Scale-dependent mechanisms underlying drag reduction (DR) in opposition-controlled (OC) turbulent channel flows are examined up to a friction Reynolds number Reτ=1000 using bidimensional empirical mode decomposition. Combined with scale-resolved spectral diagnostics, skin-friction decomposition, and amplitude-modulation analysis, the study elucidates how OC redistributes momentum transfer across scales as Reynolds number (Re) increases. Scale-resolved spectra show that OC remains highly effective in attenuating near-wall small-scale (SS) turbulence, whereas energetic large-scale (LS) structures largely retain their strength and coherence under control. A skin friction decomposition quantifies the consequence of this scale selectivity, showing that at Reτ=1000 more than 50% of the total skin friction originates from LS structures, whose contribution is only weakly affected by OC. Amplitude modulation analysis further demonstrates that the limitation of OC does not arise solely from ineffective near-wall actuation but from persistent inner–outer coupling. Although the virtual wall established by OC suppresses direct footprinting beneath it, outer-layer LS structures continue to modulate near-wall SS activity, with the resulting modulation signal detected at the sensing plane indirectly fed back toward near wall through the control loop. These findings indicate that the deterioration of DR performance at high Re arises from an increasingly pronounced scale-interaction constraint, whereby skin friction becomes progressively dominated by outer-layer and cross-scale dynamics that cannot be effectively mitigated by wall-local control alone.
Wang et al. (Wed,) studied this question.