Vortex dynamics on a cylinder

James Montaldi; Anik Soulière; Tadashi Tokieda

doi:10.1137/S1111111102415569

Vortex dynamics on a cylinder

James Montaldi, Anik Soulière, Tadashi Tokieda

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Abstract

Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a nonexistence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign, and several results on relative periodic orbits are established, including as corollaries classical results on vortex streets and leapfrogging.

Original language	English
Pages (from-to)	417-430
Number of pages	13
Journal	SIAM Journal on Applied Dynamical Systems
Volume	2
Issue number	3
DOIs	https://doi.org/10.1137/S1111111102415569
Publication status	Published - 17 Sept 2003

Keywords

Conservation laws
Geometric mechanics
Hamiltonian systems with symmetry
Point vortices

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Cite this

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title = "Vortex dynamics on a cylinder",

abstract = "Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a nonexistence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign, and several results on relative periodic orbits are established, including as corollaries classical results on vortex streets and leapfrogging.",

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AU - Tokieda, Tadashi

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AB - Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a nonexistence theorem for relative equilibria is proved, equilibria are classified when all vorticities have the same sign, and several results on relative periodic orbits are established, including as corollaries classical results on vortex streets and leapfrogging.

KW - Conservation laws

KW - Geometric mechanics

KW - Hamiltonian systems with symmetry

KW - Point vortices

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DO - 10.1137/S1111111102415569

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JO - SIAM Journal on Applied Dynamical Systems

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Vortex dynamics on a cylinder

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Keywords

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