Uncovering Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence

Abstract

A growing body of studies supports the existence of Townsend’s wall-attached eddies in wall turbulence under the condition of sufficiently high Reynolds numbers. In the present work, we uncover the signature of Townsend’s wall-attached eddies in low-Reynolds-number wall turbulence. To this end, we use a three-dimensional clustering methodology to identify the wall-attached structures of intense streamwise and spanwise velocity fluctuations in turbulent channel flows at four Reynolds numbers ( , 358, 547 and 934). The statistical properties of the structures, such as their geometric self-similarity, population density and statistical moments, are investigated and compared with the predictions of the attached-eddy model. Particular attention is paid to the asymmetries between high- and low-speed wall-attached streaky structures, and we show that the former are a closer representation of the wall-attached eddies. This observation is ascribed to the differences between the sweep and ejection events associated with the streaks. We also examine the Reynolds-number effects on the statistical properties of the structures, and find that the signature of attached eddies can be observed within the Reynolds-number range under scrutiny. Our approach paves the way to cost-efficient model development and flow prediction using computationally more affordable simulations at low Reynolds numbers.