Non-k-type behaviour of roughness when in-plane wavelength approaches the boundary layer thickness

A surface roughness from a recently cleaned and painted ship's hull was scanned, scaled and replicated for laboratory testing to systematically investigate the influence of the ratio of in-plane roughness wavelength, , with respect to the boundary layer thickness . The experiments were performed by geometrically scaling the surface which maintains a constant effective slope and solidity , while the ratio of is varied. Here we scale the scanned roughness topography by a factor of 2.5 and 15, and measure the mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of free stream velocities and streamwise measurement locations. The results show that the scaled roughness, which has , behaves in the expected -type manner, with a roughness function that is proportional to the viscous-scaled roughness height. The surface, however, which has , exhibits very different non--type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the case despite the sixfold increase in the roughness height. Measurements on a spanwise-wall-normal plane reveal that the surface has introduced a large-scale spanwise variation in mean streamwise velocity (dispersive stresses) that extend far beyond the logarithmic region. Together this evidence suggests that a demarcation between -type and non--type behaviour can occur in situations where the in-plane roughness wavelength approaches the boundary layer thickness. This finding has important implications to how we scale small-scale roughness from high Reynolds number (Re) large-scale applications for testing in low Re small-scale laboratory facilities or simulations.

Automated summary

The study systematically investigated the influence of the ratio of in-plane roughness wavelength to the boundary layer thickness on wind tunnel test results, finding a demarcation between Δ-type and non-Δ-type behavior under certain conditions.