# Enstrophy Cascade in Decaying Two-Dimensional Quantum Turbulence

## TL;DR

This paper provides evidence of an enstrophy cascade in decaying two-dimensional quantum turbulence, demonstrating classical turbulence features in superfluid vortex simulations and revealing universal behaviors across quantum and classical fluids.

## Contribution

The study introduces a method to generate quantum vortex configurations with energy localized at a single scale and characterizes the cascade using a superfluid Reynolds number, extending classical turbulence concepts to quantum systems.

## Key findings

- Observation of a $k^{-3}$ energy spectrum consistent with enstrophy cascade
- Convergence of Kraichnan-Batchelor constant to approximately 1.6 at high vortex numbers
- Scaling of the cascade's inertial range width with $ ext{Re}_s^{1/2}$

## 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, $\mathrm{Re_s}$, 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 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 $C' \approx 1.6$, and the width of the $k^{-3}$ range scales as $\mathrm{Re_s}^{1/2}$. The results support a universal phenomenology underpinning classical and quantum fluid turbulence.