  Using a four-dimensional manifestly covariant formalism suitable for
classical fluid dynamics, it is shown that the conservation of potential
vorticity is not associated with any symmetry of the equations of motion but is
instead a trivial conservation law of the second kind. The demonstration is
provided in arbitrary coordinates and therefore applies to comoving (or label)
coordinates. Since this is at odds with previous studies, which claimed that
potential vorticity conservation is associated with a symmetry under
particle-relabeling, a detailed discussion on relabeling transformations is
also presented.
