Excitation of Edge Waves and Their Role in the Formation of Beach Cusps
It is shown theoretically that surface waves incident on a beach from deep water can excite edge waves. In particular, a monochromatic wave train normally incident and reflected 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 earths 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 accord with Hasselmann's (1967) rule, only edge waves with frequencies lower than the incident wave are excited by this mechanism. Viscous effects suggest that an edge wave with mode number zero and frequency one-half that of the incident wave (a subharmonic edge wave) is preferentially excited. The minimum incident wave amplitudes for which this resonance can occur are predicted by consideration of viscous effects. Higher order terms, not studied in detail, suggest that an edge wave with frequency equal that of the incident wave (a synchronous edge wave) may also be resonantly excited when the incident wave is strongly reflected.
Experiments show that a very strong subharmonic edge wave resonance occurs on nonerodable plane laboratory beaches when single frequency incident waves are surging and strongly reflected at the beach. Smaller synchronous edge waves occur when the basin geometry or viscous effects exclude the subharmonic. Neither type edge wave is visible on the beach face when the incident wave is so large that it plunges rather than surges, incident wave energy being dissipated in the surf zone rather than reflected at the beach face as assumed in the resonance theory. This observation is quantified, and leads to a classification of beach face dynamics into reflective and dissipative systems.
Large subharmonic edge waves on plane laboratory beaches are shown to rearrange sand tracers into accumulations which resemble natural beach cusps. These edge wave induced morphologies, however, interfere with the edge wave excitation process so the edge wave amplitudes decrease as the cusps grow.
Small edge waves can form longshore periodic morphologies by providing destabilizing perturbations on a berm properly located in the swash zone. In this case, the retreating incident wave surge is channelized into breeches in the berm caused by the edge waves.
Various theories for edge wave generation on dissipative beaches with complex incident wave fields are briefly reviewed, and differences and similarities with the reflective beach case are stressed.