Correlation Analysis among Vorticity, Q method and Liutex

TL;DR

This paper compares various vortex detection methods, including vorticity, Q, Lambda ci, Lambda 2, and Liutex, revealing that vorticity alone is insufficient for accurate vortex identification and highlighting Liutex's advantages.

Contribution

The study provides a correlation analysis among multiple vortex detection methods, emphasizing Liutex's physical meaning and superiority over traditional vorticity-based approaches.

Findings

Vorticity has minimal correlation with Liutex in strong shear regions.

Vorticity alone is inadequate for vortex detection.

Liutex overcomes limitations of previous methods and has clear physical significance.

Abstract

Influenced by the fact that vorticity represents rotation for rigid body, people believe it also works for fluid flow. However, the theoretical predictions by vorticity do not match experiment results, which drove scientists to look for better methods to describe vortex. According to Dr. Liu classification, all methods applied to detect vortex can be categorized into three generations. The vorticity-based method is classified as the first generation. Methods relying on eigenvalues of velocity gradient tensor are considered as the second generation. Although so many methods appeared, people still believe vorticity is vortex since vorticity theory looks perfect in math, and all other methods are only scalars and unable to indicate swirl direction. Recently, Dr. Liu innovated a new vortex identification method called Liutex. Liutex, a vector quantity, which is regarded as the third-generation method, not only overcomes all previous methods drawbacks, but also has a clear physical meaning. The direction of Liutex represents the swirl axis of rotation, and its strength is equal to twice of angular speed. In this paper, we did a correlation analysis between vorticity, Q, Lambda ci, Lambda 2 methods and Liutex based on a DNS case of boundary layer transition. The results show that the correlation between vorticity and Liutex is minimal in strong shear region, which demonstrates the idea that using vorticity to detect vortex lacks a scientific foundation; in other words, vorticity is not vortex.