Transition from quasiperiodicity to chaos for three coaxial vortex rings

D. Blackmore*, Omar Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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.

Original languageEnglish (US)
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume80
Issue number4 SUPPL. 1
StatePublished - Dec 1 2000

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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