  Under suitable forcing a fluid exhibits turbulence, with characteristics
strongly affected by the fluid's confining geometry. Here we study
two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate
in an annular trap. As a compressible quantum fluid, this system affords a rich
phenomenology, allowing coupling between vortex and acoustic energy.
Small-scale stirring generates an experimentally observed disordered vortex
distribution that evolves into large-scale flow in the form of a persistent
current. Numerical simulation of the experiment reveals additional
characteristics of two-dimensional quantum turbulence: spontaneous clustering
of same-circulation vortices, and an incompressible energy spectrum with
$k^{-5/3}$ dependence for low wavenumbers $k$ and $k^{-3}$ dependence for high
$k$.
