Using mapping between topological defects in an easy-plane magnet and electrical charges, we study interplay between vorticity and spin currents. We demonstrate that the flow of vorticity is accompanied by the transverse spin current generation; an effect which can be termed as the spin Hall effect of vorticity. We study this effect across the BKT transition and establish the role of dissipation and spin nonconservation in the crossover from spin superfluidity to diffusive spin transport. Our results pave the way for low power computing devices relying on vorticity and spin flows that can propagate over long distances
