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

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.