  We consider the superfluid phase of a specific renormalizable relativistic
quantum field theory. We prove that, within the regime of validity of
perturbation theory and of the superfluid effective theory, there are
consistent and regular vortex solutions where the superfluid's velocity field
as traditionally defined smoothly interpolates between zero and arbitrarily
large superluminal values. We show that this solution is free of instabilities
and of superluminal excitations. We show that, in contrast, a generic vortex
solution for an ordinary fluid does develop an instability if the velocity
field becomes superluminal. All this questions the characterization of a
superfluid velocity field as the actual velocity of ``something".
