Active and inactive motions in wall turbulence

Abstract

Reynolds shear stress is the key momentum transport term in wall turbulence and as a consequence has been the focus of numerous theoretical modelling attempts in the past. Here, we investigate the seminal proposal by Townsend [35, 34] that wallbounded flows are comprised of active and inactive motions; the active motions being those that are solely responsible for producing Reynolds shear stress and follow self-similarity when normalised with the wall-normal distance and friction velocity. This paper builds on the recent work of Deshpande et al. [12], where a methodology is proposed to segregate the active and inactive contributions to the total turbulent kinetic energy. The effectiveness of this methodology is demonstrated here by applying it to three published wall-turbulence datasets, spanning over a decade change in friction Reynolds number (Ret). Active contributions to the streamwise, spanwise and wall-normal turbulence intensities are estimated individually and found to exhibit self-similar characteristics consistent with Townsend’s hypothesis. The Reynolds shear stress, estimated solely from the active contributions, is also found to closely match the one obtained conventionally from the dataset, providing direct empirical support for the concept of active and inactive motions.