Classical and quantum vortex leapfrogging in two-dimensional channels

The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement which characterises these systems motivates the study of leapf...

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Bibliographic Details
Published in:Journal of fluid mechanics 2021-02, Vol.912, Article A9
Main Authors: Galantucci, Luca, Sciacca, Michele, Parker, Nick G., Baggaley, Andrew W., Barenghi, Carlo F.
Format: Article
Language:English
Subjects:
Bose-Einstein condensates
Channels
Compressibility
Compressibility effects
Computational fluid dynamics
Experiments
Fluid mechanics
Fluids
Gases
JFM Papers
Orbits
Phase transitions
Two dimensional models
Vortex rings
Vortices
Citations: Items that this one cites
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Summary:The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement which characterises these systems motivates the study of leapfrogging of vortices within narrow channels. Using the two-dimensional point vortex model, we show that in the constrained geometry of a two-dimensional channel the dynamics is richer than in an unbounded domain: alongside the known regimes of standard leapfrogging and the absence of it, we identify new regimes of image-driven leapfrogging and periodic orbits. Moreover, by solving the Gross–Pitaevskii equation for a Bose–Einstein condensate, we show that all four regimes exist for quantum vortices too. Finally, we discuss the differences between classical and quantum vortex leapfrogging which appear when the quantum healing length becomes significant compared to the vortex separation or the channel size, and when, due to high velocity, compressibility effects in the condensate becomes significant.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.1094