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

TL;DR

This study uses direct numerical simulations to explore how spanwise wall oscillation affects turbulent boundary layers at high Reynolds numbers, revealing that drag reduction can improve with increasing Re under certain conditions.

Contribution

It introduces a new analytical relationship linking drag reduction to mean velocity shifts, and demonstrates that out-scaled actuation can enhance drag reduction at high Re, challenging previous assumptions.

Findings

Drag reduction increases with Re at large oscillation periods.

A new analytical model relates drag reduction to mean velocity shifts.

Flow diagnostics show period-dependent turbulence modulation.

Abstract

Spanwise wall oscillation (SWO) of turbulent boundary layers (TBLs) is investigated via direct numerical simulations over an extended actuation region with oscillation periods up to T_{sc}^+=600, scaled by the uncontrolled friction velocity u_{\tau 0} at the onset of SWO (i.e. Re_\theta=344). For low periods (T_{sc}^+<200), drag reduction (DR) decreases with increasing Re_\theta, consistent with conventional inner-scaled control strategies targeting near-wall turbulence. In sharp contrast, for large periods, DR increases with Re_\theta. For example, at T_{sc}^+=600, DR rises from 1.3% at Re_\theta=713 to 7.0% at Re_\theta=2340. This unexpected growth is partly explained by the streamwise evolution of the effective oscillation parameter: as TBL develops, u_{\tau 0} decreases downstream, reducing the local-scaled period T^+ and thereby enhancing suppression of near-wall turbulence. Interestingly, even the results are compared at approximately fixed T^+, DR for T^+>350 still exhibits a weak positive dependence on Re_\theta, consistent with recent experiments by Marusic et al. Nat. Commun., vol. 12, 2021, 5805. We further develop a new analytical relationship that links DR to the upward shift of mean velocity in the wake region. Unlike previous formulations, the relationship avoids logarithmic-region fitting and does not rely on an invariant Karman constant under SWO, while maintaining good agreement with DNS data. Flow diagnostics -- including Reynolds stresses, skin-friction decomposition, and energy spectra -- demonstrate that the observed variation of DR with Reynolds number (Re) arises from period-dependent modulation of near-wall turbulence. Overall, these findings challenge the conventional view that DR inevitably deteriorates with Re and demonstrate that out-scaled actuation can instead enhance DR performance -- offering new physical insights for high-Re control strategies.