Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices

SAKAJO, Takashi

Hokkaido University Preprint Series in Mathematics, 2004, 642, 1-24

Permalink : https://doi.org/10.14943/83795

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アクセス権	open access
DOI	https://doi.org/10.14943/83795
URI	https://hdl.handle.net/2115/69449
タイトル	Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices
著者	著者名 SAKAJO, Takashi
言語	英語
発行日	2004
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	642
ページ	1-24
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record