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Integrable four-vortex motion on sphere with zero moment of vorticity
| Title: | Integrable four-vortex motion on sphere with zero moment of vorticity |
| Authors: | Sakajo, Takashi Browse this author →KAKEN DB |
| Issue Date: | Jan-2007 |
| Publisher: | American Institute of Physics |
| Journal Title: | Physics of Fluids |
| Volume: | 19 |
| Issue: | 1 |
| Start Page: | 017109 |
| Publisher DOI: | 10.1063/1.2430716 |
| Abstract: | We consider the motion of N vortex points on sphere, called the N-vortex problem, which is a Hamiltonian dynamical system. The three-vortex problem is integrable and its motion has already been resolved. On the other hand, when the moment of vorticity vector, which consists of weighed sums of the vortex positions, is zero at the initial moment, the four-vortex problem is integrable, but it has not been investigated yet. The present paper gives a description of the integrable four-vortex problem with the reduction method to a three-vortex problem used by Aref and Stremler. Moreover, we examine whether the vortex points collide self-similarly in finite time. The four-vortex collapse is proved to be impossible. We consider if it is possible for not all but part of the vortex points to collapse self-similarly. Moreover, we discuss the topological structure of periodic orbits obtained in the present problem. ©2007 American Institute of Physics |
| Rights: | Copyright © 2007 American Institute of Physics |
| Type: | article |
| URI: | http://hdl.handle.net/2115/19108 |
| 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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