Liutex and Third Generation of Vortex Definition and Identification

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, proposed by Liu et al. at University of Texas at Arlington (UTA) in 2018. Since then, they have published over 40 SCI journal papers including 13 PoF papers, many of them are top cited papers. Three professional books on Liutex have been published by Bentham in 2020, Elsevier in 2020 and Springer in 2021. There are three generations of vortex identification methods in history. In 1858, Helmholtz first defined vortex as vortex tube composed by the so-called vortex filaments. It is classified as the first generation of vortex identification that vortex is defined as vorticity tubes. Science and engineering applications have shown that the correlation between vortex and vorticity is very weak, especially in the near-wall region. During the past four decades, many vortex identification criteria including Q-, Lambda_2, Lambda_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. In addition, they are all obviously 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 velocity 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 new vortex identification methods have been developed by Liu and the UTA Team including Liutex vector, Liutex vector lines, Liutex tubes, Liutex iso-surface, Liutex-Omega methods, Objective Liutex and, more recently, Liutex Core Line methods. Liutex-Omega method is very popular and Liutex-Core-Line method is unique and threshold-free. The Liutex definition, Principal Coordinate, Principal Decomposition in Principal Coordinate, vorticity RS decomposition, velocity gradient tensor UTA R-NR decomposition, and Principal Decomposition of velocity gradient tensor in Cartesian coordinates, proposed by Liu et al., integrate the Liutex theoretic system and pave the foundation for new fluid kinematics, new vortex science and new turbulence research. A new fluid kinematics has been derived in details and a new fluid dynamics is ongoing.