Eddy self-similarity in turbulent pipe flow
Date
2024-05-15
Journal Title
Journal ISSN
Volume Title
Publisher
Physical Review Fluids
Abstract
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.
Description
This article was originally published in Physical Review Fluids. The version of record is available at: https://doi.org/10.1103/PhysRevFluids.9.054607. ©2024 American Physical Society.
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Citation
Hellström, L. H. O., T. Van Buren, J. C. Vaccaro, and A. J. Smits. “Eddy Self-Similarity in Turbulent Pipe Flow.” Physical Review Fluids 9, no. 5 (May 15, 2024): 054607. https://doi.org/10.1103/PhysRevFluids.9.054607.