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Fixed equilibria of point vortices in symmetric multiply connected domains

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Title: Fixed equilibria of point vortices in symmetric multiply connected domains
Authors: Sakajo, Takashi Browse this author →KAKEN DB
Keywords: Point vortices
Multiply connected domain
Conformal mapping
Fixed equilibria
Issue Date: 1-Mar-2012
Publisher: Elsevier B.V.
Journal Title: Physica D: Nonlinear Phenomena
Volume: 241
Issue: 5
Start Page: 583
End Page: 599
Publisher DOI: 10.1016/j.physd.2011.11.021
Abstract: The paper provides with symmetric fixed configurations of point vortices in multiply connected domains in the unit circle with many circular obstacles. When the circular domain is invariant with respect to the rotation around the origin by the degree of 2π/M, a regular M-polygonal ring configuration of identical point vortices becomes a fixed equilibrium. On the other hand, when we assume a special symmetry, called the folding symmetry, on the circular domain, we find a fixed equilibrium in which M point vortices with the positive unit strength and M point vortices with the negative unit strength are arranged alternately at the vertices of a 2M-polygon. We also investigate the stability of these fixed equilibria and their bifurcation for a special circular domain with the rotational symmetry as well as the folding symmetry. Furthermore, we discuss fixed equilibria in non-circular multiply connected domains with the same symmetries. We give sufficient conditions for the conformal mappings, by which fixed equilibria in the circular domains are mapped to those in the general multiply connected domains. Some examples of such conformal mappings are also provided.
Type: article (author version)
URI: http://hdl.handle.net/2115/48587
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)

Submitter: 坂上 貴之

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