A Stochastic Representation of the Local Structure of Turbulence

Abstract

Based on the mechanics of the Euler equation at short time, we show that a Recent Fluid Deformation (RFD) closure for the vorticity field, neglecting the early stage of advection of fluid particles, allows to build a 3D incompressible velocity field that shares many properties with empirical turbulence, such as the teardrop shape of the R-Q plane. Unfortunately, non gaussianity is weak (i.e. no intermittency) and vorticity gets preferentially aligned with the wrong eigenvector of the deformation. We then show that slightly modifying the former vectorial field in order to impose the long range correlated nature of turbulence allows to reproduce the main properties of stationary flows. Doing so, we end up with a realistic incompressible, skewed and intermittent velocity field that reproduces the main characteristics of 3D turbulence in the inertial range, including correct vorticity alignment properties.

6 pages, 3 figures, final version, published.

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• Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
• Hydrodynamic turbulence and intermittent random fields
• Intermittency and universality in a Lagrangian model of velocity gradients in three-dimensional turbulence

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• Revisiting the framework for intermittency in Lagrangian stochastic models for turbulent flows: a way to an original and versatile numerical approach
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• Dynamical Fractional and Multifractal Fields