AI Article Synopsis
- The study explores the transition between different equilibrium states of hollow vortex cores related to Kelvin's theory, using nonlinear dynamics for analysis.
- It identifies the transition from polygonal patterns (N=2 to N=4) occurs in two main stages: quasiperiodicity followed by frequency locking.
- The findings suggest that this transition can be represented using a one-dimensional circle map, and the frequency ratios involved follow a Farey sum pattern, resembling a staircase as it varies with a control parameter.
Article 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.
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| http://dx.doi.org/10.1103/PhysRevE.80.066305 | DOI Listing |
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