Theoretical and numerical analysis of vertical distribution of active particles in a free-surface wetland flow

Presented in this paper is a theoretical and numerical analysis for active particles in a fully developed steady wetland flow dominated by the free-surface effect. An ecological risk assessment model for the concentration distribution of active particles is devised as an extension of the general form of concentration transport equation for passive particles in wetland flows. The vorticity in the free-surface wetland flow is found to depend on the dimensionless parameter alpha, which reflects the combined action of vertical momentum dispersion, microscopic curvature of flow passages, friction of vegetation and water depth. The large alpha results in the decrease of vorticity at the free surface and the increase at the bed bottom. The analytical solution of stable concentration distribution is rigorously derived for the active particles in both weak and strong vortical flows, under the combined action of the effective mass dispersion by the ambient flow, as well as the translational diffusion and vertical swimming by the active particles. It is found that the strong vorticity weakens the concentration of active particles in the free surface wetland flow, while the strong diffusion, by the wetland flow and active particles, enhances the concentration. The large alpha results in the increase of concentration near the free surface and the decrease of concentration near the bed bottom. The time scale for active particles to reach the stable concentration distribution is mainly dependent on the dimensionless parameter, Pe, which reflects the relative strength of the vertical swimming and the total diffusion due to the wetland flow and the active particles.