Experimental Study on the Distribution of Boundary Shear Stress at an Overfall

Overfall flow, characterized by high Froude numbers and intense turbulence, generates boundary shear stress on vertical surfaces, which is considered the direct cause of headcut erosion. This study aims to analyze the hydraulic characteristics of nappe flow over a vertical or near-vertical overfall. Detailed experiments using hot-film anemometry were conducted in an indoor flume to examine the shear stress distribution on vertical surfaces under varying flow rates, overfall heights, and backwater depths. The results show that when the jet dynamic pressure head is less than the backwater depth, the dimensionless relative shear stress and relative depth relationship can be fitted with a beta probability density function. When the dynamic pressure head exceeds the backwater depth, the distribution follows a cubic polynomial form. Dimensional analysis and flow trajectory calculation methods were used to establish shear stress distribution formulas, with determination coefficients of 0.829 and 0.652, and the mean absolute percentage error (MAPE) between the measured and predicted values being 0.106 and 0.081, respectively. The findings provide valuable insights into the effects of complex flow structures on shear stress and offer essential support for the development of scour models for overfall structures.