Excitation of edge waves by waves incident on a beach

Abstract

It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a standing wave normally incident on a beach of constant gentle slope is found to transfer energy to edge waves through a weak resonant interaction resulting from an instability of the incident wave with respect to perturbation by edge waves. The analysis is based on the shallow water approximation and ignores the earth's rotation and consequently applies only to relatively low-mode, high-frequency waves. Coupling coefficients, frequencies, and longshore wave numbers of the excited waves are given. In accordance with Hasselmann's (1967) rule, only edge waves with frequencies lower than the frequency of the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with a frequency one-half that of the incident wave is preferentially excited.