Realization of the turbulent boundary layer over the rough surface satisfied the conditions of complete similarity and its mean flow quantities

Mean flow quantities have been investigated for the equilibrium boundary layer developing over the rough surface with roughness height proportional to streamwise distance. The wall shear stress was measured by direct measurement with a floating element device of zero displacement mechanism. Local skin friction coefficient is independent of two parameters both streamwise coordinate and Reynolds number based on momentum thickness and has a value of 0.08 26. The boundary layer thickness is proportional to the streamwise distance. Then, the relative roughness height keeps a constant value. The log-law profile has same slope of that for the smooth wall turbulent boundary layer in the logarithmic linear part. The value of the roughness function increases in the streamwise direction. The wake parameter approaches to the constant value of about 0.7. Also, the value is consistent with the result deduced from the analytical method used both the momentum integral equation and Coles's wake law. Then, the wake parameter decreases with increasing the friction parameter.