Relativistic versions of Helmholtz’s three theorems on vorticity flux conservation are derived by invoking an alternative approach based on Greenberg’s theory of spacelike congruence generated by vortex lines and (1 + 1) + 2 decomposition of the gradient of fluid’s 4-velocity. It is shown that the meridional circulation causes vorticity winding due to the breakdown of gravitational isorotation via differential rotation. A new streamline invariant describing energy conservation associated with vorticity flux is shown to exist.
Part of the book: Vortex Structures in Fluid Dynamic Problems