Multiple morphodynamic equilibria in tidal embayments

The possible morphodynamic equilibria of tidal embayments are investigated within the framework of a one-dimensional model. The equilibria are defined by a steady profile of the erodible bottom. The extension with respect to earlier studies is that the embayments have arbitrary lengths L with respect to the tidal wavelength. This implies a much richer dynamics due to the possibility of tidal resonance and new sediment transport contributions that are caused by internally generated overtides and residual currents. If the system is only forced by an externally prescribed M-2 tide at the seaward boundary, a unique morphodynamic equilibrium is obtained for all embayment lengths smaller than the frictional length scale of the tide. Bottom friction causes tidal resonance to occur for a shorter length than a quarter of the frictionless tidal wavelength. This shift is smaller than would occur in the case of a fixed bed profile since the equilibrium condition induces larger water depths. If an externally prescribed overtide is added to the forcing, more than one type of morphodynamic equilibria can be found. For L values smaller than the M-4 resonance length scale the bottom profiles are strongly concave, with locally large water depths, and the water motion resembles a standing tidal wave. For longer embayments another type of equilibria, characterized by a weakly concave bottom profile and a traveling tidal wave, appears. For sufficiently strong amplitudes of the externally prescribed Mg tide, multiple morphodynamic equilibria are found. The maximum L, beyond which morphodynamic equilibria cease to exist, decreases with increasing influence of external overtide and bottom friction. These model results show an overall good agreement with field observations.