Interactions of boundary shear stress, secondary currents and velocity

This paper deals with the interaction of boundary shear stress, velocity distribution and secondary currents in open channel flows. A method for computing boundary shear stress and velocity distribution in steady, uniform and fully developed turbulent flows is developed by applying an order-of-magnitude analysis to the Reynolds equations. A simplified relationship between the wall-tangential and wall-normal terms in the Reynolds equation is hypothesized, then the Reynolds equations become solvable. This analysis suggests that the energy from the main flow is transported towards the nearest boundary to be dissipated through a minimum relative distance or normal distance of the boundary. The equations governing the boundary shear stress and Reynolds shear stress distributions are obtained, and the influence of wall-normal velocity on the streamwise velocity is assessed. It is found that the classical log-law is valid only when the wall-normal velocity is zero, the non-zero wall-normal velocity results in the derivation of measured streamwise velocity from the classical log-law. The derived equations are in good agreement with existing experimental data available in the literature.