Hydrodynamics of step-pool systems: a cross-section averaged non-hydrostatic rill-flow model

Rill flow is a major driver of soil erosion and a threat to watershed stability. As concentrated runoff evolves into gullies and steep step-pool channels, understanding its hydrodynamics becomes essential, especially once erosion rates diminish. In these conditions, strong vertical velocity gradients invalidate shallow-water assumptions. This work develops a section-averaged, non-hydrostatic rill-flow model that incorporates bed-form-related flow resistance while excluding sediment transport. A second-order finite-volume scheme with semi-implicit time stepping, solved through a Newton–Raphson method, is implemented. The model is evaluated using analytical solutions and laboratory data, showing satisfactory performance. Sensitivity analyses highlight the importance of accurate rill-width characterization. Experimental observations reveal rill widening at pools and the presence of bank cavities linked to secondary recirculating cells; incorporating these features significantly improves model accuracy. Studying steady flows in step-pool systems represents an initial step toward a comprehensive non-hydrostatic erosive flow model.