Distribution of non-buoyant material from a continuous source in shear flow: a similarity approach

Abstract

An approximate method of solution to the problem of the dispersal of a neutrally buoyant material in a shear flow regime is sought by use o f a similarity approach involving a finite number of parameters which characterize the distribution of material at a given distance from the source. Equations governing these parameters are obtained from appropriate integral moments of the basic equation governing the advection and diffusion of the material. The parameters include those characterizing the concentration of material along the core of the resulting plume, the standard deviation of the concentration profile in the lateral directions, and the position of the core of the plume. The method is applied to cases with known exact analytical solutions as a verification of the procedure. It is then applied to cases of a continuous source in a shear flow for which analytical solutions do not exist, using appropriate numerical methods.