The effect of geometry and bottom friction on local bed forms in a tidal embayment

Abstract

Using a 2DH idealized local morphodynamic model for a tidal channel, it is demonstrated that estuarine bars with typical length scales on the order of the tidal excursion length can develop as the result of a positive feedback between water motion, sediment transport and the sandy bottom. The water motion is modelled by the depth-averaged shallow water equations and driven by an externally prescribed M2 tide. Sediment is mainly transported as suspended load due to advective processes. Convergences and divergences of the tidally averaged sediment fluxes result in the evolution of the bed. It is shown that the combined effect of bottom friction and advective processes can trigger instabilities that lead to the formation of bottom patterns. Bed slope effects are required in order to prevent infinite braiding of these features. With bed slope effects, bars with longitudinal length scales of the order of the tidal excursion length are most likely to become unstable. This result is found to be independent of the ratio of the width to the tidal excursion length as well as the adopted formulation of the bed shear stress. In the case that the width is much smaller than the tidal excursion length and non-linear bottom friction is used, there is good qualitative agreement with results from 3D models reported in literature which were applied to the same parameter regime. Qualitatively, the results are recovered when bottom friction is linearized. Quantitatively, only small modifications occur: the critical friction parameter is decreased and the longitudinal length scale of the most unstable bed form increases.