The present work investigates the effectiveness of the control strategy introduced by Schoppa and Hussain [Phys. Fluids 10, 1049 (1998)] as a function of Reynolds number ($\text{Re}$). The skin-friction drag reduction method proposed by these authors, consisting of streamwise-invariant, counter-rotating vortices, was analyzed by Canton et al. [Flow, Turbul. Combust. 97, 811 (2016)] in turbulent channel flows for friction Reynolds numbers (${\text{Re}}_{\tau }$) corresponding to the value of the original study (i.e., 104) and 180. For these $\text{Re}$, a slightly modified version of the method proved to be successful and was capable of providing a drag reduction of up to 18%. The present study analyzes the Reynolds number dependence of this drag-reducing strategy by performing two sets of direct numerical simulations (DNS) for ${\text{Re}}_{\tau }=360$ and 550. A detailed analysis of the method as a function of the control parameters (amplitude and wavelength) and $\text{Re}$ confirms, on the one hand, the effectiveness of the large-scale vortices at low $\text{Re}$ and, on the other hand, the decreasing and finally vanishing effectiveness of this method for higher $\text{Re}$. In particular, no drag reduction can be achieved for ${\text{Re}}_{\tau }=550$ for any combination of the parameters controlling the vortices. For low Reynolds numbers, the large-scale vortices are able to affect the near-wall cycle and alter the wall-shear-stress distribution to cause an overall drag reduction effect, in accordance with most control strategies. For higher $\text{Re}$, instead, the present method fails to penetrate the near-wall region and cannot induce the spanwise velocity variation observed in other more established control strategies, which focus on the near-wall cycle. Despite the negative outcome, the present results demonstrate the shortcomings of the control strategy and show that future focus should be on methods that directly target the near-wall region or other suitable alternatives.

• Received 13 October 2016

DOI:https://doi.org/10.1103/PhysRevFluids.1.081501