Turbulent skin-friction drag reduction via spanwise forcing at high Reynolds number

Abstract

We address the Reynolds-number dependence of the turbulent skin-friction drag reduction induced by streamwise-travelling waves of spanwise wall oscillations. The study relies on direct numerical simulations of drag-reduced flows in a plane open channel at friction Reynolds numbers in the range $1000\le R{e}_{\tau }\le 6000$, which is the widest range considered so far in simulations with spanwise forcing. Our results corroborate the validity of the predictive model proposed by Gatti & Quadrio, J. Fluid Mech. (2016): regardless of the control parameters, the drag reduction decreases monotonically with $Re$, at a rate that depends on the drag reduction itself and on the skin-friction of the uncontrolled flow. We do not find evidence in support of the results of Marusic et al., Nat. Comm. (2021), which instead report by experiments an increase of the drag reduction with $Re$ in turbulent boundary layers, for control parameters that target low-frequency, outer-scaled motions. Possible explanations for this discrepancy are provided, including obvious differences between open channel flows and boundary layers, and possible limitations of laboratory experiments.

References in corpus (16)

• Coherent structures in wall-bounded turbulence
• Streamwise-traveling waves of spanwise wall velocity for turbulent drag reduction
• Reynolds-dependence of turbulent skin-friction drag reduction induced by spanwise forcing
• Experimental assessment of drag reduction by traveling waves in a turbulent pipe flow
• Streamwise oscillation of spanwise velocity at the wall of a channel for turbulent drag reduction
• The laminar generalized Stokes layer and turbulent drag reduction
• Changes in turbulent dissipation in a channel flow with oscillating walls
• Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number
• Natural grid stretching for DNS of wall-bounded flows
• Does the choice of the forcing term affect flow statistics in DNS of turbulent channel flow?
• Turbulent drag reduction by spanwise wall forcing. Part 2: High-Reynolds-number experiments
• Turbulent drag reduction over curved walls
• Turbulent drag reduction by spanwise wall forcing. Part 1: Large-eddy simulations
• On the relationship between manipulated inter-scale phase and energy-efficient turbulent drag reduction
• Turbulence suppression by streamwise-varying wall rotation in pipe flow
• Pressure drag reduction via imposition of spanwise wall oscillations on a rough wall