Assessing a transitional and turbulent overland flow resistance law for surfaces with different roughness

Abstract

The control and management of soil erosion phenomena caused by rainfall and runoff is a significant issue in sloping landscapes, especially if they are scarcely or not vegetated. The study of the relationship between soil roughness and flow resistance is a fundamental step in improving the knowledge of erosion processes. In this study, the suitability of a theoretically deduced flow resistance law, based on a power-velocity profile, was assessed by transitional and turbulent overland flow data obtained in laboratory and available in the literature. These measurements were obtained in a sloping (slope in the range 1–40 %) rectangular flume, testing the effects of six different roughness conditions. At first, for each investigated roughness condition, the available measurements were used to calibrate and test the equation relating the Γ function of the velocity distribution, the flow Froude number, and the channel slope. For all the investigated conditions, this analysis allowed for demonstrating that the flow resistance law gives a reliable estimate of the Darcy–Weisbach friction factor, with errors ≤±5 % for 89.8–100 % of the examined cases with reference to the considered roughness condition. Then, using coefficients b (1.05) and c (0.562) of the Γ function available in the literature, the roughness effect was exclusively attributed to the a coefficient. In this case, the friction factor values calculated by the flow resistance law, with b = 1.05 and c = 0.562 and the a values corresponding to the different roughness conditions, are characterized by errors ≤±5% for 70.4–100 % of the cases. Finally, the power relationships between the calibrated a, b, and c coefficients of the Γ function, and Manning’s n values, corresponding to the roughness of the investigated surfaces, pointed out that the a coefficient is the most affected by the roughness conditions, as the exponent of Manning’s assumes the highest value. The significance of this research is due to the fact that a relevant issue in modeling overland flow is to define the resistance coefficient for variable roughness, especially the vegetated ones.