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dc.contributor.authorSokolovskiy, Mikhail
dc.contributor.authorKoshel, Konstantin
dc.contributor.authorDritschel, David Gerard
dc.contributor.authorReinaud, Jean Noel
dc.identifier.citationSokolovskiy , M , Koshel , K , Dritschel , D G & Reinaud , J N 2020 , ' N -symmetric interaction of N hetons. Part I. Analysis of the case N = 2 ' , Physics of Fluids , vol. 32 , no. 9 , 096601 .
dc.identifier.otherORCID: /0000-0001-5449-6628/work/79917881
dc.identifier.otherORCID: /0000-0001-6489-3395/work/79917921
dc.descriptionFunding: This work was carried out as part of a joint project funded by the Russian Foundation for Basic Research (grant 20-55-10001) and UK Royal Society (grant IEC\R2\192170). MAS was also supported by the program 0147-2019-0001 (State Registration No.AAAA-A18-118022090056-0) and by the Ministry of Science and Education of the Russian Federation (Project No. N14.W03.31.0006), KVK was supp orted by RFBR project No.20-05-00083.en
dc.description.abstractWe examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-layer quasi-geostrophic model. We consider the special case of N-fold symmetry in which the original system of 4N ordinary differential equations reduces to just two equations for the so-called “equivalent” heton. We perform a qualitative analysis to classify the possible types of vortex motions for the case N = 2. We identify the regions of the parameter space corresponding to unbounded motion and to different types of bounded, or localized, motions. We focus on the properties of localized, in particular periodic, motion. We identify classes of absolute and relative “choreographies” first introduced by Simó [“New families of solutions to the N-body problems,” in Proceedings of the European 3rd Congress of Mathematics, Progress in Mathematics Vol. 201, edited by C. Casacuberta, R. M. Miró-Roig, J. Verdera, and S. Xambó-Descamps (Birkhäuser, Basel, Barcelona, 2000), pp. 101–115]. We also study the forms of vortex trajectories occurring for unbounded motion, which are of practical interest due to the associated transport of heat and mass over large distances
dc.relation.ispartofPhysics of Fluidsen
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.titleN-symmetric interaction of N hetons. Part I. Analysis of the case N = 2en
dc.typeJournal articleen
dc.contributor.sponsorThe Royal Societyen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Scottish Oceans Instituteen
dc.contributor.institutionUniversity of St Andrews. Marine Alliance for Science & Technology Scotlanden
dc.description.statusPeer revieweden

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