  The low-energy dynamics of a zero temperature superfluid or of the
compressional modes of an ordinary fluid can be described by a simple effective
theory for a scalar field---the superfluid 'phase'. However, when vortex lines
are present, to describe all interactions in a local fashion one has to switch
to a magnetic-type dual two-form description, which comes with six degrees of
freedom (in place of one) and an associated gauge redundancy, and is thus
considerably more complicated. Here we show that, in the case of vortex $rings$
and for bulk modes that are much longer than the typical ring size, one can
perform a systematic multipole expansion of the effective action and recast it
into the simpler scalar field language. In a sense, in the presence of vortex
rings the non-single valuedness of the scalar can be hidden inside the rings,
and thus out of the reach of the multipole expansion. As an application of our
techniques, we compute by standard effective field theory methods the sound
emitted by an oscillating vortex ring.
