On the relationships between local vortex identification schemes

TLDR

The study analyzes popular vortex identification criteria based on velocity‑gradient tensor analysis and introduces a new spiralling‑compactness measure that yields a local vortex identification criterion and core requirements. The authors analytically examine inter‑relationships among the criteria, applying zero and non‑zero thresholds in several flow examples to illustrate their behavior. The analysis reveals that the criteria can be interpreted through local flow kinematics, producing similar vortical structures in canonical turbulence and providing a unified framework for predicting when differences arise.

Abstract

We analyse the currently popular vortex identification criteria that are based on point-wise analysis of the velocity gradient tensor. A new measure of spiralling compactness of material orbits in vortices is introduced and using this measure a new local vortex identification criterion and requirements for a vortex core are proposed. The inter-relationships between the different criteria are explored analytically and in a few flow examples, using both zero and non-zero thresholds for the identification parameter. These inter-relationships provide a new interpretation of the various criteria in terms of the local flow kinematics. A canonical turbulent flow example is studied, and it is observed that all the criteria, given the proposed usage of threshold, result in remarkably similar looking vortical structures. A unified interpretation based on local flow kinematics is offered for when similarity or differences can be expected in the vortical structures educed using the different criteria.