A parametric model for a dense plume near a stream bed

Abstract

This dissertation considers the dispersion of a dense effluent from a steady source in a steady, uniform stream of constant density, near a stream bed. The solution is applicable to that portion of the flow regime where the plume is moving at nearly the same velocity as the ambient flow. The principal quantities investigated are the axial values of effluent concentration, and the lateral distributions of concentration and gravitationally induced circulation. The effect of the lower boundary is accounted for by using the method of images (which assumes the density distribution to be reflected by the boundary). A similarity hypothesis is employed in which the fields of concentration and flow are characterized by five parameters which are functions of the downstream coordinate only. A set of five integral 'moment' equations is deduced from the basic equations of motion (for steady state conditions with the Boussinesq approximation) and equations for conservation of effluent and of fluid. The moment equations used are: the 'zero-th' moment, the second moment in y and the first and second moments in the z of the effluent transport equation; and an equation for the variance of vorticity of transverse flow. After substitution of the assumed parametric forms of the density anomaly and stream function, this set of five equations can be integrated over the lateral plane to form a set of ordinary differential equations for the five parameters in which the independent variable is the downstream coordinate.