Dispersion of water pollutants in a turbulent shear flow

A steady state two‐dimensional turbulent diffusion equation describing the concentration distribution of a substance from a line source in a shear flow field is solved analytically. A similar formulation may be developed for any other kinds of sources. In the study the velocity and eddy diffusivity are assumed to be variables given by the power law approximations, and the depth of the water body is assumed finite, with no‐flux boundary conditions applied at the water surface and bottom. This represents a first step toward analytical water quality modeling which realistically includes the effects of both the finiteness in water depth and the nonhomogeneity in velocity and diffusivity. Results from the present model are compared with those obtained from the finite depth constant coefficient model and from the infinite depth constant coefficient model. They show significant and realistic differences in the prediction of concentration patterns. The effects of nonhomogeneous velocity and diffusivity are cancelled out by the effect of boundary reflection far away from the source.