Turbulent Boundary Layer on Steep Slopes

The development of the turbulent boundary layer in a fluid flowing down steep slopes controls not only the loss of head, but also the air entrainment. Prediction of the rate of growth of the layer is essential to proper spillway design. This paper describes a laboratory investigation of the variation in velocity distribution on smooth and rough channel beds for varying slopes and rates of discharge. The boundary-layer thickness, the coefficient of local resistance, and the parametric shape of the velocity profile are analyzed as functions of the Reynolds number and the relative roughness. Although these functions are shown to be in accordance with the general boundary-layer theory, they are essentially independent of both slope and discharge. A practical method is proposed for computing the limit of boundary-layer development on concrete spillways.