Analytical three‐dimensional transient modeling of effluent discharges

A transient, three‐dimensional turbulent diffusion equation describing the concentration distribution of a substance or heat in a time‐dependent flow field is solved analytically. Two models are considered; one treats both the depth and the width of a water body as being finite, while the other deals with finite depth but with infinite width. In the search for solutions the method of Green's function is utilized to the optimum advantage. The solutions are developed for cases in which the velocity field can be described as any integratable function of time. For practical applications the velocity is assumed to be the sum of a constant and a harmonic component. There are no limitations on the type of source conditions. Results are compared with field measurements and show the models to be capable of simulating the dye distribution in tidal water bodies. The models should provide the engineering community with a quick and easy way of predicting the distribution of effluent discharges. They should obviate the need of using tedious and time‐consuming numerical models, as occasions often arise in which such complicated models may not be warranted.