  We present the general formulation of the relativistic fluid dynamics with
vorticity (including relativistic superfluid) on a manifold with boundary.
Making use of the Hodge decomposition, we emphasize that the equations of
motion include a term due to non-trivial topology, while the pure vortex term
introduced by Carter and Langlois will be presented merely by a co-exact form.
We also consider a vortex sheet combined of individual vortices and discuss the
boundary problem.
