Reynolds number effects on surface-induced secondary flows in turbulent boundary layers

This study explores the effect of friction Reynolds number ( $\textit{Re}_\tau \approx 3000$ – $13{\,}000$ ) on secondary flows in three-dimensional turbulent boundary layers induced by spanwise surface heterogeneity. Using a combination of floating-element drag balance and high-resolution hot-wire anemometry, we examine how varying spanwise spacing ( $S/\delta$ where $\delta$ is the boundary layer thickness defined as the distance from the wall where streamwise mean velocity $U = 0.99U_\infty$ ) influences frictional drag, turbulence intensity, spectral energy distribution and the organisation of coherent structures. The results reveal that secondary flows modulate turbulence differently depending on $S/\delta$ , with strong near-wall effects at $S/\delta \lt 1$ and outer-layer modulation at $S/\delta \gtrsim 1$ . A robust spectral signature of secondary flows peaking at $\lambda _x \approx 3\delta$ and $y \approx 0.5\delta$ emerges across all cases. This peak coexists with, or suppresses, very large-scale motions (VLSMs), depending on flow region and spacing. While VLSMs are suppressed in low-momentum pathways, they gradually recover in high-momentum pathways at higher $S/\delta$ and $\textit{Re}_\tau$ . These findings offer insights into the interplay between fluctuations caused by secondary motions and boundary layer structures at high Reynolds numbers.