On the modeling of sand wave migration

TLDR

The study develops a simple mathematical model to predict sand wave migration rates and emphasizes that accurate field predictions require detailed knowledge of tide direction, strength, and phase. The model is a simple mathematical representation that predicts sand wave migration rates driven by tidal and residual currents. The model accurately predicts migration rates, including upstream propagation, which is mainly governed by the residual current strength relative to the quarter‑diurnal tide amplitude and the phase shift between semi‑diurnal and quarter‑diurnal tides.

Abstract

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.