The Longitudinal Diffusion Coefficient in the Delaware River Estuary as Determined From a Steady‐State Model

Abstract

An analytic solution of the one‐dimensional steady‐state diffusion equation for a conservative substance in an estuary of constant depth h in which the half‐width Y is related to the longitudinal distance x by the equation Y = αxμ may be found if the turbulentdiffusion coefficient Kx is given a general form Kx = KYϕ. Because the form of the diffusion coefficient allows 2 degrees of freedom in fitting the solution of the diffusion equation to data from a real estuary, it is possible to determine the magnitude of the diffusion coefficient as well as the effect, on the distribution of the conservative substance, of assuming a constant coefficient. Data from the reach of the Delaware estuary from Torresdale, Pennsylvania, to Reedy Island, Delaware, were used to test the solution, because fresh‐water inflow data are available for the reach, and its channel geometry satisfies the above requirement. This reach also contains five U. S. Geological Survey water‐quality monitors that provide salinity data to test the solution. Analysis of these data indicates that, for low fresh‐water inflow into the estuary, Kx is of the order of 100 meters squared per second and that for most operational purposes Kx may be assumed to be a constant.