Incorrectness of the Second-Generation Vortex Identification Method and Introduction to Liutex

For a long time, scientists believe that vorticity reveal the essence of vortex since vorticity is a perfect indicator of rotation for rigid object although many experimental results do not support this point of view. Even though scientists do not doubt the correctness of vorticity, they have to develop some other vortex identification methods to improve the performance of detecting vortex. Under this situation, Q method, λci method and λ2 method are innovated. However, these methods are all scalars and not able to locate the swirling direction, and threshold is needed to be used to display vortex structures. To overcome these drawbacks, Liu proposed Liutex which can correctly represent the rigid rotation of fluids. The magnitude of Liutex represents the twice angular speed and the direction of Liutex is the direction of swirling axis. In this paper, the incorrectness of the classical methods is explained as well as the rationality of the definition of Liutex. A correlation research is done between vorticity, Q, λci, λ2 methods and Liutex based on a direct numerical simulation (DNS) case of boundary layer transition. The results show that the correlation between vorticity and Liutex is very small or even negative in strong shear regions, which demonstrates that using vorticity to detect vortex lacks scientific foundation and vorticity is not appropriate to represent vortex. In the last part of this paper, new vortex structure displaying methods including Liutex iso-surface, Liutex-Omega and Liutex core line are introduced.