Stretching and Shearing Contamination Analysis for Liutex/Rortex and Other Vortex Identification Methods

TL;DR

This paper analyzes how traditional vortex identification methods are affected by shearing and stretching, demonstrating that Liutex accurately measures fluid rotation without contamination from these effects, unlike other methods.

Contribution

The paper provides a mathematical comparison showing Liutex's superiority in isolating true fluid rotation by excluding shearing and stretching effects.

Findings

Liutex accurately measures fluid rotation without contamination.

Traditional methods are affected by shearing and stretching.

Liutex has mathematical and computational advantages over other methods.

Abstract

Although traditional vortex identification methods such as Q, Delta, Lambda2, Lambdaci remain popular in the identification and visualization of vortices, these methods count on shearing and stretching as a part of vortex strength. However, shearing and stretching do not contribute to fluid rotation. In this paper, the contamination effects of stretching and shearing of these methods are investigated and compared with Liutex method. From our investigation, the Liutex is an exact definition of fluid rotation or vortex, while other vortex identification methods are contaminated by stretching and shearing at different levels. The decomposition of the velocity gradient tensor can only be conducted in a so-called Principal Coordinate for uniqueness. The mathematical relation between Liutex and other vortex identification function are derived in this paper and then the effects of shearing and stretching on different vortex identification methods are studied. The mathematical formula and computation of the stretching and shearing effects on different schemes clearly show that the Liutex method has superiority over the other vortex identification methods as it only counts on local fluid rigid rotation while other methods count on stretching/compression and shearing as a part of the fluid rotation or vortex.