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-characterised by a superfluid Reynolds number, $\mathrm{R}{\mathrm{e}}_{\mathrm{s}}$, 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 steady enstrophy flux associated with inertial transport to small scales. Clear signatures of the cascade emerge for $N\gtrsim 500$ 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 $C^{\prime }\approx 1.6$, and the width of the $k^{-3}$ range scales as ${\mathrm{R}{\mathrm{e}}_{\mathrm{s}}}^{1/2}$. The results support a universal phenomenology underpinning classical and quantum fluid turbulence.

8 pages, 3 Figures

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