forces exerted by non-breaking, normally-incident water waves on a sloping sea wall are investigated within the framework of linearised potential theory. The slope of the sea wall is assumed to be large. The solution is in the form of an eigenfunction expansion, the coefficients of which are found by two methods. The first is a perturbation scheme based on the smallness of the reciprocal of the slope and is carried out to second order in this quantity. The second is a Galerkin technique. Results are presented for the case of a planar, outward-sloping sea wall. In shallow water it is found that the normal wave force decreases as the slope of the wall increases. In deep water, the reverse is true whilst in water of intermediate depth the normal wave force is only weakly dependent upon the slope of the sea wall.