Reynolds stress anisotropy of turbulent rough wall layers

The current classification of turbulent boundary layers over different wall surfaces is based on the effect the roughness has on the mean velocity, via the roughness function ΔU+. Previous hot-wire measurements have shown that turbulent boundary layers over different rough wall surfaces, but with identical ΔU+, contain significant differences in the Reynolds stresses throughout the layer. This suggests that a detailed documentation of the effect of the roughness on the anisotropic Reynolds stress tensor may pave the way for a more general classification. This paper examines experimental (boundary layer) and direct numerical simulation (channel flow) data for the invariants of the Reynolds stress tensor. Although only a limited number of rough surfaces have been examined, the results indicate that, relative to a smooth wall, the roughness reduces the level of anisotropy. This is more prominent for k-type roughnesses, the anisotropic invariant map (AIM) signature of the d-type roughness being closer to that for a smooth surface. In the vicinity of the roughness, the AIM signature varies dramatically, within one roughness wavelength, reflecting the significant changes in the characteristics of the turbulence field.