Toward a unified theory of tidally-averaged estuarine salinity structure

Equations are developed for the tidally-averaged, width-averaged estuarine salinity and circulation in a rectangular estuary. Width and depth may vary along the length of the channel, as may coefficients of vertical turbulent mixing and along channel diffusion. The system is reduced to a single first-order, nonlinear, ordinary differential equation governing the section-averaged salinity. A technique for specifying the ocean boundary condition is given, and solutions are found by numerical integration. Under different assumptions for the diffusion it is possible to reproduce the few existing analytical solutions, in particular the Hansen and Rattray (1965) Central Regime solution, and Chatwin's (1976) solution. The mathematical framework allows easy comparison of the results of different channel geometries and mixing coefficients. Of particular interest is the along-channel distribution of the diffusive fraction of up-estuary salt flux. It is shown that the Hansen and Rattray solution is always diffusion-dominated near the mouth. A theory is presented for estimating the diffusion coefficient within a tidal excursion of the mouth. It is shown that the resulting rapid along-channel increase of diffusion may explain some observed patterns of salinity structure: a decrease in both stratification and along-channel salinity gradient near the mouth. The theory is applied to the Delaware Estuary and Northern San Francisco Bay, and shows reasonable agreement with observed sensitivities of salt intrusion distance to river flow.