Reynolds number dependence of large-scale friction control in turbulent channel flow

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 (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 (Re t) corresponding to the value of the original study (i.e., 104) and 180. For these 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 Re-tau = 360 and 550. A detailed analysis of the method as a function of the control parameters (amplitude and wavelength) and Re confirms, on the one hand, the effectiveness of the large-scale vortices at low Re and, on the other hand, the decreasing and finally vanishing effectiveness of this method for higher Re. In particular, no drag reduction can be achieved for Re t = 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 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.