On one mechanism forming linear sand banks

Asymmetric tidal currents ( Huthnance, 1973 ) provide a fluid-dynamical basis for Caston's (1972) description of linear sand-bank maintenance by converging sand transport. We suppose (i) depth-uniform tidal currents, slightly inclined to the bank crest, (ii) bottom-drag, which retards the current more over the bank and (iii) a faster-than-linear increase of sand transport with current. Then over a sloping bank side the total tidal current having an upslope component and the associated onto-bank sand transport are stronger than the retarded reverse tidal current and transport coming off the bank. Supposing that (iv) sand is more easily transported ‘downhill’ shortwavelength perturbations on a level sea floor are suppressed. There is a maximum bed-form growth rate at a particular wavelength (typically 250 times the water depth) and orientation (relative to the tidal currents) which probably evolve and persist during subsequent sand-bank growth. The orientation is sensitive to the (uncertain) formulation of supposition (iv), and is probably also susceptible to (for example) the trend of an adjacent coastline. In the representative context of friction-dominated tidal currents, the banks evolve to an equilibrium profile which is flatter on top than a sinusoid owing to wind-wave erosion and the inclination to the tidal current. For a limited sand supply the banks narrow to about one-fifth of their separation; further restriction mainly reduces their height. A net sand-transport overall due to a stronger ebb tide (say) than flood, as occurs over the Norfolk Sandbanks, yields the observed steeper slope on the obliquely downstream side of the bank (as viewed by the stronger ebb current).