Browsing by Author "Smits, A. J."
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Item Eddy self-similarity in turbulent pipe flow(Physical Review Fluids, 2024-05-15) Hellström, L. H. O.; Van Buren, T.; Vaccaro, J. C.; Smits, A. J.For wall-bounded turbulent flows, Townsend's attached eddy hypothesis proposes that the logarithmic layer is populated by a set of energetic and geometrically self-similar eddies. These eddies scale with a single length scale, their distance to the wall, while their velocity scale remains constant across all self-similar structures. To investigate the existence of such structures in fully developed turbulent pipe flow, stereoscopic particle image velocimetry measurements were performed in two parallel cross-sectional planes, spaced apart by a varying distance from 0 to 9.97𝑅, where 𝑅 is the radius of the pipe, for friction Reynolds numbers Re𝜏=1310, 2430, and 3810. The instantaneous turbulence structures are sorted by width using an azimuthal Fourier decomposition and then azimuthally aligned to create a set of average eddy velocity profiles. The profiles exhibit geometric self-similar behavior in the azimuthal plane for eddies with spanwise length scales (𝜆𝜃/𝑅) spanning from 1.03 to 0.175. The streamwise similarity is then investigated using two-point correlations, where the structures exhibit a self-similar behavior with length scales (𝜆𝜃/𝑅) ranging from approximately 0.88 to 0.203. The candidate structures thereby establish full three-dimensional geometric self-similarity. In addition, the characteristic velocity magnitudes exhibit self-similarity within these ranges, using a velocity scale that is proportional to eddy size. This unexpected result is reconciled with the attached eddy hypothesis in terms of sampling probabilities.