A Liutex based definition of vortex axis line

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.