Abstract
•Turbulent dispersion in a typical open channel flow is analytically investigated.•Gill’s generalized dispersion model up to the fourth-order is solved and compared.•Two-dimensional concentration distribution is illustrated.•Analytical solutions are validated by numerical simulation results through RDM.•The applicable time of the fourth-order generalized dispersion model is determined.
In this work, the classic problem in environmental hydraulics of solute dispersion in an open channel turbulent flow is analytically investigated by Gill’s generalized dispersion model to account for all the basic characteristics as dispersivity, skewness and kurtosis of the mean concentration evolution. A complete solution is presented for the whole process and three typical time-scales are determined: after a convection-dominated initial stage, a transient stage with essential transverse diffusion effect begins at a dimensionless time-scale of t∼0.1 and gives way to an asymptotic stage of normal distribution of mean concentration from t∼1, slowly approaching to a final stage with relative uniformity in transverse concentration distribution at t∼10. Two-dimensional concentration distribution shows that there is a high concentration zone near the free water surface at a small time due to the small velocity gradient, indicating that it is not enough to characterize the dispersion process by the mean concentration, especially for the transient stage. The obtained analytical solutions of concentration distribution consist well with numerical simulation results by the random displacement method (RDM).