Introduction of Liutex and Third Generation of Vortex Identification Methods

This paper is a try to introduce Liutex and the third generation of vortex definition and identification to the community for wide application which is critical to fluid dynamics. Basically, this is a summary of our current work. Vortex is intuitively recognized as the rotational/swirling motion of fluids. However, a rigorous mathematical definition for vortex was absent for centuries. Liutex is a new physical quantity to represent fluid rotation or vortex, introduced by Liu et al. at University of Texas at Arlington (UTA) in 2018. There are three generations of vortex identification methods in history. In 1858, Helmholtz first defined vortex as vorticity tubes, which is classified as the first generation of vortex identification. Science and engineering applications had found that the correlation between vortex and vorticity is very weak, especially in the near-wall boundary region. During the past four decades, many vortex identification criteria including Q, Δ, λ_2 and λ_ci methods have been developed, which are classified as the second generation of vortex identification. They are all based on the eigenvalues of the velocity gradient tensor. However, they are all scalars and thus strongly threshold-dependent, which have problems with uniqueness and wrong dimension. In addition to lack of physical meanings, they are all contaminated by stretching and shearing. Liutex, as the third generation of vortex definition and identification, is defined as a vector which uses the real eigenvector of velocity gradient tensor as its direction and twice the local angular speed of the rigid rotation as its magnitude. The major idea of Liutex is to extract the rigid rotation part from fluid motion to represent vortex. After that, a number of vortex identification methods have been developed by Liu and the UTA Team including Liutex vector, Liutex vector lines, Liutex tubes, Liutex iso-surfaces, Liutex-Omega methods, Objective Liutex and, more recently, Liutex Core Central Line methods. The Liutex definition, Liutex-based vortex identification, Principal Coordinate, Principal Decomposition, vorticity RS decomposition, velocity gradient tensor UTA R-NR decomposition, proposed by Liu et al., integrate the Liutex theoretic system and pave the foundation for new fluid kinematics, new vortex science and new quantified turbulence research.