Transition from quasiperiodicity to chaos for three coaxial vortex rings

Document Type

Article

Publication Date

1-1-2000

Abstract

The dynamics of three coaxial vortex rings of strengths Γ1, Γ2 and Γ3 in an ideal fluid is investigated. It is proved that if Γj, Γj + Γk and Γ1 + Γ2 + Γ3 are not zero for all j, k = 1, 2, 3, then KAM and Poincaré-Birkhoff theory can be used to prove that if the distances among the rings are sufficiently small compared to the mean radius of the rings, there are many initial configurations of the rings that produce guasiperiodic or periodic motions. Moreover, it is shown that the motion become chaotic as the inter-ring distances are increased relative to the mean radius.

Identifier

23044521286 (Scopus)

Publication Title

ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik

External Full Text Location

https://doi.org/10.1002/zamm.20000801344

e-ISSN

15214001

ISSN

00442267

First Page

S173

Last Page

S176

Issue

4 SUPPL. 1

Volume

80

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