  Eulerian local region-type vortex identification criteria, including the
criterion, the criterion and the criterion et al., are widely used for vortex
identification due to the simplicity in applications. However, most of these
criteria are based on a scalar quantity, unable to identify vortex axis (core)
lines. On the other hand, the current line-type methods, which seek to extract
line-type features such as vortex core lines, are not entirely satisfactory
since most of these methods are based on vorticity or pressure minimum which
will fail in many cases. To address this issue, a novel Liutex (previously
named Rortex) based definition of vortex axis line is proposed in this paper.
Mathematically, the vortex axis lines are defined by points where the gradient
of Liutex magnitude is aligned with the direction of the Liutex vector, which
implies that the cross product of the gradient of Liutex magnitude and the
Liutex vector is equal to zero. A preliminary manual process for extracting
vortex axis lines is presented. Two test cases, namely Burgers vortex and
hairpin vortex, are examined to verify the proposed method.
