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Mechanisms of extensive spatiotemporal chaos in Rayleigh–Bénard convection

Author

Listed:
  • David A. Egolf

    (Center for Nonlinear Studies
    Los Alamos National Laboratory)

  • Ilarion V. Melnikov

    (Center for Nonlinear Studies
    Duke University)

  • Werner Pesch

    (University of Bayreuth)

  • Robert E. Ecke

    (Center for Nonlinear Studies
    Los Alamos National Laboratory)

Abstract

Spatially extended dynamical systems exhibit complex behaviour in both space and time—spatiotemporal chaos1,2. Analysis of dynamical quantities (such as fractal dimensions and Lyapunov exponents3) has provided insights into low-dimensional systems; but it has proven more difficult to understand spatiotemporal chaos in high-dimensional systems, despite abundant data describing its statistical properties1,4,5. Initial attempts have been made to extend the dynamical approach to higher-dimensional systems, demonstrating numerically that the spatiotemporal chaos in several simple models is extensive6,7,8 (the number of dynamical degrees of freedom scales with the system volume). Here we report a computational investigation of a phenomenon found in nature, ‘spiral defect’ chaos5,9 in Rayleigh–Bénard convection, in which we find that the spatiotemporal chaos in this state is extensive and characterized by about a hundred dynamical degrees of freedom. By studying the detailed space–time evolution of the dynamical degrees of freedom, we find that the mechanism for the generation of chaotic disorder is spatially and temporally localized to events associated with the creation and annihilation of defects.

Suggested Citation

  • David A. Egolf & Ilarion V. Melnikov & Werner Pesch & Robert E. Ecke, 2000. "Mechanisms of extensive spatiotemporal chaos in Rayleigh–Bénard convection," Nature, Nature, vol. 404(6779), pages 733-736, April.
    • Handle: RePEc:nat:nature:v:404:y:2000:i:6779:d:10.1038_35008013
    DOI: 10.1038/35008013
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    Cited by:

    1. Gancio, Juan & Rubido, Nicolás, 2024. "Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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