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Although traditional vortex identification methods such as Q, Delta, Lambda2,Lambdaci remain popular in the identification and visualization of vortices,these methods count on shearing and stretching as a part of vortex strength.However, shearing and stretching do not contribute to fluid rotation. In thispaper, the contamination effects of stretching and shearing of these methodsare investigated and compared with Liutex method. From our investigation, theLiutex is an exact definition of fluid rotation or vortex, while other vortexidentification methods are contaminated by stretching and shearing at differentlevels. The decomposition of the velocity gradient tensor can only be conductedin a so-called Principal Coordinate for uniqueness. The mathematical relationbetween Liutex and other vortex identification function are derived in thispaper and then the effects of shearing and stretching on different vortexidentification methods are studied. The mathematical formula and computation ofthe stretching and shearing effects on different schemes clearly show that theLiutex method has superiority over the other vortex identification methods asit only counts on local fluid rigid rotation while other methods count onstretching/compression and shearing as a part of the fluid rotation or vortex.

Stretching and Shearing Contamination Analysis for Liutex/Rortex and Other Vortex Identification Methods