Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence.

ABSTRACT

We report evidence for an enstrophy cascade in large-scale point-vortex simulations of decaying two-dimensional quantum turbulence. Devising a method to generate quantum vortex configurations with kinetic energy narrowly localized near a single length scale, the dynamics are found to be well characterized by a superfluid Reynolds number Re_{s} that depends only on the number of vortices and the initial kinetic energy scale. Under free evolution the vortices exhibit features of a classical enstrophy cascade, including a k^{-3} power-law kinetic energy spectrum, and constant enstrophy flux associated with inertial transport to small scales. Clear signatures of the cascade emerge for N≳500 vortices. Simulating up to very large Reynolds numbers (N=32 768 vortices), additional features of the classical theory are observed the Kraichnan-Batchelor constant is found to converge to C^{'}≈1.6, and the width of the k^{-3} range scales as Re_{s}^{1/2}.