Transition between Kelvin's equilibria

Hamid Ait Abderrahamne, Kamran Siddiqui, Georgios H. Vatistas

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageBritish English
Article number066305
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - 10 Dec 2009


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