Reservoir Model of Ebb - Tidal Shoal Evolution and Sand Bypassing

A mathematical model is presented for calculating the change in volume and sand-bypassing rate at ebb-tidal shoals. Conceptually and mathematically, the ebb-tidal shoal is distinguished from bypassing bars that emerge from it and from attachment bars where the bypassing bars merge with the beach. The volumes and bypassing rates of these morphologic entities are calculated by analogy to a reservoir system, where each reservoir can fill to a maximum (equilibrium) volume. The ratio of the input longshore sand transport rate and the equilibrium volume of the morphologic feature is found to be a key parameter governing morphologic evolution. The analytical model gives explicit expressions for the time delays in evolution of the bypassing bar and the attachment bar, which are directly related to the delays in sand bypassing. Predictions of morphology change agree with observations made at Ocean City Inlet, Maryland. Examples of extension of the model by numerical solution are given for a hypothetical case of mining of an ebb-tidal shoal and for an idealized case of bi-directional longshore sand transport, in which updrift and downdrift bypassing bars and attachment bars are generated.