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Hierarchical modeling of a forced Roberts dynamo. (English) Zbl 1141.37380

Summary: We investigate the dynamo effect in a flow configuration introduced by G. O. Roberts [Philos. Trans. roy. Soc. London, Ser. A 271, 411–454 (1972; Zbl 0235.76061)]. Based on a clear energetic hierarchy of Fourier components on the steady-state dynamo branch, an approximate model of interacting modes is constructed covering all essential features of the complete system but allowing simulations with a minimum amount of computation time. We use this model to study the excitation mechanism of the dynamo, the transition from stationary to time-dependent dynamo solutions and the characteristic properties of the latter ones.

MSC:

37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
93A30 Mathematical modelling of systems (MSC2010)
37G99 Local and nonlocal bifurcation theory for dynamical systems

Citations:

Zbl 0235.76061
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References:

[1] DOI: 10.1016/S0375-9601(97)00319-8 · Zbl 1053.37517 · doi:10.1016/S0375-9601(97)00319-8
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[6] DOI: 10.1098/rsta.1972.0015 · doi:10.1098/rsta.1972.0015
[7] DOI: 10.1103/PhysRevE.57.5533 · doi:10.1103/PhysRevE.57.5533
[8] DOI: 10.1063/1.1331315 · Zbl 1184.76529 · doi:10.1063/1.1331315
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