Transition from quasiperiodicity to chaos for three coaxial vortex rings
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.
Volume / Issue
Electronic International Standard Serial Number (EISSN)
International Standard Serial Number (ISSN)