Outer-layer similarity in the presence of a practical rough-wall topography

High-resolution particle image velocimetry measurements are made in the streamwise–wall-normal plane of a zero-pressure-gradient turbulent boundary layer over smooth and rough walls at Re 13000. The roughness considered herein is replicated from a surface scan of a turbine blade damaged by deposition of foreign materials and its topography is highly irregular and contains a broad range of topographical scales. Two physical scalings of the same roughness topography are considered, yielding two different rough surfaces: RF1 with k=4.2 mm and RF2 with k=2.1 mm, where k is the average peak-to-valley roughness height. At Re 13000, these roughness conditions yield k+ k /y*=207, /k=28, ks =115, and /ks=48 for RF1 and k +=91, /k=50, ks =29, and /ks=162 for RF2 where is the boundary-layer thickness, ks is the equivalent sand-grain height, and y* is the viscous length scale . The mean velocity deficits along with the Reynolds normal and shear stress profiles for both roughness conditions collapse on the smooth-wall baseline in the outer layer when appropriately scaled by the friction velocity, u . Probability density functions and quadrant analysis of the instantaneous events contributing to the mean Reynolds shear stress show similar outer-layer consistency between the smooth and rough cases when scaled appropriately with u . In addition, one-dimensional, two-point streamwise, and wall-normal velocity autocorrelation coefficients are also found to collapse in the outer region, indicating a similarity in the spatial structure of the outer-layer turbulence. The observed collapse of the smoothand rough-wall turbulence statistics in the outer layer supports Townsend’s wall similarity hypothesis for flow over the unique surface topography considered herein. © 2007 American Institute of Physics. DOI: 10.1063/1.2741256