Spectral energy transport in two-dimensional quantum vortex dynamics

TL;DR

This paper investigates how energy moves across different scales in two-dimensional quantum turbulence by modeling vortex interactions, revealing regimes of inverse energy cascade and dissipation effects.

Contribution

It introduces a dissipative point-vortex model with vortex-sound interactions to analyze spectral energy transport in quantum vortex dynamics.

Findings

Weak dissipation leads to inverse energy cascade similar to classical turbulence.

Strong dissipation suppresses spectral energy transport.

The model applies to large systems with varying dissipation levels.

Abstract

We explore the possible regimes of decaying two-dimensional quantum turbulence, and elucidate the nature of spectral energy transport by introducing a dissipative point-vortex model with phenomenological vortex-sound interactions. The model is valid for a large system with weak dissipation, and also for systems with strong dissipation, and allows us to extract a meaningful and unambiguous spectral energy flux associated with quantum vortex motion. For weak dissipation and large system size we find a regime of hydrodynamic vortex turbulence in which energy is transported to large spatial scales, resembling the phenomenology of the transient inverse cascade observed in decaying turbulence in classical incompressible fluids. For strong dissipation the vortex dynamics are dominated by dipole recombination and exhibit no appreciable spectral transport of energy.