  The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted
by accounting for the way in which vortex ellipticity is coupled to the
gradient in background fluid density. In the absence of nonlinear interactions,
a harmonically trapped fluid can be analyzed analytically to show that single
vortices will move in an elliptic trajectory that has the same orientation and
aspect ratio as the vortex projection itself. This allows the vortex
ellipticity to be estimated through observation of its trajectory. A
combination of analysis and numerical simulation is then used to show that
nonlinear interactions cause the vortex orientation to precess, and that the
rate of vortex precession is once again mimicked by a precession of the
elliptical trajectory. Both vortex ellipticity and rate of precession can
therefore be inferred by observing its motion in a trap. An ability to
anticipate and control local vortex structure and vortex trajectory is expected
to prove useful in designing few-vortex systems in which ellipticity is a
ubiquitous, as-yet-unharnessed feature.
