Three-Dimensional Pollutant Modeling in Shear Flow

A steady-state three-dimensional turbulent diffusion equation with variable coefficients describing the concentration distribution of a substance from a point source in a shear flow field is solved analytically. A similar formulation may be developed for line, area, or other kinds of sources. Two models are considered: one treats both the depth and width of the water body as finite, while the other deals with finite depth but with infinite width. In the search for solutions, the integral transformation and the Green’s function constructed earlier by the writer are utilized to the optimum advantage. The solutions are developed for cases in which the velocity and the vertical and lateral eddy diffusion coefficients are given by a power law. Results are compared with those obtained from the uniform flow field. They show a significant difference in the concentration distribution. The magnitude of differences depends on the location of sources and the vertical variations of the velocity and the diffusion coefficients of the flow field.