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Mechanisms of extensive spatiotemporal chaos in Rayleigh–Bénard convection

Nature volume 404, pages 733–736 (2000)Cite this article

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.

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Figure 1: Spiral defect chaos in Rayleigh–Bénard convection.
Figure 2: Lyapunov spectral density and its integral.
Figure 3: Magnitudes of the temperature–field components of the Lyapunov vector corresponding to the largest Lyapunov exponent, scaled by the first finite-time exponents.

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Acknowledgements

We acknowledge helpful discussions with E. Bodenschatz and R. Mainieri. This work was funded by the US Department of Energy, and significant computational resources were provided on the Nirvana machines of the Advanced Computing Laboratory at Los Alamos National Laboratory. The development of a related version of the Boussinesq equation solver benefited from the support of a US National Science Foundation grant from the Division of Materials Research.

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Author notes

  1. Ilarion V. Melnikov

    Present address: Department of Physics, Duke University, Durham, North Carolina, 27708, USA

Authors and Affiliations

  1. Theoretical Division,, Center for Nonlinear Studies,

    David A. Egolf, Ilarion V. Melnikov & Robert E. Ecke

  2. Condensed Matter and Thermal Physics, Los Alamos National Laboratory, Los Alamos, 87545, New Mexico, USA

    David A. Egolf & Robert E. Ecke

  3. Theoretical Physics II, Physikalisches Institut, University of Bayreuth, Universitätstrasse 30 , Bayreuth, D-95440, Germany

    Werner Pesch

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  1. David A. Egolf
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  3. Werner Pesch
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  4. Robert E. Ecke
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Correspondence to David A. Egolf.

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Egolf, D., Melnikov, I., Pesch, W. et al. Mechanisms of extensive spatiotemporal chaos in Rayleigh–Bénard convection. Nature 404, 733–736 (2000). https://doi.org/10.1038/35008013

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