Files in this item
The motion of point vortices on closed surfaces
Item metadata
dc.contributor.author | Dritschel, David Gerard | |
dc.contributor.author | Boatto, S | |
dc.date.accessioned | 2015-03-24T12:01:03Z | |
dc.date.available | 2015-03-24T12:01:03Z | |
dc.date.issued | 2015-04 | |
dc.identifier | 165219999 | |
dc.identifier | d03d3b44-f252-4aa2-bb14-c8efd7dd55e3 | |
dc.identifier | 000351236200014 | |
dc.identifier | 84926336770 | |
dc.identifier.citation | Dritschel , 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.2014.0890 | en |
dc.identifier.issn | 1364-5021 | |
dc.identifier.other | ORCID: /0000-0001-6489-3395/work/64697794 | |
dc.identifier.uri | https://hdl.handle.net/10023/6297 | |
dc.description.abstract | We 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.extent | 25 | |
dc.format.extent | 1451341 | |
dc.language.iso | eng | |
dc.relation.ispartof | Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences | en |
dc.subject | Vortex dynamics | en |
dc.subject | Point vortices | en |
dc.subject | Closed surfaces | en |
dc.subject | QA Mathematics | en |
dc.subject | NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.title | The motion of point vortices on closed surfaces | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.contributor.institution | University of St Andrews. Marine Alliance for Science & Technology Scotland | en |
dc.contributor.institution | University of St Andrews. Scottish Oceans Institute | en |
dc.identifier.doi | 10.1098/rspa.2014.0890 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/H001794/1 | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.