Unsteady one‐dimensional settling of suspended sediment

Abstract

A one‐dimensional, unsteady numerical model for the prediction of the vertical distribution of suspended sediment concentration and rate of suspended sediment deposition in water stirred uniformly has been developed. The model is derived from the convective‐diffusive transport equation and uses a fully implicit, exponential finite difference scheme. The model is unconditionally stable regardless of vertical diffusivities and particle fall velocities. Such a model has not previously been given in the sedimentation literature and is of interest for theory and applications. A generic study of vertical suspended sediment profiles and trap efficiencies has been made. The results, presented in dimensionless form, cover Peclet numbers Vh/D from zero to infinity. V is the particle fall velocity, h is the water depth, and D is the mean vertical exchange coefficient. In studies of suspended sediment behavior the parameters V and D are often unknown or not well determined. The generic results generated show what kind of variations in suspended sediment concentrations and trap efficiencies can be expected with different values of V and D. Sediment deposition is shown to occur through downward frontal movement when Vh/D is large (≥ 20) and through columnar precipitation when Vh/D is small (≤ 0.2). Residence time is shown theoretically to be far more important for estimates of sediment deposition rate than turbulence. This is in agreement with empirical findings for reservoir trap efficiency.