Estuarine circulation induced by diffusion

Similarity solutions of the equations for estuarine circulation and salt balance are presented for a circulation generated by diffusive modification of stratification maintained at the entrance of an inlet by external dynamics rather than by fresh water discharged directly into the inlet. The explicit dependence may be factored from the governing equations if the inlet geometry and longitudinal variation in turbulent exchange coefficients are expressible as power or exponential functions of distance along the inlet, and the ordinary differential equations so obtained are solved approximately by perturbation in a function of the Rayleigh number. Salinity in the model decreases inward along the bottom but increases inward along the surface of the inlet, and the flow is 3-layered-inward at the top and bottom, outward at the mid-depth - as have been shown and inferred for Baltimore Harbor. Inclusion of bottom friction increases the salinity gradient along the bottom and decreases it along the surface, giving the salinity distribution some resemblance to that expected in conventional estuaries. The induced circulation in all cases is a strong function of total depth and a weaker function of length and turbulent exchange coefficients for salt and momentum. The model can serve as an aid to interpretation of observations in this type of estuary, and it provides simple means of evaluating the circulation and mixing rates from salinity measurements to whatever precision the eddy viscosity can be estimated, or current measurement can be obtained to scale the flow.