We study vortices in a radially inhomogeneous superfluid, as realized by a
trapped degenerate Bose gas in a uniaxially symmetric potential. We show that,
in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an
anisotropic superflow whose profile strongly depends on the distance to the
trap axis. One consequence of this superflow anisotropy is vortex precession
about the trap axis in the absence of an imposed rotation. In the complementary
regime of a finite prescribed rotation, we compute the minimum-energy vortex
density, showing that in the rapid-rotation limit it is extremely uniform,
despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density
Οsβ(r). The weak radially-dependent contribution (ββ2lnΟsβ(r)) to the vortex distribution, that vanishes with the
number of vortices Nvβ as Nvβ1β, arises from the interplay between
vortex quantum discretness (namely their inability to faithfully support the
imposed rigid-body rotation) and the inhomogeneous superfluid density. This
leads to an enhancement of the vortex density at the center of a typical
concave trap, a prediction that is in quantitative agreement with recent
experiments (cond-mat/0405240). One striking consequence of the inhomogeneous
vortex distribution is an azimuthally-directed, radially-shearing superflow.Comment: 22 RevTeX pages, 20 figures, Submitted to PR