  STAR collaboration at RHIC has recently measured the polarization of
$\Lambda$ hyperons in non-central heavy ion collisions in the RHIC Beam Energy
Scan (BES) program. The magnitude of the polarization was found to decrease
from few percents at the lowest BES energies to $\approx0.2$% at the top RHIC
energy. The polarization signal has been reproduced in different hydrodynamic
calculations assuming a thermodynamic spin-vorticity coupling mechanism at the
Cooper-Frye hypersurface.
  In this work an extension of our existing calculations of the $\Lambda$
polarization in the RHIC BES program to the top RHIC and 2.76 TeV LHC energies
is presented. The longitudinal component of the $\Lambda$ polarization, which
is the dominant component of the polarization at the LHC energies, is
discussed. Finally we show that the global polarization of $\Lambda$ originates
dominantly from the relativistic analogue of the classical vorticity, whereas
the quadrupole longitudinal component originates from the gradients of
temperature and acceleration of the medium when the $\Lambda$s are produced out
of the fluid.
