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

Abstract: This study explores the effect of friction Reynolds number ($Re_\tau \approx 3{,}000$--$13{,}000$) 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 ($S/\delta$) 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 $S/\delta < 1$ 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 (LMPs), they gradually recover in high-momentum pathways (HMPs) at higher $S/\delta$ and $Re_\tau$. These findings offer new insight into the interplay between secondary motions and scale interactions in three-dimensional turbulent boundary layers, with implications for drag control, mixing, and surface design.