Equilibria and stability of four point vortices on a sphere
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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.
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
Proceedings of the Royal Society A - Mathematical, Physical & Engineering Sciences
Copyright © 2020 the Author(s). Published by the Royal Society. 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 https://doi.org/10.1098/rspa.2020.0344.
DescriptionFunding: UK Engineering and Physical Sciences Research Council (grant EP/H001794/1).
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