Tidal and residual flows in the western Dutch Wadden Sea II: An analytical model to study the constant flow between connected tidal basins

Abstract

In a one-dimensional analytical model the origin of constant flows between connected tidal basins, as well as the origin of the associated residual levels, is examined. Linearized shallow water equations are used to describe the propagation and damping of a tidal wave in schematized (uniform width and depth) connected basins. Analytical expressions are derived for the tidal stress terms, including the contribution of the non-linear bottom-friction term, which serve as the forcing functions in the equations for the mean field. It is shown that in a first approximation the residual levels in the tidal inlets, which give boundary conditions for the tidally-averaged equations, are dependent on the tidal velocities in the inlet because of a “Bernoulli effect”. The model shows that in general differences between the fluctuating water levels at the inlets influence the residual flow more than morphological differences between two connected basins. The tidally-driven mass transport in the western Dutch Wadden Sea, directed southwards from the Vlie basin towards the Marsdiep basin, can be explained from the larger water-level amplitude at the inlet of the Vlie basin.