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Periodic motions of vortices on surfaces with symmetry

Published online by Cambridge University Press:  25 June 2002

ANIK SOULIÈRE  and
TADASHI TOKIEDA
ANIK SOULIÈRE
Affiliation:
Département de Mathématiques, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal H3C 3J7, Canadasouliere@dms.umontreal.ca, tokieda@dms.umontreal.ca
TADASHI TOKIEDA
Affiliation:
Département de Mathématiques, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal H3C 3J7, Canadasouliere@dms.umontreal.ca, tokieda@dms.umontreal.ca
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Abstract

The theory of point vortices in a two-dimensional ideal fluid has a long history, but on surfaces other than the plane no method of finding periodic motions (except relative equilibria) of N vortices is known. We present one such method and find infinite families of periodic motions on surfaces possessing certain symmetries, including spheres, ellipsoids of revolution and cylinders. Our families exhibit bifurcations. N can be made arbitrarily large. Numerical plots of bifurcations are given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 460 , 10 June 2002 , pp. 83 - 92
Copyright
© 2002 Cambridge University Press

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