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 Re_ 2340) with oscillation periods up to Tₒ₂^+=600, scaled by the uncontrolled friction velocity u ₀ at the onset of SWO (i. e. Re_ =344). For low periods (Tₒ₂^+ 200), drag reduction (DR) decreases with increasing Re_, consistent with conventional inner-scaled control strategies targeting near-wall turbulence. In sharp contrast, for large periods (Tₒ₂^+ 200), DR increases with Re_. For example, at Tₒ₂^+=600, DR rises from 1. 3 % at Re_ =713 to 7. 0 % at Re_ =2340. This unexpected growth is partly explained by the streamwise evolution of the effective oscillation parameter: as a TBL develops, u 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 DR for T^+ 350 still exhibits a weak positive dependence on Re_, consistent with recent experiments by Marusic et al. (2021, Nat. Commun. , vol. 12, 5805). We further develop a new analytical relationship that links DR
Zhang et al. (Mon,) studied this question.