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Vortices in a radially inhomogeneous superfluid, as realized by a trapped degenerate Bose gas in a uniaxially symmetric potential was analyzed. It was found 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. The minimum-energy vortex density was computed in the complementary regime of a finite prescribed rotation, showing that in the rapid-rotation limit it is extremely uniform, despite a strongly inhomogeneous Thomas-Fermi condensate density. It was shown that one striking consequence of the inhomogeneous vortex distribution is an azimuthally directed, radially shearing superflow.

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Physical Review A - Atomic, Molecular, and Optical Physics