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

The effect of Reynolds number (Re-tau) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Re-tau 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-tau = 200 to 22.3% +/- 0.7% at Re-tau = 2000. The oscillation frequency omega(+) for maximum DR slightly increases with Re-tau, i.e., from omega(+) approximate to 0.06 at Re-tau = 200 to 0.08 at Re-tau = 2000, with DRmax=23.2%+/- 0.6%. These results show that DR progressively decreases with increasing Re-tau. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Re-tau. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Re-tau 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 (DR proportional to Re tau-gamma) and the log-law model [DR = f(Re-tau, Delta B), where Delta B 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-tau = 10(5). Published under license by AIP Publishing.