DIFFUSION FROM A CONTINUOUS SOURCE IN A UNIFORM SHEAR FLOW1

Abstract

The importance of velocity shear in the diffusion of a patch of passive contaminant from an instantaneous source is well recognized. Shear is also expected to play an important role in the spread of contaminant from a continuous source, since a continuous source may be considered as a superposition of instantaneous sources. A model for the diffusion of a dynamically passive contaminant from such a continuous source is presented. This source is superposed on a mean flow with uniform shear. An equation is derived which shows— by numerical solution—that the maximum concentration of the contaminant in the resulting plume decreases nearly as the reciprocal of the distance. Small and large time approximations verify this result analytically. The skewness of the concentration distribution at various distances from the source is also presented. This diffusion model compares favorably with diffusion experiments conducted in seas and lakes.