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Circular vortex arrays in generalised Euler's and quasi-geostrophic dynamics
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dc.contributor.author | Reinaud, Jean Noel | |
dc.date.accessioned | 2023-06-01T23:44:29Z | |
dc.date.available | 2023-06-01T23:44:29Z | |
dc.date.issued | 2022-06-02 | |
dc.identifier | 278413594 | |
dc.identifier | c45304c4-6301-4391-ada5-c9a7ec33fbda | |
dc.identifier | 85131203005 | |
dc.identifier | 000805325000006 | |
dc.identifier.citation | Reinaud , J N 2022 , ' Circular vortex arrays in generalised Euler's and quasi-geostrophic dynamics ' , Regular and Chaotic Dynamics , vol. 27 , no. 3 , pp. 352–368 . https://doi.org/10.1134/S1560354722030066 | en |
dc.identifier.issn | 1560-3547 | |
dc.identifier.other | ORCID: /0000-0001-5449-6628/work/114023189 | |
dc.identifier.uri | https://hdl.handle.net/10023/27733 | |
dc.description.abstract | We investigate the stability of circular point vortex arrays and their evolution when their dynamics is governed by the generalised two-dimensional Euler's equations and the three-dimensional Quasi-Geostrophic equations. These sets of equations offer a family of dynamical models depending continuously on a single parameter β which sets how fast the velocity induced by a vortex falls away from it. In this paper, we show that the differences between the stability properties of the classical two-dimensional point vortex arrays and the standard quasi-geostrophic vortex arrays can be understood as a bifurcation in the family of models. For a given β, the stability depends on the number N of vortices along the circular array and on the possible addition of a vortex at the centre of the array. On a practical point of view, the most important vortex arrays are the stable ones, as they are robust and long-lived. Unstable vortex arrays can however lead to interesting and convoluted evolutions, exhibiting quasi-periodic and chaotic motion. We briefly illustrate the evolution of a small selection of representative unstable vortex arrays. | |
dc.format.extent | 17 | |
dc.format.extent | 1177568 | |
dc.language.iso | eng | |
dc.relation.ispartof | Regular and Chaotic Dynamics | en |
dc.subject | Point vortices dynamics | en |
dc.subject | Generalised Euler's equations | en |
dc.subject | Quasi-geostophy | en |
dc.subject | QA Mathematics | en |
dc.subject | QC Physics | en |
dc.subject | T-NDAS | en |
dc.subject | MCC | en |
dc.subject.lcc | QA | en |
dc.subject.lcc | QC | en |
dc.title | Circular vortex arrays in generalised Euler's and quasi-geostrophic dynamics | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Scottish Oceans Institute | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | 10.1134/S1560354722030066 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2023-06-02 |
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