On the relationship between manipulated inter-scale phase and energy-efficient turbulent drag reduction

TL;DR

This study explores how manipulating phase relationships between different turbulent scales can enhance energy-efficient drag reduction strategies at high Reynolds numbers by increasing inner-outer scale coupling.

Contribution

It reveals that adjusting inter-scale phase relationships boosts inner-outer coupling, improving the effectiveness of energy-efficient drag reduction methods at high Reynolds numbers.

Findings

Enhanced inner-outer scale coupling correlates with increased drag reduction.

Manipulating inter-scale phase relationships increases with Reynolds number.

Energy-efficient drag reduction benefits from stronger non-linear scale interactions.

Abstract

We investigate the role of inter-scale interactions in the high-Reynolds number skin-friction drag reduction strategy reported by Marusic et al. (Nat. Commun., vol. 12, 2021). The strategy involves imposing relatively low-frequency streamwise travelling waves of spanwise velocity at the wall to actuate the drag generating outer-scales. This approach has proven to be more energy-efficient than the conventional method of directly targeting the drag producing inner-scales, which typically requires actuation at higher frequencies. Notably, it is observed that actuating the outer-scales at low frequencies leads to a substantial attenuation of the major drag producing inner-scales, suggesting that the actuations affect the non-linear inner-outer coupling inherently existing in wall-bounded flows. In the present study, we find that increased drag reduction, through imposition of spanwise wall oscillations, is always associated with an increased coupling between the inner and outer scales. This enhanced coupling emerges through manipulation of the phase relationships between these triadically linked scales, with the actuation forcing the entire range of energy-containing scales, from the inner (viscous) to the outer (inertial) scales, to be more in-phase. We also find that a similar enhancement of this non-linear coupling, via manipulation of the inter-scale phase relationships, occurs with increasing Reynolds number for canonical turbulent boundary layers. This indicates improved efficacy of the energy-efficient drag reduction strategy at very high Reynolds numbers, where the energised outer-scales are known to more strongly superimpose and modulate the inner-scales. Leveraging the inter-scale interactions, therefore, offers a plausible mechanism for achieving energy-efficient drag reduction at high Reynolds numbers.