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Motion of a vortex sheet on a sphere with pole vortices

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タイトル: Motion of a vortex sheet on a sphere with pole vortices
著者: Sakajo, Takashi 著作を一覧する
発行日: 2004年 2月 4日
出版者: American Institute of Physics
誌名: Physics of Fluids
巻: 16
号: 3
開始ページ: 717
終了ページ: 727
出版社 DOI: 10.1063/1.1644148
抄録: We consider the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices fixed on north and south poles. Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties. First, the vortex sheet is linearly unstable due to Kelvin–Helmholtz instability. Second, the curvature of the vortex sheet diverges in finite time. Last, the vortex sheet evolves into a rolling-up doubly branched spiral, when the equation of motion is regularized by the vortex method. The purpose of this paper is to investigate how the curvature of the sphere and the presence of the pole vortices affect these three properties mathematically and numerically. We show that some low spectra of disturbance become linearly stable due to the pole vortices and thus the singularity formation tends to be delayed. On the other hand, however, the vortex sheet, which is regularized by the vortex method, acquires complex structure of many rolling-up spirals.
Rights: Copyright © 2004 American Institute of Physics
Relation (URI): http://www.aip.org/
資料タイプ: article
URI: http://hdl.handle.net/2115/5433
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 坂上 貴之

 

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