Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence

TL;DR

This study uses DNS to analyze how Lagrangian velocity gradient correlations evolve in isotropic turbulence, revealing short-time increases in cross-correlation and decreases in auto-correlation, explained by invariants and modeled by local shear and rotation effects.

Contribution

It provides new insights into the short-time evolution of velocity gradient correlations using DNS and heuristic models, linking physical mechanisms to observed behaviors.

Findings

Cross correlation increases at short times

Auto-correlation decreases at short times

Models reproduce DNS observations

Abstract

We show by direct numerical simulation (DNS) that the Lagrangian cross correlation of velocity gradients in homogeneous isotropic turbulence increases at short times, whereas its auto-correlation decreases. Kinematic considerations allow to show that two invariants of the turbulent velocity field determine the short-time velocity gradient correlations. In order to get a more intuitive understanding of the dynamics for longer times, heuristic models are proposed involving the combined action of local shear and rotation. These models quantitatively reproduce the effects and disentangle the different physical mechanisms leading to the observations in the DNS.