Analysis of a Power Law and Log Law for a Turbulent Wall Jet Over a Transitional Rough Surface: Universal Relations

Abstract

The power law and log law velocity profiles and an integral analysis in a turbulent wall jet over a transitional rough surface have been proposed. Based on open mean momentum Reynolds equations, a two layer theory for large Reynolds numbers is presented and the matching in the overlap region is carried out by the Izakson-Millikan-Kolmogorov hypothesis. The velocity profiles and skin friction are shown to be governed by universal log laws as well as by universal power laws, explicitly independent of surface roughness, having the same constants as a fully smooth surface wall jet (or fully rough surface wall jet, as appropriate). The novel scalings for stream-wise variations of the flow over a rough wall jet have been analyzed, and best fit relations for maximum wall jet velocity, boundary layer thickness at maxima of wall jet velocity, the jet half width, the friction factor, and momentum integral are supported by the experimental data. There is no universality of scalings in traditional variables, and different expressions are needed for transitional roughness. The experimental data provides very good support to our universal relations proposed in terms of alternate variables.