Lagrangian time correlations of vorticity alignments in isotropic turbulence: observations and model predictions

TL;DR

This paper investigates how vorticity aligns with deformation-rate tensor eigenvectors in turbulence, using DNS data and models to understand their time correlations and compare predictions with experimental observations.

Contribution

It provides a detailed analysis of Lagrangian vorticity alignment correlations in turbulence and evaluates a velocity gradient tensor model against DNS and experimental data.

Findings

Model accurately reproduces initial vorticity alignment increase.

Model captures evolution of correlations with deformation eigenvectors.

Differences observed in correlations with pressure Hessian eigen-frame.

Abstract

Motivated by results from recent particle tracking experiments in turbulence (Xu et al., Nat. Phys. 7, 709 (2011)), we study the Lagrangian time correlations of vorticity alignments with the three eigenvectors of the deformation-rate tensor. We use data from direct numerical simulations (DNS), and explore the predictions of a Lagrangian model for the velocity gradient tensor. We find that the initial increase of correlation of vorticity direction with the most extensive eigen-direction observed by Xu et al. is reproduced accurately using the Lagrangian model, as well as the evolution of correlation with the other two eigendirections. Conversely, time correlations of vorticity direction with the eigen-frame of the pressure Hessian tensor show differences with the model.