Initial formation of channels and shoals in a short tidal embayment

Abstract

It is demonstrated by using a simple model that bedforms in a short tidal embayment can develop due to a positive feedback between tidal currents sediment transport and bedforms The system is forced by a prescribed free surface elevations at the entrance of the embayment The water motions are modelled by the depthintegrated shallow water equations For the sediment dynamics a diusively dominated suspended load transport model is considered Tidal averaging is used to obtain the bottom proles at the long morphological time scale The stability of the linearly sloping equilibrium bottom prole is studied for various combinations of the model parameters It turns out that without a mechanism that generates vorticity the equilibrium prole is stable In that case smallscale perturbations can at most become marginally stable if no slope correction term in the bottom evolution equation is added If vorticity is generated in our model by bottom friction torques the basic state is unstable Which modes are unstable and what their growth rate is depends among others on the strength of the bottom friction the width of the embayment and the grain size if the sediment under consideration consists of large particles the equilibrium will be more stable than when smaller particles are considered Without a diusive term in the bed evolution equation small scale perturbations become unstable To avoid this physically unrealistic behaviour slope correction terms are included in the sediment transport Furthermore it is shown that using an asymptotic expansion for the concentration as given in earlier literature is only valid for small or moderate mode numbers and the technique is extended to large mode numbers A physical interpretation of these results is also given