Long bed waves in tidal seas: an idealized model

An idealized model is proposed to explain the appearance of the long bed waves that have been recently observed in shallow tidal seas. The model assumes that these bedforms grow due to tide-topography interaction. The water motion is described by means of the depth averaged shallow water equations and the bottom evolution is governed by conservation of sediment mass. The sediment transport formulation includes a critical bottom stress below which no sediment moves. Also, anisotropic sediment transport, due to local bottom slopes in the longitudinal and transverse directions, is taken into account. A linear stability analysis of the flat bottom configuration reveals that different bottom patterns can emerge. In accordance with previous analyses, for strong tidal currents, the fastest growing modes are sand banks. However, if the tidal currents are elliptical and the maximum bottom stress is just above its threshold value for the initiation of sediment motion, the model shows the presence of further growing modes which resemble the long bed waves observed in the field.