Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Perturbed three point vortex problems

D. Blackmorea,*, O. Kniob, L. Tingc
aNew Jersey Institute of Technology, Department of Mathematical Sciences, Newark, NJ 07102-1982, USA bThe Johns Hopkins University, Department of Mechanical Engineering, Baltimore, MD 21218, USA cNew York University, Courant Institute of Mathematical Sciences, New York, NY 10012-1185, USA
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ABSTRACT
Making use of the knowledge of the motions of three point vortices in a planar incompressible flow, which are integrable, we investigate the motions of three-point vortices in a half-plane as perturbations of the original integrable system. Numerical investigations are carried out to show whether the perturbations will remain small or will diverge, respectively, from those corresponding to stable or unstable critical points of the original ones.

Keywords:  Three point vortices; Integrable system; Perturbation; Stability
* Corresponding author. Tel.: +1 973 596 3495; Fax: +1 973 596 5591; E-mail: deblac@m.njit.edu