Spectral analysis of near-wall turbulence in channel flow at Reτ=4200 with emphasis on the attached-eddy hypothesis

Direct numerical simulation data for channel flow at a friction Reynolds number of 4200, generated by Lozano-Durán and Jiménez [J. Fluid Mech. 759, 432 (2014)], are used to examine the properties of near-wall turbulence within subranges of eddy-length scale. Attention is primarily focused on the intermediate layer (mesolayer) covering the logarithmic velocity region within the range of wall-scaled wall-normal distance of 80–1500. The examination is based on a number of statistical properties, including premultiplied and compensated spectra, the premultiplied derivative of the second-order structure function, and three scalar parameters that characterize the anisotropic or isotropic state of the various length-scale subranges. This analysis leads to the delineation of three regions within the map of wall-normal-wise premultiplied spectra, each characterized by distinct turbulence properties. A question of particular interest is whether the Townsend-Perry attached-eddy hypothesis (AEH) can be shown to be valid across the entire mesolayer, in contrast to the usual focus on the outer portion of the logarithmic-velocity layer at high Reynolds numbers, which is populated with very-large-scale motions. This question is addressed by reference to properties in the premultiplied scalewise derivative of the second-order structure function (PMDS2) and joint probability density functions of streamwise-velocity fluctuations and their streamwise and spanwise derivatives. This examination provides evidence, based primarily on the existence of a plateau region in the PMDS2, for the qualified validity of the AEH right down the lower limit of the logarithmic velocity range.