An objective vortex identification method

TL;DR

This paper introduces an objective method for vortex identification that remains consistent across different observer frames, using velocity data and a zero-vorticity point to accurately determine vortex structures in an inertial coordinate system.

Contribution

The paper proposes a novel approach to transfer non-inertial observations to inertial coordinates for vortex identification, ensuring objective results independent of observer motion.

Findings

Methods accurately transfer velocity data to inertial coordinates

Objective vortex structures are reliably identified using the proposed approach

Relative errors in vortex detection are extremely small

Abstract

Generally, the vortex structures should be independent of the observers who are moving, especially when their coordinates are non-inertial, which may result in confusions in communications between researchers. The property that not being influenced by the choice of coordinate is called objective. Mostly, researchers would like to gather data in the inertial coordinate because most physical laws are valid in the inertial coordinate. As a result, how to transfer the observations in a non-inertial coordinate to those in an inertial coordinate raises interest. In this paper, methods are provided to obtain velocity and velocity gradient tensor in an inertial coordinate from the non-inertial observations based on one known zero-vorticity point which can be chosen from physical fact such as the point is located in the inviscid region.Further, objective vortex structure can be calculated from the objective velocity or velocity gradient tensor. With Liutex chosen as the indicator of the vortex, two numerical examples are used to test the proposed methods. The results show that the methods perform very well and the relative error is extremely small.