Rill erosion and morphological evolution: a simulation model

A mathematical model is advanced to simulate dynamically and spatially varied shallow water flow and soil detachment, transport, and deposition in rills. The model mimics the dynamic process of rill evolution, including variable rates of sediment redistribution along the bed and changes in local bed morphology. The sediment source term in the model uses a point scale, probabilistic relationship based on turbulent flow mechanics and a recently developed sediment transport relationship for rills based on stream power. The interdependent feedback loops between channel bed morphology, local flow hydraulics, and local scour and deposition, within the framework of the full hydrodynamic equations with inertial terms, constitute a mathematical model with the capacity to represent spatial variability and temporal evolution of the rill. Finite elements were applied to numerically solve the hydrodynamic and sediment continuity equations. A series of laboratory flume experiments were performed to evaluate the model. Initial bed slopes were 3, 5, and 7% with step increases of water inflow rates of 7.6, 11.4, and 15.2 L min-1. The soil material used in the flume was a kaolinitic, sandy-clay loam. The rill model equations were solved for increasingly complex cases of spatial and temporal variabilities. The model followed measured patterns of morphological changes as the rill evolved, which suggests that the feedback loops in the model between erosion, bed morphological changes, and hydraulics were adequate to capture the essence of rill evolution.