On solute dispersion from an elevated line source in an open-channel flow

Abstract

The streamwise dispersion of contaminant molecules due to a turbulent shear flow over a gravel-bed surface is examined when the solute is released from an elevated line source. A finite-difference, implicit method is used to solve the unsteady turbulent convection-diffusion equation, employing a combined scheme of central and four-point upwind differences for the steady-state condition and the Alternating Direction Implicit (ADI) method for the unsteady equation. It is shown how the mixing of contaminant is effected by the mean velocity due to the `log-wake law' and the corresponding eddy-diffusivity, when the solute is released in terms of a δ-function. The results for the steady-state condition are compared with existing experimental data and some other numerical results. The results obtained by the present method are in much better agreement with the experimental data than those obtained by the previous solution scheme, when the `log-wake-law' and the corresponding eddy-diffusivity are used. Far from the source, the concentration increases with time (the rate of increase is rapid near the source), asymptotically approaching a steady state after a certain time; concentrations are about two thirds of those near the source. The behaviour of iso-concentration lines in the vertical plane is also studied.