Characteristics of active and inactive motions in high Reynolds number turbulent boundary layers

Turbulent boundary layers (TBL) at high friction Reynolds numbers (Re_τ) are characterized by an extended region and high level of Reynolds shear stresses in their log region. This makes the associated coherent motions of this region (i.e., the attached eddies) a significant contributor to the skin-friction drag produced by the high Re_τ TBL. The present study investigates the underlying mechanism behind their drag contribution by analysing the active and inactive components of the attached eddies postulated by Townsend¹. A recently proposed energy decomposition scheme² is implemented on TBL datasets spanning a large Re_τ range of ∼ Ο(10³) - Ο(10⁶), to reveal the individual role played by these two components in drag generation. We find that while the active motions are solely responsible for turbulence energy production, the inactive motions transport a part of this turbulent kinetic energy from the log region to the wall, yielding empirical evidence to the hypothesis of Bradshaw³ for the first time.

¹Townsend, A.A. 1976 Cambridge University Press.

²Deshpande, R. et al. 2021 J. Fluid Mech. 914, A5.

³Bradshaw, P. 1967 J. Fluid Mech. 30 (2), 241–258.