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Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices
| Title: | Transition of global dynamics of a polygonal vortex ring on a sphere with pole vortices |
| Authors: | SAKAJO, Takashi Browse this author →KAKEN DB |
| Keywords: | Vortex points | | Flows on sphere | | Transition of periodic orbits |
| Issue Date: | Sep-2004 |
| Publisher: | Elsevier |
| Journal Title: | Physica D: Nonlinear Phenomena |
| Volume: | 196 |
| Issue: | 3-4 |
| Start Page: | 243 |
| End Page: | 264 |
| Publisher DOI: | 10.1016/j.physd.2004.05.009 |
| Abstract: | 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. |
| Relation: | http://www.sciencedirect.com/science/journal/01672789 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/8558 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂上 貴之
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