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On the velocity distribution in homogeneous isotropic turbulence: correlations and deviations from Gaussianity

Published online by Cambridge University Press:  12 April 2011

MICHAEL WILCZEK ,
ANTON DAITCHE  and
RUDOLF FRIEDRICH
MICHAEL WILCZEK*
Affiliation:
Institute for Theoretical Physics, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
ANTON DAITCHE
Affiliation:
Institute for Theoretical Physics, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
RUDOLF FRIEDRICH
Affiliation:
Institute for Theoretical Physics, Westfälische Wilhelms-Universität, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end, we apply the statistical framework of the Lundgren–Monin–Novikov hierarchy combined with conditional averaging, identifying the quantities that determine the shape of the probability density function. In this framework, the conditional averages of the rate of energy dissipation, the velocity diffusion and the pressure gradient with respect to velocity play a key role. Direct numerical simulations of the Navier–Stokes equation are used to complement the theoretical results and assess deviations from Gaussianity.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 676 , 10 June 2011 , pp. 191 - 217
Copyright
Copyright © Cambridge University Press 2011

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