Liutex – Unique and Rigorous Definition and Identification of Vortex

This paper explains why Liutex is the unique and rigorous definition and identification method of vortex. Liutex itself represents local fluid rotation axis and local rotation strength/angular speed. The Liutex core line, where gradient of Liutex and Liutex vector coincide, is the global vortex core. Like Liutex, the first generation of vortex definition or vorticity is also a vector, but it is a combination of shear and rotation, not local rotational axis, or angular speed. The second generation of vortex identification methods are all scalers, which have no local rotation direction with incorrect vortex strength, which is not local angular speed but contaminated by shear and stretching/compression in different degrees. Their physical meaning is not clear, and their strength has no linear relation with the vortex strength. As vectors cannot be represented by scalars and nonlinear correlation cannot be used for a physical quantity, it is not appropriate to use any first and second vortex identification methods to represent vortex as they are scalar, not unique, and contaminated by shears and stretching/compression. Liutex is a unique mathematical definition for local and global fluid rotation or vortex. Some important applications of Liutex like Liutex spectrum in the dissipation subregions of turbulence, Liutex-based Wang’s subgrid model, and Liutex-based new fluid kinematics are also briefly described.