A 1‐D morphodynamic model for rill erosion

Abstract

The key objective of this paper is to develop a 1‐D hydrodynamic and sediment transport model, namely, RILL1D, that handles transcritical flows over abrupt changes (e.g., formation of pool crests and width change) in a single rill and also predicts changes in rill bed elevation. Replication of rill conditions in terms of flow and bed evolution changes necessitated the use of an enhanced TVD‐MacCormack scheme with implementation of Tseng's surface gradient method, to provide an oscillation free solution over formed pool crests. The model at the end of each time step calculates the flow depth, velocity, and bed shear stress and provides changes in bed elevation and grain size distribution within a cell. The hydrodynamic performance of RILL1D is evaluated by comparing its results with either analytical solutions or experimental observations from various benchmark tests with rigid bed conditions that include (1) formation of a hydraulic jump in a rectangular channel, (2) steady subcritical and transcritical flow (without a shock) over a hump, (3) formation of a hydraulic jump in a converging‐diverging frictionless channel, and (4) flows over step‐pools. It is shown that the enhanced TVD‐MacCormack scheme adequately simulates transcritical flows by preserving the mass conservation and reducing the artificial numerical error. The scheme also approximates satisfactorily depth and velocity for a single rill, with a fixed bed consisting of steps and pools, except near the pool headwalls where a backroller forms with negative velocities. The sediment component of RILL1D is evaluated by two field investigations of single rills with mobile beds. With the field data the code is tested for its ability to reproduce measured values of sediment transport rates. A sensitivity analysis is performed to assess the effects of cell size and critical erosional strength in the predictive ability of the model. RILL1D performs reasonably well in these simulations in terms of sediment prediction rates and fared adequately in terms of replicating rill bed morphology.