  We treat string propagation and interaction in the presence of a background
Neveu-Schwarz three-form field strength, suitable for describing vortex rings
in a superfluid or low-viscosity normal fluid. A circular vortex ring exhibits
instabilities which have been recognized for many years, but whose precise
boundaries we determine for the first time analytically in the small core
limit. Two circular vortices colliding head-on exhibit stronger instabilities
which cause splitting into many small vortices at late times. We provide an
approximate analytic treatment of these instabilities and show that the most
unstable wavelength is parametrically larger than a dynamically generated
length scale which in many hydrodynamic systems is close to the cutoff. We also
summarize how the string construction we discuss can be derived from the
Gross-Pitaevskii lagrangian, and also how it compares to the action for giant
gravitons.
