One-dimensional Morphodynamic Model for Retrogressive Erosion Based on a Modified Sediment Entrainment Law at High Flow Velocity

Retrogressive erosion is a high-velocity erosion process that usually occurs during rapid releasing of stored water in reservoirs built on sandy rivers. It has been utilized in the practice of reservoir sedimentation control, but accurate prediction to the bed deformation process by numerical model has rarely been reported. This paper presents a one-dimensional morphodynamic model for simulating the generation and evolving process of retrogressive erosion induced by high-velocity flows on steep slope. The governing equations adopt a Cartesian coordinate system with vertically oriented z axis. The surface gradient and friction terms in the flow equations contain correction factors to take account of the effects of large slope on flow movement. The net vertical sediment flux term in the sediment transport and bed deformation equations is calculated using an equation of erosion velocity. Particularly, this equation is based on an empirical relationship between the sediment entrainment rate and the Shields parameter in contrast to the traditional sediment transport capacity, and the critical Shields parameter is modified by taking into account the permeability of the sediment. The feedback of scoured sediment on the flow movement is considered by additional terms in the governing equations. The Godunov-type FVM scheme is used to solve the governing equations so that high stability is ensured in transcritical flow regime. A flume experiment and a retrogressive erosion event in the Sanmenxia Reservoir were simulated to validate the model. The temporal variations of the longitudinal profiles of free surface and channel bed and the sediment transport rate are well predicted. The modeling results were compared with those from traditional models established under the conditions of mild slope and low erosion rate, demonstrating its improvement in accuracy and simulation capability. Therefore, the 1D morphodynamic model proposed herein can help to enhance the understanding of the patterns of longitudinal channel evolution subject to large variation in base level and to explore the potential of retrogressive erosion for alleviating reservoir sedimentation.