A Stochastic Representation of the Local Structure of Turbulence

TL;DR

This paper introduces a stochastic model based on the Euler equation mechanics to replicate key features of 3D turbulence, including velocity field properties and vorticity alignment, by modifying a fluid deformation closure.

Contribution

It develops a stochastic representation of turbulence that captures its main statistical and structural properties through a modified fluid deformation approach.

Findings

Reproduces teardrop shape of the R-Q plane

Achieves realistic vorticity alignment with deformation eigenvectors

Models stationary, skewed, and intermittent velocity fields

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.