The effect of a systematic change in surface roughness skewness on turbulence and drag

Previous work by the authors (Flack and Schultz, 2010) has identified the root-mean-square roughness height, k_rms, and the skewness, Sk, of the surface elevation distribution as important parameters in scaling the skin-friction drag on rough surfaces. In this study, three surfaces are tested in turbulent boundary layer flow at a friction Reynolds number, Re_τ = 1600–2200. All the surfaces have similar root-mean-square roughness height, while the skewness is varied. Measurements are presented using both two-component LDV and PIV. The results show the anticipated trend of increasing skin-friction drag with increasing skewness. The largest increase in drag occurs going from negative skewness to zero skewness with a more modest increase going from zero to positive skewness. Some differences in the mean velocity and Reynolds stress profiles are observed for the three surfaces. However, these differences are confined to a region close to the rough surface, and the mean velocity and Reynolds stress profiles collapse away from the wall when scaled in outer variables. The turbulence structure as documented through two-point spatial correlations of velocity is also observed to be very similar over the three surfaces. These results support Townsend’s (1976) concept of outer-layer similarity that the wall boundary condition exerts no direct influence on the turbulence structure away from the wall except in setting the velocity and length scales for the outer layer.