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Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at a friction Reynolds number of 932

Published online by Cambridge University Press:  30 August 2016

A. Lozano-Durán ,
M. Holzner  and
J. Jiménez
A. Lozano-Durán*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
M. Holzner
Affiliation:
ETH Zurich, 8093 Zurich, Switzerland
J. Jiménez
Affiliation:
School of Aeronautics, U. Politécnica de Madrid, 28040 Madrid, Spain
*
†Email address for correspondence: [email protected]
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Abstract

The invariants of the velocity gradient tensor, $R$ and $Q$, and their enstrophy and strain components are studied in the logarithmic layer of an incompressible turbulent channel flow. The velocities are filtered in the three spatial directions and the results are analysed at different scales. We show that the $R$–$Q$ plane does not capture the changes undergone by the flow as the filter width increases, and that the enstrophy/enstrophy-production and strain/strain-production planes represent better choices. We also show that the conditional mean trajectories may differ significantly from the instantaneous behaviour of the flow since they are the result of an averaging process where the mean is 3–5 times smaller than the corresponding standard deviation. The orbital periods in the $R$–$Q$ plane are shown to be independent of the intensity of the events, and of the same order of magnitude as those in the enstrophy/enstrophy-production and strain/strain-production planes. Our final goal is to test whether the dynamics of the flow is self-similar in the inertial range, and the answer turns out to be that it is not. The mean shear is found to be responsible for the absence of self-similarity and progressively controls the dynamics of the eddies observed as the filter width increases. However, a self-similar behaviour emerges when the calculations are repeated for the fluctuating velocity gradient tensor. Finally, the turbulent cascade in terms of vortex stretching is considered by computing the alignment of the vorticity at a given scale with the strain at a different one. These results generally support a non-negligible role of the phenomenological energy-cascade model formulated in terms of vortex stretching.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 803 , 25 September 2016 , pp. 356 - 394
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Copyright
© 2016 Cambridge University Press 

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