Direct numerical simulations of out-scale-actuated spanwise wall oscillation in turbulent boundary layers

Spanwise wall oscillation (SWO) of turbulent boundary layers (TBLs) is investigated via direct numerical simulations (DNS) over an extended actuation region (momentum Reynolds number $344\lt Re_\theta \lt 2340$ ) with oscillation periods up to $T_{\textit{sc}}^+=600$ , scaled by the uncontrolled friction velocity $u_{\tau 0}$ at the onset of SWO (i.e. $ \textit{Re}_\theta =344$ ). For low periods ( $T_{\textit{sc}}^+\lt 200$ ), drag reduction ( $ \textit{DR} $ ) decreases with increasing $ \textit{Re}_\theta$ , consistent with conventional inner-scaled control strategies targeting near-wall turbulence. In sharp contrast, for large periods ( $T_{\textit{sc}}^+\gt 200$ ), $ \textit{DR} $ increases with $ \textit{Re}_\theta$ . For example, at $T_{\textit{sc}}^+=600$ , $ \textit{DR} $ rises from 1.3 % at $ \textit{Re}_\theta =713$ to 7.0 % at $ \textit{Re}_\theta =2340$ . This unexpected growth is partly explained by the streamwise evolution of the effective oscillation parameter: as a TBL develops, $u_{\tau 0}$ decreases downstream, reducing the local-scaled period $T^+$ and thereby enhancing suppression of near-wall turbulence. Interestingly, if the results are compared at approximately fixed $T^+$ , then $ \textit{DR} $ for $T^+\gt 350$ still exhibits a weak positive dependence on $ \textit{Re}_\theta$ , consistent with recent experiments by Marusic et al. (2021, Nat. Commun. , vol. 12, 5805). We further develop a new analytical relationship that links $ \textit{DR} $