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Nonlocal Pressure Contributions to the Small-Scale Statistics of Homogeneous Isotropic Turbulence

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The topology and statistics of the small scales of homogeneous isotropic turbulence can comprehensively be described in terms of the velocity gradient tensor. Here, one of the key problems is to quantify the nonlocal pressure contributions, which enter the velocity gradient tensor dynamics in form of the pressure Hessian. This nonlocality, which tightly interacts with the local self- amplification mechanisms, also poses severe challenges on the closure of statistical models for the small scales of turbulence. In this paper, we systematically elaborate the statistical structure of the pressure Hessian and explicitly evaluate it for Gaussian random fields. The results then are compared to those obtained by direct numerical simulations, and possible implications for improved closure schemes are discussed.

Author(s):

Michael Wilczek    
Department of Mechanical Engineering, JHU Baltimore
United States

Charles Meneveau    
Department of Mechanical Engineering, JHU Baltimore
United States