Transition from quasiperiodicity to chaos for three coaxial vortex rings


Journal Article

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.

Duke Authors

Cited Authors

  • Blackmore, D; Knio, O

Published Date

  • 2000-12-01

Published In

Volume / Issue

  • 80 / 4 SUPPL. 1

Electronic International Standard Serial Number (EISSN)

  • 1521-4001

International Standard Serial Number (ISSN)

  • 0044-2267

Citation Source

  • Scopus