  We introduce a new method of statistical analysis to characterise the
dynamics of turbulent fluids in two dimensions. We establish that, in
equilibrium, the vortex distributions can be uniquely connected to the
temperature of the vortex gas, and apply this vortex thermometry to
characterise simulations of decaying superfluid turbulence. We confirm the
hypothesis of vortex evaporative heating leading to Onsager vortices proposed
in Phys. Rev. Lett. 113, 165302 (2014), and find previously unidentified vortex
power-law distributions that emerge from the dynamics.
