THE GENERATION OF OFFSHORE TIDAL SAND BANKS AND SAND WAVES

A simple morphological model is considered which describes the interac tion between a tidal flow and an erodible bed in a shallow sea. The ba sic state of this model describes a spatially uniform tide over a flat bottom where the flow vector is represented as a tidal ellipse. The l inear stability of this solution is analysed with respect to bed form perturbations. Results are presented for both a uni-directional and ci rcular tide. In the former case the wave-length and the orientation of the fastest growing bed mode agree well with those of tidal sand bank s. However, this model only predicts the growth of large-scale sand ri dges. With a simplified numerical model we tentatively show that the e ffects of secondary currents on the sediment transport trigger the for mation of instabilities at an essentially smaller scale, viz, sand wav es. Another limitation of a model with uni-directional tides is that n o selective modes found are the first to become unstable if the model parameters are varied. In the case of a circular tide, critical model parameters are found below which the basic state is stable. We conclud e that this provides a starting point for the development of a weakly non-linear analysis, which will yield information on the amplitude beh aviour of marginally growing bed forms.