The Liutex (previously known Rortex) method introduces a vortex vector field
to mathematically and systematically describe vortices in flow fields. In this study, the
previous calculation procedures of Liutex which includes a two-step reference coordinate
rotation is revisited first. An explicit formula to calculate Liutex is then derived and the
physical intuition and efficiency improvement brought by this formula are discussed. It
is estimated that the computation time of Liutex vector from velocity gradient field can
be reduced by 36.6% compared with that of the previous method. Besides, the Galilean
invariance widely accepted as a preliminary check for a successful vortex identification
method is discussed for Liutex vector.
Keywords: Angular velocity, Coherent structures, Galilean invariance, Liutex,
Vortex identification, Velocity gradient tensor.
