On the modeling of sand wave migration

We describe a simple mathematical model capable of reproducing the main features of sand wave inception and growth. In particular we focus on the prediction of the migration rates that sand waves undergo because of tidal and residual currents. The model adequately predicts migration rates even for the cases of upstream-propagating sand waves, i.e., for sand waves which migrate in the direction opposite to that of the residual current. We show that upstream/downstream propagation is mainly controlled by the relative strength of the residual current with respect to the amplitude of the quarter-diurnal tide constituent and by the phase shift between the semi-diurnal and quarter-diurnal tide constituents. Therefore, to accurately predict field cases, a detailed knowledge of the direction, strength, and phase of the different tide constituents is required.