Abstract
The streamwise velocity component in fully-developed turbulent channel flow is studied for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a non-Gaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (± the standard deviation) are, respectively, about 76 ± 42 and 145 ± 150 wall units. The mean velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0:03 ≤ y/h ≤ 0.05, but the profile over the mesh surface exhibits only a small region with a slope tangential to log-law slope scaled on outer variables. However, the mean velocity deficit and higher moments (up to the fourth order) all exhibit some degree of outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. Spatial correlations show that the dominant large-scale features are very large quasi-streamwise structures with circulation in the cross-flow plane, similar to those found in smooth-wall internal and external flows. However, in the present case, the spanwise length scales are considerably larger. © Springer Science+Business Media B.V. 2010.