SPECTRAL BEHAVIOR OF SELF-SIMILAR COHERENT STRUCTURES IN CANONICAL WALL-BOUNDED TURBULENT FLOWS

Abstract

The attached-eddy hypothesis (AEH) conjectured by Townsend (1976) predicts asymptotic behaviours of turbulence statistics in the logarithmic region in terms of self-similar coherent motions, yet revealing such behaviours has remained an elusive task because the proposed description is established within the limits of asymptotically high Reynolds numbers. In the present work, we scrutinized the self-similar behaviour of turbulence motions contained within wall-attached structures of streamwise velocity fluctuations (u) using the direct numerical simulation dataset of turbulent boundary layer, channel, and pipe flows (Reτ ≈ 1000). The physical sizes of the identified structures across the logarithmic region are geometrically self-similar in terms of height. In addition, the two-dimensional energy spectra of u within the self-similar structures follow a linear relationship between the streamwise and spanwise wavelengths in the large-scale range, which is reminiscent of self-similarity. The present results revealed that the asymptotic behaviors can be captured by extracting the self-similar coherent motions in canonical wall turbulence, even at relatively low-Reynolds-number flows. More details can be found in Hwang et al. (2020).