  The nonequilibrium dynamics of vortices in 2D quantum fluids are shown to
obey a kinetic equation in which vortex tilt (ellipticity) is coupled to the
gradient in background fluid density. In the absence of nonlinear interactions,
a trapped, tilted vortex is analytically found to move in an elliptic
trajectory that has the same orientation and aspect ratio as the vortex
projection itself, allowing experimental measurement of vortex tilt via path
observation. A combination of analysis and simulation is then used to show that
nonlinear interactions cause the vortex tilt to precess, and that the rate of
vortex precession is once again mimicked by a precession of the elliptical
trajectory. Both vortex tilt and rate of precession can therefore be inferred
by observing its motion in a trap. An ability to anticipate local vortex
structure is expected to prove useful in designing few-vortex systems in which
tilt is a ubiquitous, as-yet-unharnessed feature.
