title: Transition between Kelvin's equilibria.
abstract: A transition between Kelvin's equilibrium states is investigated. Using nonlinear theory, we have shown that the transition of polygonal patterns of the hollow vortex core from mode N=2 through N=4 occurs in two steps: quasiperiodicity and frequency locking. We have also shown that this transition can be modeled by a one-dimensional circle map. We extrapolate the present result and hypothesize that the transition between Kelvin's equilibria follows the same route and the ratios of locking frequencies form a Farey sum and staircase function against the control parameter, where the staircase corresponds to the rational frequency ratio, (N-1)/N.
authors.affiliation: Department of Mechanical and Industrial Engineering, Concordia University Montreal, 1455 de Maisonneuve Boulevard West, Quebec, Canada.
authors.forename: Hamid Ait
authors.initials: HA
authors.lastname: Abderrahamne
authors.forename: Kamran
authors.initials: K
authors.lastname: Siddiqui
authors.forename: Georgios H
authors.initials: GH
authors.lastname: Vatistas