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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… (More)
We experimentally corroborate the core analytical deductions of Thomson's 124-year-old theorem, vis-à-vis the stability of a ring of N vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular N-gons are stable for N<or=6 and unstable for N>or=8. The N<or=6 equilibria are exceptionally resilient.… (More)
This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study, where the radial flow perturbation was neglected. This assumption led to the classical planar Korteweg-de… (More)
We report on the symmetrization phenomenon of a hollow-core vortex in shallow liquid conditions. This phenomenon accompanies the transition of m wave into (m+1) wave and involves a beat-wave resonance that mediates energy transfer between the background flow and the vortex core. It is shown that this beat wave has a frequency m/(m-1)times the frequency of… (More)
This Brief Report is devoted to the study of the solitary surface wave rotating in the azimuthal direction, arising during water drainage from a cylindrical reservoir, when shallow flow conditions are reached. The linear dependence between the wave speed and its amplitude is shown to be similar to that expected from the classical Korteweg-de Vries equation.