Equilibria and stability of four point vortices on a sphere
Abstract
This paper discusses the problem of finding the equilibrium positions of four point vortices, of generally unequal circulations, on the surface of asphere. A random search method is developed which utilises a modification of the linearised equations to converge on distinct equilibria. Many equilibria (47 and possibly more) may exist for prescribed circulations and angular impulse. A linear stability analysis indicates that they are generally unstable,though stable equilibria do exist. Overall, there is a surprising diversity of equilibria, including those which rotate about an axis opposite to the angular impulse vector.
Citation
Dritschel , D G 2020 , ' Equilibria and stability of four point vortices on a sphere ' , Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences , vol. 476 , no. 2241 , 20200344 . https://doi.org/10.1098/rspa.2020.0344
Publication
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Status
Peer reviewed
ISSN
1364-5021Type
Journal article
Description
Funding: UK Engineering and Physical Sciences Research Council (grant EP/H001794/1).Collections
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