Crescentic bedforms in the nearshore region

A wave of small amplitude is considered which approaches a straight beach n ormally and which is partially reflected at the coastline. By assuming that the local depth is much smaller than the length of the incoming wave, the shallow water equations are used to determine the water motion. The surf zo ne width is assumed to be small compared to the length of the incoming wave and hence the effect of wave breaking is included only parametrically. The time development of the cohesionless bottom is described by the Exner cont inuity equation and by an empirical sediment transport rate formula which r elates the sediment flux to the steady currents and wave stirring. It is sh own that the basic-state solution, which does not depend on the longshore c oordinate, may be unstable with respect to longshore bedform perturbations, so that rhythmic topographies form. The instability process is due to a po sitive feedback mechanism involving the incoming wave, synchronous edge wav es and the bedforms. The growth of the bottom perturbations is related to t he presence of steady currents caused by the interaction of the incoming wa ve with synchronous edge waves which in turn are excited by the incoming wa ve moving over the wavy bed. For natural beaches the model predicts two max ima in the amplification rate: one is related to incoming waves of low freq uency, the other to wind waves. Thus two bedforms of different wavelengths can coexist in the nearshore region with longshore spacings of a few hundre d and a few tens of metres, respectively. To illustrate the potential valid ity of the model, its results are compared with field data. The overall agr eement is fairly satisfactory.