On the formation of sand banks of finite extent

We consider a model where the fluid depth depends on both horizontal coordinates, quasi-steady depth-uniform non-divergent fluid flow is governed by inertial, pressure and bottom-frictional forces, sand transport is proportional to the cube of the instantaneous current but augmented by a down-slope component and by wind-wave action, and sand is conserved. It is found that low parallel banks grow fastest, so that in an extensive spatially uniform sea previous calculations for linear banks are appropriate. The inclination of banks to the tidal currents can be interpreted in terms of similarly inclined deposition bands resulting from vorticity generation and advection in flow over a small isolated hump. A small bump can evolve to an equilibrium bank (typically after an initial rapid extension across the tidal currents) provided that sand is sufficiently restricted and particularly if some wind-wave action prevents growth up to the sea surface. Sand banks are likely to be in a late stage of evolution, when the main change is a slow lengthening as the net current and transport along the bank side slows and turns around the bank end with net deposition. The equilibrium is apparently stable except when there is an overall bed slope in the direction of the tidal currents, or when sand is abundant.