Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

TL;DR

This paper investigates the evolution and decay of quantum vortex tangles in superfluids using the Gross-Pitaevskii equation, revealing decay laws, topological changes, and turbulence spectra.

Contribution

It introduces a robust vortex tracking algorithm and provides detailed analysis of vortex topology, decay, and turbulence development in superfluid simulations.

Findings

Vinen's decay law is confirmed with quantitative agreement.

Linked vortex rings can form during decay.

Kelvin wave spectrum shows evidence of weak-wave turbulence cascade.

Abstract

The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently-developed accurate and robust tracking algorithm, all quantised vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in Helium II is observed. The topology of the tangle is then studied showing that linked rings may appear during the decay. The tracking also allows for determining the statistics of small-scales quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.