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Chaotic Behavior in Shell Models and Shell Maps

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Abstract

We study the chaotic behavior of the GOY shell model by measuring the variation of the maximal Lyapunov exponent with the parameter ε which determines the nature of the second invariant (the generalized “helicity” invariant). After a Hopf bifurcation, we observe a critical point at ε c ∼0.38704 above which the maximal Lyapunov exponent grows nearly linearly. For high values of ε the evolution becomes regular again, which can be explained by a simple analytic argument. A model with few shells shows two transitions. To simplify the model substantially we introduce a shell map which exhibits similar properties as the GOY model.

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Author notes

  1. Julien Kockelkoren

    Present address: Institute of Theoretical Physics;, University of Nijmegen, 6525 ED, Nijmegen, The Netherlands

Authors and Affiliations

  1. Niels Bohr Institute and Center for Chaos and Turbulence Studies, DK-2100, Copenhagen Ø, Denmark;

    Julien Kockelkoren, Fridolin Okkels & Mogens H. Jensen

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  1. Julien Kockelkoren
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  2. Fridolin Okkels
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  3. Mogens H. Jensen
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Kockelkoren, J., Okkels, F. & Jensen, M.H. Chaotic Behavior in Shell Models and Shell Maps. Journal of Statistical Physics 93, 833–842 (1998). https://doi.org/10.1023/B:JOSS.0000033165.51531.8c

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  • DOI: https://doi.org/10.1023/B:JOSS.0000033165.51531.8c

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