Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physical meaning of vorticity based on the RS decomposition and an
  explicit formula for the Liutex vector   In the present study, the physical meaning of vorticity is revisited based on
the RS decomposition proposed by Liu et al. in the framework of Liutex
(previously named Rortex), a vortex vector field with information of both
rotation axis and swirling strength [ C. Liu et al., "Rortex-A new vortex
vector definition and vorticity tensor and vector decomposition", Phys. Fluids
30, 035103 (2018)]. It is demonstrated that the vorticity in the direction of
rotational axis is twice the spatial mean angular velocity in the small
neighborhood around the considered point while the imaginary part of the
complex eigenvalue ({\lambda}_ci) of the velocity gradient tensor (if exist) is
the pseudo-time average angular velocity of a trajectory moving circularly or
spirally around the axis. In addition, an explicit expression of the Liutex
vector in terms of the eigenvalues and eigenvectors of velocity gradient is
obtained for the first time from above understanding, which can further, though
mildly, accelerate the calculation and give more physical comprehension of the
Liutex vector.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int