Unsteady overland sedimentation

Abstract

Sediment flux to fluid flow in a rill is represented with physically based models for simultaneous sediment entrainment (detachment), deposition (settlement) and lateral inflow, and is shown to be an improvement over existing concepts for describing low sediment concentrations. Unsteady flow and sedimentation in overland rills are then described by continuity equations and approximations for flow, entrainment and transport capacity. The equations are reduced, for an assumed rill pattern on an overland plot, to one-dimensional equations of motion which do not utilize sheet flow approximations. The method of characteristics' solution to these equations for uniform rainfall excess yields both the hydrograph (rising limb and uniform crest) and a three-part sediment concentration graph, with a predicted time lag between peaks of these graphs. The resulting model allows substitution of reasonable parameter values as opposed to the requirements of conventional sheet flow approximations. Sediment concentration is given by steady-uniform transport capacity equations only when the flow is steady-uniform (no lateral inflow) over infinite channel length (or recirculating flume) or when the steady-uniform transport capacity concentration in the rill is equal to the lateral inflow concentration. It then appears that rill topographies develop to the point where the latter condition is satisfied. Boundary conditions on the first derivative of sediment concentration with time suggest constraints on the form of the equations for fluid flow, entrainment, and transport capacity which agree well with empirical evidence. General observations on the solution are made which outline the expected nature of overland sedimentation.