Flow resistance in step-pool rills

Abstract

Rills evolve morphologically, and the adjustment of rill channel geometry to flow affects the relationships among velocity, discharge, and slope. The resistance to flow in step-pool rills is mainly due to form-induced mechanisms and, in comparison, grain resistance is of minor significance. Previous studies on rill flow resistance have been performed exclusively for grainresistance conditions and use a stream flow equation. In this study, a new flow resistance equation, deduced by applying dimensional analysis and self-similarity theory, was applied to rill flow in step-pool channels. First, the incomplete self-similarity hypothesis was used for establishing a power flow velocity profile whose integration gives the theoretical expression of the Darcy-Weisbach friction factor. Then the deduced theoretical resistance equation was tested by measurements of flow velocity, water depth, channel width, and bed slope performed in 49 reaches of some rills having a step-pool bed. A relationship between the velocity profile, the channel slope, and the flow Froude number was established. The analysis showed that the Darcy-Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power-velocity profile. The Darcy-Weisbach friction factor values related to rills with step-pool sequences, on average, are higher than those related to rills without step pools, signifying that rills where step-pool sequences occur are characterized by a total resistance (grain and morphological) that is higher than grain resistance. Finally, this investigation showed that step pools that maximize flow resistance may develop at Froude numbers below the range at which step pools may form as antidunes.