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Dynamo and Dynamics, a Mathematical Challenge pp 355–362Cite as

Convection-Driven Dynamos, Amplitude Equations and Large-Scale Fields

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Part of the book series: NATO Science Series ((NAII,volume 26))

Abstract

This paper describes the weakly nonlinear behaviour of a dynamo driven by rotating convection in the form of two-dimensional rolls. The linear problem is separable and the onset of dynamo action occurs at small wavenumbers m with a growth rate proportional to m2. In the weakly nonlinear regime a band of wavenumbers is unstable, and an amplitude equation is obtained describing the nonlinear interactions between modes of different wavenumber. The behaviour of the amplitude equation shows an inverse cascade, with the mode of fastest growth rate giving way to solutions with longer and longer wavelength, over long timescales.

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References

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    P.C. Matthews

Authors
  1. P.C. Matthews
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Editor information

Editors and Affiliations

  1. I.N.L.N.(CNRS,UMR 6618), Valbonne, France

    P. Chossat

  2. Department of Mathematics, Arizona State University, Tempe, Arizona, USA

    D. Ambruster

  3. University of Bucarest, Romania

    I. Oprea (Faculty of Mathematics) (Faculty of Mathematics)

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© 2001 Springer Science+Business Media Dordrecht

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Matthews, P. (2001). Convection-Driven Dynamos, Amplitude Equations and Large-Scale Fields. In: Chossat, P., Ambruster, D., Oprea, I. (eds) Dynamo and Dynamics, a Mathematical Challenge. NATO Science Series, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0788-7_42

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  • DOI: https://doi.org/10.1007/978-94-010-0788-7_42

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-7070-3

  • Online ISBN: 978-94-010-0788-7

  • eBook Packages: Springer Book Archive

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