Pattern formation in a thin layer of sediment

A stability analysis is performed to investigate the process which leads to the formation of bottom forms, when a thin layer of sediment covers a rigid substratum subject to the oscillatory flow induced by a surface gravity wave. The amplitude of the bottom perturbation is assumed to be so small to linearize the hydrodynamic problem and the flow field is determined by analytical means. However, nonlinear effects are significant and play a fundamental role into the morphodynamic problem, when the rigid substratum is bared by the growth of the most unstable mode. Hence, the development of the bottom profile is evaluated by a numerical approach. The model results show that the wavelength of the morphological patterns, which are generated when the rigid substratum is bared, is longer than the wavelength of the bottom forms which appear when the rigid substratum is always covered by the sediment. The results of the theoretical model are supported by some experimental observations made in our laboratory