Interaction between bed roughness and flow hydraulics in eroding rills

Govers [1992] showed that the flow velocity in rills eroding loose, nonlayered materials could be predicted from knowledge of discharge only (without significant slope or soil effect). The objective of this paper is to investigate to what extent the observed slope independence of flow velocity in eroding rills can be explained by the interaction between rill bed roughness and flow hydraulics. In a laboratory study, two situations were compared: (1) rills which can freely erode a uniform soil layer and (2) rills with a fixed bed geometry. During the experiments, rill discharge and flow velocity were recorded. After each experiment, a detailed topographic survey of the rill bed was carried out using a laser scanner. From these data the main hydraulic variables (mean values of flow depth, wetted perimeter, and hydraulic radius) were estimated. The experiments confirmed the slope independence of rill flow velocities on mobile beds. When the bed is fixed, the flow velocity in rills is clearly slope-dependent. The slope independence of flow velocity on mobile beds is due to a feedback between rill bed morphology and flow conditions. The roughness amplitude (which was assessed from the standard deviation of corrected height values) and the frequency of macroroughness elements (which was assessed by counting the number of peaks per unit length in a previously simplified longitudinal profiles) both increase and tend to counteract the effect of the increase in slope gradient on rill flow velocity. The final rill flow velocity appears to be characterized by a constant average Froude number.