Reynolds number effect on drag reduction via spanwise wall oscillation in turbulent boundary layers

The effect of Reynolds number on drag reduction via spanwise wall oscillation (SWO) is investigated through direct numerical simulations of flat plate turbulent boundary layers (TBLs) over a wide range of Reynolds numbers (i.e., 344≤Reθ≤2340). Five oscillation periods with a fixed maximum velocity amplitude are considered. In particular, the oscillation periods scaled using the uncontrolled wall friction velocity uτ,0 at the starting position of the control xsc=250δ0 (Reθ=344) are Tsc+ = 50, 75, 100, 125, and 150, and the maximum velocity amplitude Wm,sc+=12. Drag reduction progressively decreases with increasing Reynolds numbers, with the rate of decay strongly depending on Tsc+. For the optimal case (i.e., Tsc+=100), a local drag reduction of approximately 32% is achieved at Reθ≈480, decreasing to 22% near the end of the oscillation. Although the dependence of drag reduction on T+ at a given Reynolds number is similar to those of channel flows—initially increasing and then decreasing with T+—the overall drag reduction achieved in TBLs is much lower. With an increasing Reynolds number, the optimal T+ to achieve the maximum drag reduction shifts to lower values, and this shift appears to be more noticeable than that observed in channel flow. For all cases, the global drag reduction, which quantifies the cumulative effect of SWO, stabilizes near the end of the oscillation, with a maximum value of 22% achieved for the Tsc+=100 case. Statistical analyses reveal that the Kármán constant κ decreases under SWO, and this reduction appears to be more closely associated with the oscillation period than the extent of drag reduction. Moreover, the decreased suppression of the turbulent contribution to skin friction drag is the primary mechanism responsible for the deterioration of drag reduction at higher Reynolds numbers. In summary, these findings offer valuable insight into the Reynolds number dependence of SWO in TBLs.