An idealized long-term morphodynamic model of a tidal embayment

Abstract

A model is discussed which describes the interaction between tidal currents, sediment transport and bedform changes in a one dimensional short embayment with a constant width. The water motions are described by the depth{ integrated shallow water equations. They are forced by prescribed free surface elevations at the entrance which consist of a basic tide and a rst overtide. For the sediment dynamics both a bedload and a suspended load transport model are considered. The sediment balance is averaged over a tidal period to retain only the long{term behaviour of the bottom prole. The equilibrium proles are calculated and the stability properties of these proles are studied for various combinations of the model parameters. If the forcing does not contain overtides the suspended load model has a unique stable equilibrium which represents a constantly sloping bottom with zero depth at the closed end and spatially uniform tidal currents. In contrast the equilibrium prole of the bedload model is a at bottom. The introduction of overtides in the forcing results in more complex dynamics. The equilibrium bottom proles in the suspended load model can be convex or concave, depending on the ratio of advective and diusive transports. Solutions of the bedload model tend to a bottom of constant slope where the water depth at the closed end may be nite. A physical interpretation of these results is also given.