Wave Diffraction Through a Gap in a Breakwater of Non-Zero Thickness

Abstract

We consider the diffraction of a prescribed train of monochromatic plane surface water waves incident on a vertical-sided, perfectly reflecting thick breakwater standing on a horizontal bed in water of uniform undisturbed depth, and containing a single gap. The corresponding linearised boundary value problem is reduced to a pair of uncoupled first kind integral equations which display a particular structure; embedding formulae are then derived for a general integral equation of the type encountered. Within the context of the diffraction problem, the embedding result gives the solution for any incident wave angle explicitly in terms of the solutions for any two other distinct angles.