Developed log-wake law and turbulent behaviour of flow along a stepped spillway

Abstract The log-wake law for turbulent current has been developed and tested with laboratory data on turbulent flow in smooth pipes. However, flow with turbulence and vortices in a stepped spillway have not been described. Therefore, in this study, a log-wake law has been developed for use in stepped spillway systems. It can be divided into three parts. The first part, a logarithmic equation, describes the effect of shear stress between the flow layers with a von Kármán constant of 0.41. The second part, a third-degree polynomial, describes the effect of the shear stress on the wall. The last part, a fourth-degree polynomial, describes the effect of changing the flow pressure distribution, similar to the wall-free shear stress. Calibration tests (68 datasets) are used with a flow rate between 0.0233 and 3.285 m3/s, a spillway slope of 14–30°, and a step height of 0.0380–0.610 m. The developed log-wake law characterized the flow in a stepped spillway well. The limitation of the equation is a maximum flow velocity of 4 m/s; the accuracy of this equation decreases as the step height increases.