Lagrangian dynamics and statistical geometric structure of turbulence

TL;DR

This paper develops a stochastic Lagrangian model for the velocity gradient tensor in 3D turbulence, capturing key statistical and geometric features observed in experiments and simulations.

Contribution

It introduces a novel stochastic framework that models the evolution of the velocity gradient tensor, incorporating nonlinear self-stretching and non-local effects.

Findings

Reproduces non-Gaussian statistics of turbulence

Captures geometric alignment trends in velocity gradients

Models anomalous relative scaling in turbulent flows

Abstract

The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The non-local pressure and viscous effects are accounted for by a closure that models the material deformation history of fluid elements. The resulting stochastic system reproduces many statistical and geometric trends observed in numerical and experimental 3D turbulent flows, including anomalous relative scaling.