Dissipative scaling of step-pool features

This paper focuses on the dissipative similarity of step-pool units at rill, flume and stream scale. This investigation is carried out using recent advances in open channel flow resistance, applications of close-range photogrammetry to rill erosion, available published data on step-pool features in flumes and streams and a new dataset of measurements in fixed bed step-pool rills. A theoretically-based equation for calculating the Darcy-Weisbach friction factor obtained by integration of a power velocity profile is presented. The scale factor Γ of this power velocity profile, which is included in the flow resistance equation, was previously calibrated (Eq. 10) for mobile bed rills with step-pool units. At first, in this investigation an additional test of this flow resistance equation is developed using measurements carried out in fixed bed rills with step-pool features. In particular, the proposed Γ function is tested using the measurements carried out in 63 fixed bed rill reaches incised on a 24 and 26% sloped plot. This test shows that the effect of sediment transport on the flow resistance law can be considered negligible as compared to the effect of the form-induced dissipative mechanisms due to the presence of step-pools structures. Then, using measurements carried out in 61 flume experimental runs and 109 reaches of step-pool streams, this investigation demonstrates that the Γ function for flume and stream conditions can be obtained scaling that (Eq. 10) determined for step-pool rills. The Darcy-Weisbach friction factor values measured in flumes and streams are, on average, higher than those related to rills. Finally, the application of the theoretical equation for calculating the Darcy-Weisbach friction factor for flume and stream conditions requires Γ, estimated by Eq. (10), to be multiplied by a specific scale factor.