  Possible correlations of the global polarization of $\Lambda$ hyperons with
the angular momentum and transverse flow in the central region of colliding
nuclei are studied based on refined estimate of the global polarization.
Simulations of Au+Au collisions at collision energies $\sqrt{s_{NN}}=$ 6-40 GeV
are performed within the model of the three-fluid dynamics. Within the
crossover and first-order-phase-transition scenarios this refined estimate
quite satisfactorily reproduces the experimental STAR data. Hadronic scenario
fails at high collision energies, $\sqrt{s_{NN}}>$ 10 GeV, and even predicts
opposite sign of the global polarization. It is found that the global
polarization correlates with neither the angular momentum accumulated in the
central region nor with directed and elliptic flow. At the same time we
observed correlation between the angular momentum and directed flow in both
their time and collision-energy dependence. These results suggest that,
although initially the angular momentum is the driving force for the vortex
generation, later the angular momentum and vortex motion become decorrelated in
the midrapidity region. Then the midrapidity angular momentum is determined by
the pattern of the directed flow and even becomes negative when the antiflow
occurs. At the freeze-out stage, the dominant part of the participant angular
momentum is accumulated in the fragmentation regions.
