Estuarine adjustment to changes in river flow and tidal mixing

The adjustment of estuarine circulation and density to changes in river flow and tidal mixing is investigated using analytical and numerical models. Tidally averaged momentum and salinity equations in a rectangular estuary are vertically averaged over two levels, resulting in equations that are analytically tractable while retaining a broad range of time-dependent behavior. It is found that both strongly stratified and well-mixed estuaries respond rapidly to either type of forcing change, while those of intermediate stratification respond more slowly. Intermediate estuaries also have the greatest sensitivity to change. Exchange flow dominates the up-estuary salt flux in strongly stratified cases. Changing the river flow in such cases leads to an internal wave propagating the length of the estuary, which accomplishes much of the adjustment. The internal wave speed thus controls the adjustment time. Increased tidal mixing in strongly stratified cases initially decreases the exchange flow contribution to up-estuary salt flux by decreasing both the stratification and the vertical current shear. However, the decreased up-estuary salt flux leads to a loss of total salt in the estuary, and hence a greater longitudinal salinity gradient. The increasing gradient eventually restores the exchange-flow salt flux to near its original value. Well-mixed solutions have an advective-diffusive balance between river flow and longitudinal tidal mixing. In these cases the adjustment time corresponds to the time it takes the depth-averaged flow to travel the length scale of the salt intrusion, a result that applies to both types of changes considered. In all cases the adjustment depends upon the dynamical feedback between the longitudinal salt flux and the longitudinal salinity gradient, which varies as the estuary gains or loses total salt.