Local and Nonlocal Strain Rate Fields and Vorticity Alignment in Turbulent Flows

TL;DR

This paper develops a method to separate local and nonlocal strain rate contributions in turbulent flows using vorticity expansion, enabling better understanding of vorticity alignment with strain axes and improving turbulence analysis.

Contribution

It introduces an exact expansion-based approach to extract background strain rates from total strain in turbulence, clarifying vorticity alignment phenomena.

Findings

Converges to background strain field with increasing radius and order.

Resolves anomalous vorticity alignment near vortical structures.

Shows increased vorticity alignment with extensional strain in DNS data.

Abstract

Local and nonlocal contributions to the total strain rate tensor at any point in a flow are formulated from an expansion of the vorticity field in a local spherical neighborhood of radius R centered on x. The resulting exact expression allows the nonlocal (background) strain rate tensor to be obtained from the total strain rate tensor. In turbulent flows, where the vorticity naturally concentrates into relatively compact structures, this allows the local alignment of vorticity with the most extensional principal axis of the background strain rate tensor to be evaluated. In the vicinity of any vortical structure, the required radius R and corresponding order n to which the expansion must be carried are determined by the viscous lengthscale. We demonstrate the convergence to the background strain rate field with increasing R and n for an equilibrium Burgers vortex, and show that this resolves the anomalous alignment of vorticity with the intermediate eigenvector of the total strain rate tensor. We then evaluate the background strain field in DNS of homogeneous isotropic turbulence where, even for the limited R and n corresponding to the truncated series expansion, the results show an increase in the expected equilibrium alignment of vorticity with the most extensional principal axis of the background strain rate tensor.