Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices
Description
We study the motion of a polygonal ring consists of identical vortex points that are equally spaced at a line of latitude on a sphere with vortex points fixed at the both poles. First, we calculate explicitly all the eigenvalues and the eigenvectors corresponding to them for the linearized problem, from which we consider the stability of the polygonal vortex ring in the presence of the pole vortices. Next, when the number of the vortex points is even in particular, the equations of the vortex points are reduced to those for a pair of two vortex points by assuming a special symmetry. Studying the reduced system mathematically and numerically, we describe an universal transition of global periodic motion of the perturbed polygonal ring. Moreover, we also discuss the stability of the periodic motion.
Journal
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- Hokkaido University Preprint Series in Mathematics
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Hokkaido University Preprint Series in Mathematics 642 1-24, 2004
Department of Mathematics, Hokkaido University
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Details 詳細情報について
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- CRID
- 1390009224795283200
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- NII Article ID
- 120006459355
- 120000958318
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- HANDLE
- 2115/69449
- 2115/8558
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- ISSN
- 01672789
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- Text Lang
- en
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- Data Source
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- JaLC
- IRDB
- Crossref
- CiNii Articles
- OpenAIRE
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- Abstract License Flag
- Allowed