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Erschienen in:
2001 | OriginalPaper | Buchkapitel
Convection-Driven Dynamos, Amplitude Equations and Large-Scale Fields
verfasst von : P.C. Matthews
Erschienen in: Dynamo and Dynamics, a Mathematical Challenge
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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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.