Explicit Expression for Beach Response to Non-Stationary Forcing near a Groyne

Abstract

Analytical solutions to a beach evolution equation are obtained for the case where the initial beach shape may be an arbitrary function of position and where the forcing conditions may be a (known) function of time. The focus of this paper is the derivation of a generalized solution to the one-line equation describing the impact that time varying forcing can have on beach development close to a groyne. Explicit solutions are obtained using an integral transform technique. The solutions are found in terms of closed-form integrals which, for all but the simplest cases, require numerical evaluation. Example applications of the new solutions are described.