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dc.contributor.authorReinaud, Jean Noel
dc.identifier.citationReinaud , J N 2021 , ' Three-dimensional quasi-geostrophic staggered vortex arrays ' , Regular and Chaotic Dynamics , vol. 26 , no. 5 , pp. 505–525 .
dc.identifier.otherPURE: 275334546
dc.identifier.otherPURE UUID: 644fc9d5-8241-4bc9-a9fe-4d2ecbb31c9b
dc.identifier.otherORCID: /0000-0001-5449-6628/work/101581540
dc.identifier.otherScopus: 85117323249
dc.identifier.otherWOS: 000705305600004
dc.description.abstractWe determine and characterise relative equilibria for arrays of point vortices in a three-dimensional quasi-geostrophic flow. The vortices are equally spaced along two horizontal rings whose centre lies on the same vertical axis. An additional vortex may be placed along this vertical axis. Depending on the parameters defining the array, the vortices on the two rings are of equal or opposite sign. We address the linear stability of the point vortex arrays. We find both stable equilibria and unstable equilibria, depending on the geometry of the array. For unstable arrays, the instability may lead to the quasi-regular or to the chaotic motion of the point vortices. The linear stability of the vortex arrays depends on the number of vortices in the array, on the radius ratio between the two rings, on the vertical offset between the rings and on the vertical offset between the rings and the central vortex, when the latter is present. In this case the linear stability also depends on the strength of the central vortex. The nonlinear evolution of a selection of unstable cases is presented exhibiting examples of quasi-regular motion and of chaotic motion.
dc.relation.ispartofRegular and Chaotic Dynamicsen
dc.rightsCopyright © 2021 Pleiades Publishing Ltd. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectPoint vortex dynamicsen
dc.subjectVortex arraysen
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.titleThree-dimensional quasi-geostrophic staggered vortex arraysen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews.Scottish Oceans Instituteen
dc.description.statusPeer revieweden

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