No abstract

An unsteady, three dimensional diffusion equation has been solved for the dispersion of pollutants, with or without chemical reaction, from an instantaneous point source in a semi‐bounded water under the influence of a vertical shear. The solution, which has been shown to be valid for two limiting cases: unbounded waters and large diffusion time, shows that the concentration ellipsoids would elongate themselves under the influence of a vertical shear, although the degree of elongation would also depend on diffusion coefficient and diffusion time. The effect of chemical reactions is to reduce the concentration level around the moving center of mass. The boundary affects profoundly the concentration distribution when the source is close to the shore.

By using the method of successive approximations, the one‐dimensional diffusion equation was solved for the distribution of pollutant from an instantaneous point source in a semi‐infinite body of water under the influence of wind‐generated waves. The solution was obtained with the aid of an expression developed in this study to relate the dispersion coefficient to wind speed, characteristics of a wind‐generated wave, and drift current velocities. The results indicate that the wave causes the local concentration to oscillate with respect to time around a mean concentration distribution curve. The period of the oscillation is about that of the wave, and its amplitude is always less than 7 percent of the mean. The effect of a chemical reaction is to reduce the level of pollutant concentration, the magnitude of the reduction being dependent upon both the rate constant and the order of reaction. The case of simultaneous dumping of one pollutant at different sites was also considered.