| A model for the formation and evolution of three-dimensional sedimentary structures such as longshore sand ridges, on the continental shelf in water deeper than that of the shoaling region, is proposed. The model is based on the interaction between surficial or internal weakly nonlinear shallow water waves having weak span-wise spatial dependence and the bottom topography.;While these ridges are not the result of a single formative agent, it is argued that the mechanism proposed in this study does contribute significantly to their generation and evolution. Testing the hypothesis, however, is as difficult as formulating it. Comparisons of this model with oceanographic data must wait for sufficient data to become available. In conjunction with developing the sand ridge model, this study proposes a new mathematical equation, properties of which are explored here in some detail. This equation potentially applies to other physical processes and raises questions which are themselves good avenues for further research.;The numerical implementation of the model combines fixed point methods with finite difference techniques, resulting in a scheme which is found to be superior to conventional finite difference techniques in economy of computational resources and speed. Details of the scheme's inner workings and its performance are included. |
