Fermions become polarized in a vortical fluid due to spin-vorticity coupling, and the polarization density is proportional to the local fluid vorticity. The radial expansion converts spatial vortical structures in the transverse plane to spin correlations in the azimuthal angle of final Λ hyperons' transverse momentum in high-energy heavy-ion collisions. Using a (3+1)D viscous hydrodynamic model with fluctuating initial conditions from a multiphase transport (AMPT) model, we reveal two vortical structures that are common in many fluid dynamic systems: a right-handed toroidal structure around each beam direction for transverse vorticity and pairing of longitudinal vortices with opposite signs in the transverse plane. The calculated azimuthal correlation of the transverse spin is shown to have a cosine form plus an offset due to the toroidal structure of the transverse vorticity around the beam direction and the global spin polarization. The longitudinal spin correlation in the azimuthal angle shows an oscillatory structure due to multiple vorticity pairs in the transverse plane. Mechanisms of these vortical structures, physical implications of hyperon spin correlations, dependence on colliding energy, rapidity, centrality, and sensitivity to the shear viscosity are also investigated.