The origin of swash cusps on beaches

Abstract Genetically, there are two types of beach cusps; those formed in the surfzone by the nearshore circulation system, and those formed on the beachface by the swash and backwash. The latter are here called “swash” cusps, and a simple model relating the physical dimensions of swash cusps to the properties of the incident wave field and the mean beach slope is developed. As in some previous models, the cusp wavelength is controlled by the longshore wavelength of edge waves, but the edge waves are now required only to provide small periodic perturbations on an originally uniform beach. Further cusp growth occurs because of the interactions between the incident waves and the perturbed topography. The maximum cusp height (apex to valley) is hypothesized to be proportional to the significant vertical excursion of swash motions. It follows from the above assumptions that the maximum possible cusp steepness (cusp height/cusp longshore wavelength) is proportional to the mean on-offshore beach slope. This result agrees with field data, and the value of the ratio of maximum cusp height to beach slope differs from that obtained theoretically by Guza and Bowen (1981) using a complicated non-linear model with rather different physics. The present model implies that edge waves, although necessary for initiating the initial bedform perturbation, need not persist for the development of mature cusp topography.

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