Wave response to a submerged wedge-shaped rubble mound breakwater

Abstract

The action of a wedge-shaped breakwater similar to that at Ramsgate harbour, UK, is investigated by means of an idealised analytical model which permits a solution process involving a pair of singular integral equations of the second kind where the integrals are of the Cauchy Principal Value type. It is found that an integrable singularity in velocity components emerges at the tip of the breakwater wedge assumed coincident with the mean free surface. Nevertheless, the wave profile is continuous across the breakwater though, because of the singularity, it steepens significantly near the tip. The absence of other parameters facilitates an investigation of the intrinsic relationship between friction and dissipation in wedge-shaped breakwaters. Expressions are derived for total energy dissipation measured against the friction term which is, in common with other investigations, linearised according to the Lorentz law of equivalent work. That dissipation is found to have a maximum at a relatively low critical value of the friction parameter, an outcome which could jeopardise the strategy of increasing the parameter to mimic wave breaking losses over trapezoidal breakwaters as suggested by Sollit and Cross (Proc. 13th Coastal Eng. Conf. (Vancouver, ASCE 1972) 1827–1846).