Renormalized analytic solution for the enstrophy cascade in two-dimensional quantum turbulence

Analytic solutions for the forward enstrophy cascade in two-dimensional quantum turbulence are found using nonequilibrium Kosterlitz-Thouless renormalization. Vortex pairs of large separation are injected into a superfluid film at a constant rate, and cascade to smaller separation due to frictional forces on the vortex cores, annihilating at the same rate they are injected. From the cascade dynamics it is shown that the vortex decay in temperature-quenched superfluids proceeds via the turbulent cascade, and we speculate this may be a fundamental characteristic of phase-ordering transitions in general.