Vortex pairs on surfaces

Journal Article · Wed May 06 00:00:00 EDT 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3146241· OSTI ID:21304927

Koiller, Jair ^[1]; Boatto, Stefanella ^[2]

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1. Centro de Matematica Aplicada, FGV/RJ, Praia de Botafogo 190 Rio de Janeiro, RJ, 22250-40 (Brazil)
2. Instituto de Matematica da UFRJ, C.P. 68530, Cidade Universitaria Rio de Janeiro, RJ 21945-970 (Brazil)

A pair of infinitesimally close opposite vortices moving on a curved surface moves along a geodesic, according to a conjecture by Kimura. We outline a proof. Numerical simulations are presented for a pair of opposite vortices at a close but nonzero distance on a surface of revolution, the catenoid. We conjecture that the vortex pair system on a triaxial ellipsoid is a KAM perturbation of Jacobi's geodesic problem. We outline some preliminary calculations required for this study. Finding the surfaces for which the vortex pair system is integrable is in order.

• OSTI ID: 21304927
• Journal Information: AIP Conference Proceedings, Vol. 1130, Issue 1; Conference: 17. international fall workshop on geometry and physics, Castro Urdiales (Spain), 3-6 Sep 2008; Other Information: DOI: 10.1063/1.3146241; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTERIZED SIMULATION
DISTANCE
FUNCTIONAL ANALYSIS
GEODESICS
INTEGRAL CALCULUS
INTEGRAL EQUATIONS
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
SURFACES
VORTICES