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Chaotic advection and the emergence of tori in the Küppers–Lortz state

Chaos 18, 033104 (2008); doi:10.1063/1.2953575

Published 15 July 2008

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Paul Mullowney, Keith Julien, and James D. Meiss
Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA
Motivated by the roll-switching behavior observed in rotating Rayleigh–Bénard convection, we define a Küppers–Lortz (K–L) state as a volume-preserving flow with periodic roll switching. For an individual roll state, the Lagrangian particle trajectories are periodic. In a system with roll-switching, the particles can exhibit three-dimensional, chaotic motion. We study a simple phenomenological map that models the Lagrangian dynamics in a K–L state. When the roll axes differ by 120° in the plane of rotation, we show that the phase space is dominated by invariant tori if the ratio of switching time to roll turnover time is small. When this parameter approaches zero these tori limit onto the classical hexagonal convection patterns, and, as it gets large, the dynamics becomes fully chaotic and well mixed. For intermediate values, there are interlinked toroidal and poloidal structures separated by chaotic regions. We also compute the exit time distributions and show that the unbounded chaotic orbits are normally diffusive. Although the map presumes instantaneous switching between roll states, we show that the qualitative features of the flow persist when the model has smooth, overlapping time-dependence for the roll amplitudes (the Busse–Heikes model). ©2008 American Institute of Physics
History: Received 10 January 2008; accepted 6 June 2008; published 15 July 2008
Permalink: http://link.aip.org/link/?CHAOEH/18/033104/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.52.+j
    Chaos in fluid dynamics
  • 47.32.Ef
    Rotating and swirling flows
  • YEAR: 2008

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ISSN:
1054-1500 (print)   1089-7682 (online)
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