Longshore patterns of the sea bottom morphology

It is shown that the two-dimensional flow field and the bottom configuration induced by a wave of small amplitude normally approaching a straight beach may be unstable with respect to infinitesimal perturbations. The time development of the bottom perturbation leads to the formation of crescentic forms periodic in the longshore direction. The growth of the perturbation is due to a positive feedback mechanism, involving the incoming wave, synchronous edge waves and the bedforms. In particular the growth is related to the presence of steady currents caused by the interaction of the incoming wave with synchronous edge waves which in turn are excited by the incoming wave moving over the wavy bed. For natural beaches the model predicts two maxima in the amplification rate; the former is related to incoming waves of low-frequency, the latter to wind waves. Thus two bedforms of different wavelengths can coexist in the nearshore region, the longshore spacing of which is few hundreds and few decades of metres respectively. To illustrate the potential validity of the model, its results are compared with field data.