A note on tidally generated sand waves

A fully three-dimensional model is proposed for the generation of tidal sand waves and sand banks from small bottom perturbations of a flat seabed subject to tidal currents. The model predicts the conditions leading to the appearance of both tidal sand waves and sand banks and determines their main geometrical characteristics. A finite wavelength of both sand waves and sand banks is found around the critical conditions, thus opening the possibility of performing a weakly nonlinear stability analysis able to predict the equilibrium amplitude of the bottom forms. As shown by previous works on the subject, the sand wave crests turn out to be orthogonal to the direction of the main tidal current. The present results also show that in the Northern Hemisphere sand bank crests are clockwise or counter-clockwise rotated with respect to the main tidal current depending on the counter-clockwise or clockwise rotation of the velocity vector induced by the tide. Only for unidirectional or quasi-unidirectional tidal currents are sand banks always counter-clockwise rotated. The predictions of the model are supported by comparisons with field data. Finally, the mechanisms leading to the appearance of sand waves and sand banks are discussed in the light of the model findings. In particular, it is shown that the growth of sand banks is not only induced by the depth-averaged residual circulation which is present around the bedforms and is parallel to the crests of the bottom forms: a steady drift of the sediment from the troughs towards the crests is also driven by the steady velocity component orthogonal to the crests which is present close to the bottom and can be quantified only by a three-dimensional model. While the former mechanism appears to trigger the formation of counter-clockwise sand banks only, the latter mechanism can give rise to both counter-clockwise and clockwise rotated sand banks.