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dc.contributor.authorDritschel, David Gerard
dc.contributor.authorBoatto, S
dc.date.accessioned2015-03-24T12:01:03Z
dc.date.available2015-03-24T12:01:03Z
dc.date.issued2015-04
dc.identifier165219999
dc.identifierd03d3b44-f252-4aa2-bb14-c8efd7dd55e3
dc.identifier000351236200014
dc.identifier84926336770
dc.identifier.citationDritschel , D G & Boatto , S 2015 , ' The motion of point vortices on closed surfaces ' , Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences , vol. 471 , no. 2176 , 20140890 , pp. 1-25 . https://doi.org/10.1098/rspa.2014.0890en
dc.identifier.issn1364-5021
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697794
dc.identifier.urihttps://hdl.handle.net/10023/6297
dc.description.abstractWe develop a mathematical framework for the dynamics of a set of point vortices on a class of differentiable surfaces conformal to the unit sphere. When the sum of the vortex circulations is non-zero, a compensating uniform vorticity field is required to satisfy the Gauss condition (that the integral of the Laplace–Beltrami operator must vanish). On variable Gaussian curvature surfaces, this results in self-induced vortex motion, a feature entirely absent on the plane, the sphere or the hyperboloid. We derive explicit equations of motion for vortices on surfaces of revolution and compute their solutions for a variety of surfaces. We also apply these equations to study the linear stability of a ring of vortices on any surface of revolution. On an ellipsoid of revolution, as few as two vortices can be unstable on oblate surfaces or sufficiently prolate ones. This extends known results for the plane, where seven vortices are marginally unstable (Thomson 1883 A treatise on the motion of vortex rings, pp. 94–108; Dritschel 1985 J. Fluid Mech. 157 , 95–134 (doi:10.1017/S0022112088003088)), and the sphere, where four vortices may be unstable if sufficiently close to the equator (Polvani & Dritschel 1993 J. Fluid Mech. 255 , 35–64 (doi:10.1017/S0022112093002381)).
dc.format.extent25
dc.format.extent1451341
dc.language.isoeng
dc.relation.ispartofProceedings of the Royal Society A - Mathematical, Physical & Engineering Sciencesen
dc.subjectVortex dynamicsen
dc.subjectPoint vorticesen
dc.subjectClosed surfacesen
dc.subjectQA Mathematicsen
dc.subjectNDASen
dc.subjectBDCen
dc.subjectR2Cen
dc.subject.lccQAen
dc.titleThe motion of point vortices on closed surfacesen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Marine Alliance for Science & Technology Scotlanden
dc.contributor.institutionUniversity of St Andrews. Scottish Oceans Instituteen
dc.identifier.doi10.1098/rspa.2014.0890
dc.description.statusPeer revieweden
dc.identifier.grantnumberEP/H001794/1en


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