Alignment of vorticity and rods with Lagrangian fluid stretching in turbulence

TL;DR

This paper investigates how vorticity and anisotropic particles align with Lagrangian stretching in turbulence, revealing that both tend to align with the strongest stretching direction, with particles nearly perfectly aligned.

Contribution

It demonstrates that vorticity and anisotropic particles align with the principal Lagrangian stretching direction, a novel insight into turbulence dynamics.

Findings

Anisotropic particles nearly perfectly align with the strongest Lagrangian stretching direction.

Vorticity alignment with stretching is stronger than with Eulerian strain rate eigenvectors.

Strong vorticity aligns similarly to rods experiencing the same stretching.

Abstract

Stretching in continuum mechanics is naturally described using the Cauchy-Green strain tensors. These tensors quantify the Lagrangian stretching experienced by a material element, and provide a powerful way to study processes in turbulent fluid flows that involve stretching such as vortex stretching and alignment of anisotropic particles. Analyzing data from a simulation of isotropic turbulence, we observe preferential alignment between anisotropic particles and vorticity. We show that this alignment arises because both of these quantities independently tend to align with the strongest Lagrangian stretching direction, as defined by the maximum eigenvector of the left Cauchy-Green strain tensor. In particular, anisotropic particles approach almost perfect alignment with the strongest stretching direction. The alignment of vorticity with stretching is weaker, but still much stronger than previously observed alignment of vorticity with the eigenvectors of the Eulerian strain rate tensor. The alignment of strong vorticity is almost the same as that of rods that have experienced the same stretching.