Liutex and Third Generation of Vortex Definition and Identification

Abstract

Liutex is a physical quantity like velocity, vorticity, pressure, temperature, etc., describing local fluid rotation or vortex, which was ignored for centuries. Liutex was defined by the University of Arlington at Texas (UTA) team in 2018 as a vector for vortex. Its direction is the local rotation axis, and magnitude is twice local angular rotation speed. As the third generation of vortex definition and identification, Liutex has been widely applied for visualization of vortex structure to replace the first generation or vorticity, which cannot distinguish shear from rotation and the second generation such as Q, Δ, λ2, and λci methods, which are all scalar without rotation axis, dependent on threshold and contaminated by shear and stretching. Several new vortex identification methods have been developed, especially the modified Liutex-Omega method, which is threshold insensitive, and the Liutex-Core-Line method, which is unique and threshold-free. According to the Liutex vector, a unique coordinate system called Principal Coordinate can be set up, and consequent Principal Decomposition of velocity gradient tensor can be made. Different from classical fluid kinematics, the Liutex-based new fluid kinematics decomposes the fluid motion to a rotational part and a non-rotational part (UTA R-NR decomposition). The non-rotational part can be further decomposed to stretching and shear consisting of symmetric shear and anti-symmetric shear in contrast with the classical fluid kinematics, which decomposes fluid motion to deformation and vorticity, that was misunderstood as rotation. According to the constitutive relation between stress and strain, the new fluid kinematics may give significant influence to new fluid dynamics.