A unified erosion formulation for fine sediments

Different models of fine sediment transport often employ very different, fr equently incompatible formulations for surface erosion of bottom sediment. In this paper, we develop a simple extension of the standard linear erosion formulation that allows it to be used to describe either Type I (depth-lim ited) erosion or Type II (unlimited) erosion, with a seamless transition be tween the two behaviors. The formulation is cast in terms of either the dep th of erosion or eroded sediment mass. Assuming a locally constant rate of increase in critical stress with depth and direct proportionality between t he erosion constant and sediment concentration at the interface, the model predicts the exponentially decaying erosion rate often observed in Type I e rosion tests after application of each new shear stress step. The predicted decay rate is proportional to the rate of erosion per unit excess stress t imes the rate of increase in critical stress with depth. The formulation is tested by re-analyzing the data set presented by Maa et al. (1998) describ ing in situ erosion tests in Baltimore Harbor, MD, with generally favorable results. Solutions of the erosion formulation with time varying forcing sh ow that erosion behavior is controlled by the ratio of the rate of change o f shear stress to the rate of depletion of erodible sediment. If the time s cale of shear stress change is long compare to the time scale of sediment d epletion, then erosion rate is controlled by the time rate of increase in s hear stress balanced against the depth rate of increase in critical stress (Type I behavior). If the time scale of shear stress change is short compar ed to the time scale of sediment depletion, then erosion rate is controlled by the instantaneous difference between bottom shear stress and critical s hear stress (Type II behavior). A general algorithm for implementation in n umerical sediment transport models is presented. (C) 2001 Elsevier Science B.V. All rights reserved.