A stochastic representation of the local structure of turbulence

¹  Laboratoire de Physique de l'ENS Lyon, CNRS, Université de Lyon - 46 allée d'Italie, 69007 Lyon, France, EU
²  Institut Fourier, CNRS, Université Grenoble 1 - 100 rue des Mathématiques, BP 74, 38402 Saint-Martin d'Hères cedex, France, EU
³  Ceremade, CNRS, Université Paris-Dauphine - F-75016 Paris, France, EU

Corresponding author: laurent.chevillard@ens-lyon.fr

Received: 20 November 2009
Accepted: 19 February 2010

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 RQ-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.