Dissipative analogies of step-pool features: From rills to mountain streams

In this paper the dissipative similarity of step-pool units at different spatial scales ranging from rills to streams is analyzed. This investigation benefits from the latest theoretical advances in open channel flow resistance, high-resolution topography from close-range photogrammetry applied to rill erosion and the availability of published data from literature on step-pool streams. At first, the integration of a power velocity distribution allowed to obtain a theoretically-based expression of Darcy-Weisbach friction factor, in which Γ function and δ exponent of the velocity profile are included. Then this theoretically-deduced flow resistance relationship is calibrated and tested by flow measurements carried out in rill reaches where the step-pool units occurred. In particular, the proposed Γ function is calibrated using the measurements corresponding to 88 rill reaches shaped on a plot having a slope equal to 14, 22 and 24% and the calibrated equation is also positively tested with measurements carried out in 48 rill reaches shaped on a 26% sloping plot. For the rill flow the developed analysis stated that the friction factor is characterized by estimate errors which are less than or equal to ±15% for 86% of cases and less than or equal to ±10% for 70% of cases. Using measurements of flow velocity, water depth, width and bed slope measurements carried out in 109 reaches of step-pool streams, this investigation demonstrates that the theoretical flow resistance equation can be applicable to step-pool streams carrying out a specific calibration of the Γ function. The comparison between the Darcy-Weisbach friction factor values measured in streams and step-pool rills demonstrates that in the stream features the friction factor values are, on average, higher than those related to rills with step-pool sequences. In conclusion, the comparison between rills and streams with step-pool units highlights that the same theoretical flow resistance equation can be applied even if a scale effect between the two features is detected.