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- W1972806956 abstract "The present study addresses the classical problem of the dynamics and stability of a cluster of N-point vortices of equal strength arranged in a polygonal configuration (‘N-vortex polygons’). In unbounded domains, such N-vortex polygons are unconditionally stable for . Confinement in a circular domain tightens the stability conditions to and a maximum polygon size relative to the domain radius. This work expands on existing studies on stability and integrability by a first giving an exploratory spectral analysis of the dynamics of N vortex polygons in circular domains. Key to this is that the spectral signature of the time evolution of vortex positions reflects their qualitative behaviour. Expressing vortex motion by a generic evolution operator (the so-called Koopman operator) provides a rigorous framework for such spectral analyses. This paves the way to further differentiation and classification of point-vortex behaviour beyond stability and integrability. The concept of Koopman-based spectral analysis is demonstrated for N-vortex polygons. This reveals that conditional stability can be seen as a local form of integrability and confirms an important generic link between spectrum and dynamics: discrete spectra imply regular (quasi-periodic) motion; continuous (sub-)spectra imply chaotic motion. Moreover, this exposes rich nonlinear dynamics as intermittency between regular and chaotic motion and quasi-coherent structures formed by chaotic vortices." @default.
- W1972806956 created "2016-06-24" @default.
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- W1972806956 date "2014-05-28" @default.
- W1972806956 modified "2023-09-25" @default.
- W1972806956 title "Spectral analysis of point-vortex dynamics: first application to vortex polygons in a circular domain" @default.
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- W1972806956 doi "https://doi.org/10.1088/0169-5983/46/3/031402" @default.
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