A model for alignment between microscopic rods and vorticity

TL;DR

This paper presents an analytical model explaining how microscopic rods in turbulent flows tend to align with vorticity, especially under certain strain conditions, supported by simulations and theoretical analysis.

Contribution

It introduces an analytically solvable limit for rod alignment in a random, isotropic velocity field with slow vorticity variation, revealing new alignment behaviors.

Findings

Rods tend to align with vorticity when strain and vorticity interactions are strong.

Alignment is predominantly parallel or perpendicular to vorticity at high strain-vorticity interaction.

The model matches numerical simulations under specific flow conditions.

Abstract

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the product of the strain relaxation time $\tau_{\rm s}$ and the angular velocity $\omega$ about the vorticity axis. We find that when $\omega\tau_{\rm s}\gg 1$, the rods are predominantly either perpendicular or parallel to the vorticity.