A note on tidally generated sand waves

Abstract

The process leading to the formation of sand waves in tide dominated coastal areas is investigated by means of the linear stability analysis of a flat sandy bottom subject to oscillatory tidal currents. The conditions for the decay or amplification of small bottom perturbations are determined for arbitrary values of the parameters of the problem. According to field observations, the initial growth of sand waves requires a minimum amplitude of the tidal current, even when the critical bed shear stress for the initial motion of sediment is set equal to zero. Moreover the minimum amplitude depends on sediment characteristics. In particular, the analysis shows that sand waves appear only for a sandy bottom and their growth does not take place when a coarse sediment covers the sea bed. The solution procedure extends the truncation method which is often used to describe the flow generated by the interaction of bottom perturbations with the oscillatory tidal current. The obtained results show that the truncation method describes the mechanism inducing the growth of sand waves, but values of the parameters exist for which its results are not quantitatively accurate. Finally, the asymptotic approach for large values of both r, which is the ratio between the amplitude of the horizontal tidal excursion and the wavelength of the bottom perturbations, and of the stress parameter s is modified in the bottom boundary layer to describe cases characterized by values of s of order one, which is the order of magnitude suggested by an analysis of field data.