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Universality of the energy-containing structures in wall-bounded turbulence

Published online by Cambridge University Press:  21 June 2017

Charitha M. de Silva*
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Dominik Krug
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Detlef Lohse
Physics of Fluids Group and Twente Max Planck Center, Department of Science and Technology, Mesa+ Institute, and J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
Ivan Marusic
Department of Mechanical Engineering, University of Melbourne, Victoria 3010, Australia
Email address for correspondence:


The scaling behaviour of the longitudinal velocity structure functions $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}$ (where $2p$ represents the order) is studied for various wall-bounded turbulent flows. It has been known that for very large Reynolds numbers within the logarithmic region, the structure functions can be described by $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}/U_{\unicode[STIX]{x1D70F}}^{2}\approx D_{p}\ln (r/z)+E_{p}$ (where $r$ is the longitudinal distance, $z$ the distance from the wall, $U_{\unicode[STIX]{x1D70F}}$ the friction velocity and $D_{p}$, $E_{p}$ are constants) in accordance with Townsend’s attached eddy hypothesis. Here we show that the ratios $D_{p}/D_{1}$ extracted from plots between structure functions – in the spirit of the extended self-similarity hypothesis – have further reaching universality for the energy containing range of scales. Specifically, we confirm that this description is universal across wall-bounded flows with different flow geometries, and also for both the longitudinal and transversal structure functions, where previously the scaling has been either difficult to discern or differences have been reported when examining the direct representation of $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}$. In addition, we present evidence of this universality at much lower Reynolds numbers, which opens up avenues to examine structure functions that are not readily available from high Reynolds number databases.

© 2017 Cambridge University Press 

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