Influence of geometrical variations on morphodynamic equilibria in short tidal basins

Abstract

The existence of cross-sectionally averaged morphodynamic equilibria of tidal inlets is investigated, using a cross-sectionally averaged model, and their sensitivity to variations of geometry, deposition parameter, frictional effects and advective sediment transport is analysed. Different geometries, from exponentially converging to exponentially diverging, are considered for inlets with lengths typical for the Dutch Wadden Sea. Standard continuation techniques are employed to numerically obtain morphodynamic equilibrium solutions, i.e. solutions for which the tidally averaged bed level does not change anymore. It is known that when the water motion at the entrance of the inlet is only forced by a M₂ tidal constituent assuming the water level to be spatially uniform and only diffusive sediment transport is considered, the morphodynamic bed equilibrium has a constantly sloping profile for a rectangular inlet. We find that the bed profile in equilibrium becomes convex (concave) when we change the frictionless embayment geometry to a diverging (converging) geometry. Upon letting the deposition parameter depend on the depth, a more convex bed profile for all geometries considered is found. Including frictional effects in the momentum equation has a minor effect when only diffusion is considered, but the bed profile changes significantly when advection is included. When the tidal forcing of the sea surface elevation depends on a M₄ tidal constituent as well, the morphodynamic equilibrium bed varies from very deep to shallow, depending on the relative phase. For a diverging inlet geometry, there are combinations of the relative phase and tidal basin length for which we show the existence of multiple equilibria. This implies that for these geometries, the cross-sectionally averaged bed profile in morphodynamic equilibrium can change significantly when the relative phase or the embayment length is changed. The magnitude of the perturbation necessary to actually evolve towards the other equilibrium and the time scale associated with this change can not be inferred from the analysis presented in this paper.