Enstrophy Cascade in Two-Dimensional Quantum Turbulence

The forward enstrophy cascade in 2D turbulence in an incompressible superfluid film is investigated using the dynamic renormalization group. Out of equilibrium vortex pairs are injected into the film, which is connected to a thermal bath at low temperature. The constant-current cascade has a logarithmic two-point correlation function, and resulting k^-3 energy spectrum. The spectrum differs from the classical fluid cascade, varying linearly with the enstrophy injection rate instead of a 2/3 power, since there is an additional factor of the vortex diffusion time. The dynamics of the constant-current cascade is studied by switching on and off the input forcing, and by following the decay from an initially non-uniform state. A fundamental connection to temperature-quenched 2D superfluids is made, where the phase-ordering decay of the vortex density is the result of the turbulent cascade to small scales.