Flume experimental evaluation of the effect of rill flow path tortuosity on rill roughness based on the Manning–Strickler equatio

Abstract

Numerous soil erosion models compute concentrated flow hydraulics based on the Manning–Strickler equation (v = kSt R2/3 I1/2) even though the range of the application on rill flow is unclear. Unconfined rill morphologies generate local friction effects and consequently spatially variable rill roughness which is in conflict with the assumptions of (sectional) uniform channel flow and constant channel roughness of the Manning–Strickler equation. The objective of this study is to evaluate the effect of rill morphology on roughness and hence to assess the Manning–Strickler roughness coefficient (kSt) by rill morphological data. A laboratory experiment was set up to analyse rill hydraulics and roughness of I.) Free Developed Rill (FDR) flows and II.) Straight Constrained Rill (SCR) flows in the flume. The flume experiment generated Manning–Strickler roughness coefficients (kSt) between 22 m1/3 s−1 and 44 m1/3 s−1 reflecting a potential area of the roughness parameter uncertainty. It was found that FDR experiments generated significantly lower kSt values compared to SCR experiments, because skin and local friction effects in the FDR experiments were more efficient reducing flow velocity probably due to higher energy dissipation. Rill flow path tortuosity (Tort) was used to describe the rill morphology of the experiments and correlation statistics between Tort and kSt identified considerable explanatory capacity of rill flow path tortuosity on rill roughness. The flume study demonstrated that a regression model between Tort and kSt can be used to assess local friction effects of unconfined rill morphologies and hence to reduce the area of uncertainty of the Manning–Strickler roughness parameter