Toggle Main Menu Toggle Search

Open Access padlockePrints

Classical and quantum vortex leapfrogging in two-dimensional channels

Lookup NU author(s): Dr Luca Galantucci, Dr Michele Sciacca, Professor Nick ParkerORCiD, Dr Andrew BaggaleyORCiD, Professor Carlo Barenghi



This is the authors' accepted manuscript of an article that has been published in its final definitive form by Cambridge University Press, 2021.

For re-use rights please refer to the publisher's terms and conditions.


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.

Publication metadata

Author(s): Galantucci L, Sciacca M, Parker N, Baggaley A, Barenghi C

Publication type: Article

Publication status: Published

Journal: Journal of Fluid Mechanics

Year: 2021

Volume: 912

Print publication date: 10/04/2021

Online publication date: 05/02/2021

Acceptance date: 01/12/2020

Date deposited: 10/02/2021

ISSN (print): 0022-1120

ISSN (electronic): 1469-7645

Publisher: Cambridge University Press


DOI: 10.1017/jfm.2020.1094


Altmetrics provided by Altmetric