  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 this
paper, the contamination effects of stretching and shearing of these methods
are investigated and compared with Liutex method. From our investigation, the
Liutex is an exact definition of fluid rotation or vortex, while other vortex
identification methods are contaminated by stretching and shearing at different
levels. The decomposition of the velocity gradient tensor can only be conducted
in a so-called Principal Coordinate for uniqueness. The mathematical relation
between Liutex and other vortex identification function are derived in this
paper and then the effects of shearing and stretching on different vortex
identification methods are studied. The mathematical formula and computation of
the stretching and shearing effects on different schemes clearly show that the
Liutex method has superiority over the other vortex identification methods as
it only counts on local fluid rigid rotation while other methods count on
stretching/compression and shearing as a part of the fluid rotation or vortex.
