Time-varying secondary flows in turbulent boundary layers over surfaces with spanwise heterogeneity

Abstract

The behaviour of turbulent boundary layers over surfaces composed of spanwise-alternating smooth and rough strips is investigated experimentally. The width of the strips S vary such that 0.32 < S/\delta < 6.81, where \delta is the boundary-layer thickness averaged over one spanwise wavelength of the heterogeneity. The experiments are configured to examine the influence of spanwise variation in wall shear stress over a large S/\delta range.

Hot-wire anemometry (HWA) and particle image velocimetry (PIV) reveal that the half-wavelength S/\delta governs the diameter and strength of the resulting mean secondary flows. Three possible cases are observed: limiting cases where S/\delta << 1 or S/\delta >> 1 and the secondary flows are either confined near the wall or near the roughness change, respectively, and intermediate cases (S/\delta \approx 1), where the secondary flows fill the entire boundary layer and the outer layer similarity is destroyed. The size and strength of the time-averaged secondary flows are approximately capped by either the boundary-layer thickness \delta or the roughness patch width S.

Instantaneously, however, these secondary flows appear very similar to naturally occurring large-scale structures that are spanwise-locked by the roughness transition with a residual meandering tendency about these locations. The efficacy of the roughness to lock the secondary flows in place and the meandering of the secondary flows are a function of S/\delta, most prominent when S/\delta \approx 1. Further analysis of the energy spectrograms and fluctuating flow fields obtained from PIV show that both secondary flows and the naturally occurring large-scale structures formed in turbulence over smooth walls meander in a similar manner and both coexist in the limits where S/\delta << 1 and S/\delta >> 1.