Towards energy-efficient drag reduction through manipulation of inter-scale phase relationships

This study investigates the mechanism of a new turbulent drag reduction strategy for high-Reynolds number wall-bounded flows that was reported by Marusic et al.¹The strategy imposes streamwise traveling waves of spanwise velocity at the wall that targets the low-frequency, outer scales. This strategy has proven to be more energy-efficient than the conventional method of actuating the inner scales. Both pathways achieve drag reduction with an accompanying broadband attenuation of the wall-shear stress spectrum and modified inter-scale phase relationships. Statistics such as the amplitude modulation coefficient and skewness of the streamwise velocity, representing the average measures of phase between triadically consistent scales, reveal that higher drag reduction is associated with enhanced coupling between the inner and outer scales. This enhancement is due to a reduction of the inter-scale phase. The energy-efficient pathway to achieve drag reduction, thus, involves actuating the outer-scales with the corresponding low-frequency surface oscillations, and consequently, also leading to a substantial attenuation of the major drag contributing inner-scales.

¹Marusic, I., et al. (2021) An energy-efficient pathway to turbulent drag reduction. Nat. Commun., 12, 5805.