Numerical Studies of Unsteady Dispersion in Estuaries

A one-dimensional mathematical model is developed which describes the longitudinal concentration distribution of a pollutant in an estuary. The importance of including the tidal velocity in the advective term of the mass balance equation is emphasized. The cross-sectional area, the tidal and fresh water velocities and the longitudinal dispersion coefficient may all be functions of distance and time. The unsteady equation for the concentration distribution is solved by an implicit, finite-difference technique on a digital computer. The difference in the magnitude of the longitudinal dispersion coefficient, E, in the salinity intrusion region and in the fresh water tidal portion is described. A modification of Taylor's dispersion equation is presented for the determination of E in the fresh water tidal portion of an estuary. The mathematical model is applied to the upper portion of the Potomac estuary and the results are compared with field observations for a 13-day period in which dye was injected into the estuary. The predicted concentration distributions are in reasonable agreement with the measured values. The magnitude of E is of the order of 0.1 sq mile per day. The importance of nonlinear tidal motion effects is described in relation to the distribution of pollutants in estuaries.