Numerical generation of a vortex ring cascade in quantum turbulence

TL;DR

This paper simulates quantum vortex dynamics, revealing vortex reconnections, wave emissions, and the formation of vortex rings, with spectral features similar to classical turbulence, all without energy dissipation.

Contribution

It presents a detailed numerical simulation of vortex ring cascade in quantum turbulence, highlighting reconnection processes and spectral behaviors.

Findings

Vortex reconnections produce vortex rings and waves.

Spectral analysis shows -3 and -5/3 power-law regimes.

Energy is conserved despite complex vortex interactions.

Abstract

A symmetric anti-parallel quantum pair of vortices is simulated using the three-dimensional Gross-Pitaevski equations. The initial development before cores interact directly demonstrates the traditional vortex dynamics of stretching, curvature and torsion in a manner consistent with a filament calculation and simulations of the classical, ideal Euler equations. Once the cores begin to interact, reconnection develops in the vacuum that forms between the pair. Out of the reconnection region, vortex waves are emitted with properties similar to waves in the local induction approximation. These waves propagate down the initial vortex and deepen. When they deepen far enough, secondary reconnections occur and vortex rings form. Near this time, spectra have a $k^{-3}$ regime. As the vortex rings fully separate, the high wavenumber spectra grow until, at the final time simulated, spectra in two directions develop nearly -5/3 subranges. This occurs without the dissipation of energy. Preliminary analysis of the flow of energies in spectral scale and physical space is discussed.