TY - JOUR
T1 - Transition between Kelvin's equilibria
AU - Ait Abderrahamne, Hamid
AU - Siddiqui, Kamran
AU - Vatistas, Georgios H.
PY - 2009/12/10
Y1 - 2009/12/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=73649136857&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.80.066305
DO - 10.1103/PhysRevE.80.066305
M3 - Article
AN - SCOPUS:73649136857
SN - 1539-3755
VL - 80
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 6
M1 - 066305
ER -