The effect of a barrier on tidally forced flow in a density-stratified estuary

Numerical simulations of a two-layer set of shallow water equations are used to study the effect of density stratification on tidally forced flow over a barrier in large estuaries. Previous work has shown that for a homogeneous fluid, the blocking effect of the barrier is strongly affected by the quadratic bottom stress. In particular, it was found that there was a nonlinear response to the tidal forcing, in that as the tidal forcing amplitude increased, so did the effect of the barrier in reducing the tidal range on the landward side of the barrier, but the magnitude of this blocking effect was greater than would be predicted by a linear relationship with the tidal forcing amplitude. Here, we find a similar phenomenon for a two-layer fluid model, which has both a free-surface displacement and an interface displacement. We find that the density stratification tends to enhance the blocking effect of the barrier when compared to a homogeneous fluid. Further, we find that the barrier induces significant internal tides, and also can cause a mean set-up of both layers on the landward side of the barrier.