Analytical Model of Dispersion in Tidal Fjords

Using the integral transforms technique, the unsteady three-dimensional advective-diffusion equation was solved analytically for the dispersion of pollutants from an instantaneous point source in open channels of finite width. The flow velocity through the channel was the mean current velocity which was assumed to vary sinusoidally with time but linearly with water depth. The effect of first-order reactions is to reduce the concentration level throughout the channel. The spread of pollutants in the direction of mean flow is accelerated as a result of the existence of a vertical shear. The width of the channel is important, as is the boundary in the y direction that profoundly affects the horizontal dispersion when the source is close to the bank, but its effect diminishes as the source is moving farther away from the bank. These findings, as well as others, are examined and illustrated graphically.