  Fermions become polarized in a vortical fluid due to spin-vorticity coupling.
The spin polarization density is proportional to the local fluid vorticity at
the next-to-leading order of a gradient expansion in a quantum kinetic theory.
Spin correlations of two $\Lambda$-hyperons can therefore reveal the vortical
structure of the dense matter in high-energy heavy-ion collisions. We employ a
(3+1)D viscous hydrodynamic model with event-by-event fluctuating initial
conditions from A MultiPhase Transport (AMPT) model to calculate the vorticity
distributions and $\Lambda$ spin correlations. The azimuthal correlation of the
transverse spin is shown to have a cosine form plus an offset due to a circular
structure of the transverse vorticity around the beam direction and global spin
polarization. The longitudinal spin correlation shows a structure of
vortex-pairing in the transverse plane due to the convective flow of hot spots
in the radial direction. The dependence on colliding energy, rapidity,
centrality and sensitivity to the shear viscosity are also investigated.

High Energy Physics - Phenomenology;Nuclear Experiment;Nuclear Theory