Two dimensional mixing of conservative pollutants in open channels

Abstract

Streams act as sinks for accidental or intentional spillage of pollutants from various industrial and municipal sources. Therefore, it becomes necessary to know the concentration distribution of these pollutants in the downstream, to check whether the required environmental standards are being satisfied or not. Some of the pollutants however, can have devastating impacts on the environment. Therefore, prediction of spreading of pollutants in streams is very important. Accurate prediction of the transport of pollutants is thus crucial for effective water quality management. As the pollutants travel downstream along the stream, they undergo various stages of mixing and their concentration decreases. The pollutants are mixed longitudinally, transversely and vertically by the action of advection and diffusion (molecular and turbulent) processes and velocity shear. Near the injection site, the mixing is three-dimensional in nature. After some distance from the injection site, the pollutants get mixed uniformly along the depth and the concentration varies only in longitudinal and transverse directions. The assumption of complete vertical mixing within a short reach is accepted because the aspect ratio (flow width/ flow depth) of streams is very large. After a time lapse the pollutants are completely mixed across the cross-section of the stream and the primary variation of concentration is only in the longitudinal direction and mixing beyond this section is called longitudinal dispersion. If a transverse line source injects tracer uniformly into the stream at any elevation along the depth, instantaneously or continuously, the mixing in the downstream occurs only in longitudinal and vertical directions and a two-dimensional mixing model is required to describe such a mixing process. Vertical mixing is not as important in water quality management as the transverse mixing. However, vertical mixing has great importance close to the source.