  Vorticity generated in heavy-ion collisions at energy of $\sqrt{s_{NN}}=$ 39
GeV is studied. Simulations are performed within a model of the three-fluid
dynamics. A peculiar structure consisting of two vortex rings is found: one
ring in the target fragmentation region and another one in the projectile
fragmentation region. These rings are also formed in central collisions. The
matter rotation is opposite in this two rings. These vortex rings are already
formed at the early stage of the collision together with primordial
fragmentation regions. The average vorticity, responsible for the global
polarization of the observed $\Lambda$ and $\bar{\Lambda}$, is also studied. In
the semi-central collisions the average vorticity in the midrapidity region
turns out to be more than an order of magnitude lower than the total one. The
total vorticity is dominated by the contributions of the fragmentation regions
and is produced because of asymmetry of the vortex rings in noncentral
collisions. This suggests that in semi-central collisions the global
polarization in the fragmentation regions should be at least an order of
magnitude higher than that observed by the STAR collaboration in the
midrapidity. This polarization should be asymmetrical in the reaction plain and
correlate with the corresponding directed flow.
