Velocity profile for developing flow over stepped spillway

Stepped spillways are currently being designed and installed all over the world, due to their ability to adsorb kinetic energy and thus reduce stilling basin size. There are two distinct regions of the flow important to spillway design, the fully developed region where air is entrained into the flow, and the developing region where air is not entrained. It is important to predict the length of the developing region because of a greater potential for cavitations damage, the lack of bulking in the design of side walls and the lack of gas transfer in this region. A turbulent boundary layer develops along the flow down a stepped spillway until reaches the free surface. Based on physical experiments and numerical simulation, a detailed analysis of the turbulent velocity profiles is made, including mean values for the parameters of the complete turbulent velocity profile in the turbulent rough flow regime, given by the log-wake law. The results show that the log-wake law can be applicable for describing the velocity profiles over stepped spillway. The wake parameter π along the flow is not nearly affected by the pressure gradient. Accounting for the law of the wall and the law of the wake, a rational approach is developed for a power-law velocity profile within the boundary layer. However, the power law is worse to describe the velocity profiles compared to the log-wake law. According to the turbulent boundary layer thickness, the friction velocities calculated by log-wake law, the function between the length of the non-aerated zone and the hydraulic roughness height is herein determined and function between the skin friction coefficient, the turbulent boundary thickness and hydraulic roughness height is obtained.