The formation of tidal sand waves: fully three-dimensional versus shallow water approaches

Tidal sand waves, also named tidal dunes, are large scale bedforms generated by the growth of perturbations of the sea bottom driven by tidal currents. Indeed, the interaction of an oscillatory tidal current with a bottom waviness gives rise to steady recirculating cells which tend to drag the sediment from the troughs towards the crests of the bottom perturbation. The net motion of the sediment towards the crests is opposed by gravity force and the growth of the perturbation is controlled by a balance between these two effects. In the literature, to determine the conditions which lead to the formation of sand waves and to determine the characteristics of the bedforms generated by this instability mechanism, both fully three-dimensional and shallow water approaches are employed. The shallow water approach is computationally less expensive than the fully three-dimensional one but, in many cases, it might be less accurate. This paper compares the quantitative predictions obtained by means of the two approaches and quantifies the range of the parameters such that the shallow water approximation provides reliable predictions.