Realization of the Turbulent Boundary Layer over the Rough Wall Satisfied the Conditions of Complete Similarity and Its Mean Flow Quantities

Abstract

Mean flow quantities have been investigated for the equilibrium boundary layer evolving over the rough wall with a roughness height that is proportional to streamwise distance. The wall shear stress measured by drag balance with a floating element device of a zero displacement mechanism. The local skin friction coefficient is independent of both streamwise distance and momentum thickness Reynolds number and has a value of 0.00826. The boundary layer thickness is proportional to the streamwise distance. The relative roughness height then maintains a constant value. The log-law profile has the same slope of that of the smooth wall turbulent boundary layer in the logarithmic liner part. The value of the roughness function increases in the streamwise direction. The wake parameter approaches to a constant value of approximately 0.70. In addition, the value is consistent with the result determined from the analytical method using the momentum integral equation and Coles's wake law. For the analytical result, the wake parameter decreases with increasing friction parameter.