Linear Stability of Sand Ridges in Three-Dimensional Models: The Role of Mass Conservation and Velocity Shear

Depth-averaged 2D models have shown considerable success at predicting the presence of tidal sand ridges in the nearshore environment while only requiring minimal efforts of parameter tuning. 3D models, on the other hand, fail to predict the growth of coarse-grain sand waves unless unrealistic assumptions on eddy viscosity are applied. When a vertically varying eddy viscosity profile is adopted in the model, sand waves will invariably be the fastest growing mode unless suspended load dominates, which contradicts observations. Through both numerical and analytical approaches, this paper will show that the residual circulation in the vertical plane due to mass continuity and vertical shear is a possible underlying mechanism that accounts for the dominant growth of sand waves. The strength of this residual circulation is proportional to the shear of the tidal velocity. A consequence is that sand ridges are more likely to develop in certain models with a small slip parameter in the bottom boundary condition (hence, less shear in tidal velocity), and such a parameter choice often, though not necessarily, leads to stronger mixing due to model configurations. Hence, sand waves are favoured in coastal seas due to the strong shear of the tidal current. The above findings suggest that there could be some unresolved processes that cause a transition in the bedform-building mechanism, which eventually inhibits the growth of sand waves and promotes the growth of sand ridges.