Reynolds number effect on drag control via spanwise wall oscillation in turbulent channel flows

The effect of Reynolds number (Re_τ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Re_τ ranging from 200 to 2000. For the nondimensional oscillation period T⁺ = 100 with maximum velocity amplitude A⁺ = 12, the drag reduction (DR) decreases from 35.3% ± 0.5% at Re_τ = 200 to 22.3% ± 0.7% at Re_τ = 2000. The oscillation frequency ω⁺ for maximum DR slightly increases with Re_τ, i.e., from ω⁺ ≈ 0.06 at Re_τ = 200 to 0.08 at Re_τ = 2000, with DRmax=23.2%±0.6%. These results show that DR progressively decreases with increasing Re_τ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Re_τ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Re_τ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model (DRâ Reτ-γ) and the log-law model [DR = f(Re_τ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Re_τ = 10⁵.