Turbulent flows over rough walls

We review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number k(s)(+), which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low k(s)(+) depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with delta/k less than or similar to 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness elements themselves.