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Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields

Published online by Cambridge University Press:  01 September 2014

Michael Wilczek  and
Charles Meneveau
Michael Wilczek*
Affiliation:
Department of Mechanical Engineering and Institute for Data Intensive Engineering and Science, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering and Institute for Data Intensive Engineering and Science, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
*
†Email address for correspondence: mwilczek@jhu.edu
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Abstract

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Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the velocity gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian velocity gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 191 - 225
Copyright
© 2014 Cambridge University Press 

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