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On the strength of the nonlinearity in isotropic turbulence

Published online by Cambridge University Press:  19 September 2013

W. J. T. Bos  and
R. Rubinstein
W. J. T. Bos*
Affiliation:
LMFA-CNRS, Université de Lyon, Ecole Centrale de Lyon, 69134 Ecully, France
R. Rubinstein
Affiliation:
Newport News, VA, USA
*
†Email address for correspondence: wouter.bos@ec-lyon.fr
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Abstract

Turbulence governed by the Navier–Stokes equations shows a tendency to evolve towards a state in which the nonlinearity is diminished. In fully developed turbulence, this tendency can be measured by comparing the variance of the nonlinear term to the variance of the same quantity measured in a Gaussian field with the same energy distribution. In order to study this phenomenon at high Reynolds numbers, a version of the direct interaction approximation is used to obtain a closed expression for the statistical average of the mean-square nonlinearity. The wavenumber spectrum of the mean-square nonlinear term is evaluated and its scaling in the inertial range is investigated as a function of the Reynolds number. Its scaling is dominated by the sweeping by the energetic scales, but this sweeping is weaker than predicted by a random sweeping estimate. At inertial range scales, the depletion of nonlinearity as a function of the wavenumber is observed to be constant. At large scales it is observed that the mean-square nonlinearity is larger than its Gaussian estimate, which is shown to be related to the non-Gaussianity of the Reynolds-stress fluctuations at these scales.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 733 , 25 October 2013 , pp. 158 - 170
Copyright
©2013 Cambridge University Press 

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