SOME SOLUTIONS OF THE SOLUTE DIFFUSION EQUATION FOR AN ESSENTIALLY VERTICALLY HOMOGENEOUS ESTUARY
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
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Solutions were obtained for the differential equation governing the concentration of salinity in an estuary. The first solution was obtained by an approximation method with the assumptions that the river discharge R is a function of time alone, and that no solute q is added externally. The variation-of-parameters method was used to solve the same equation for an expression which gives the concentration of an externally introduced solute. R was assumed constant, and q was assumed to depend only upon the distance along the estuary measured downstream from the zero tidal-motion position. Choices of q were made to represent 1 solute introduction at a point in the estuary, and 2 uniform introduction of solute over the entire effective estuary length. Curves are given for the former choice. A curve is also included which is believed to be useful for the determination of the maximum distance from the estuary mouth that a known pollution source may be discharged into the estuary with specified limits upon the permissible pollution density.