Low-dimensional dynamo modelling and symmetry-breaking bifurcations
- Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers ($Rm ll 1$). To obtain dynamo action under more general conditions, secondary mode
Author details: | Reik Volker DonnerORCiDGND, Norbert SeehaferORCiD, Miguel Angel Fernandez Sanjuan, Fred Feudel |
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URL: | http://www.sciencedirect.com/science/journal/01672789 |
DOI: | https://doi.org/10.1016/j.physd.2006.08.022 |
ISSN: | 0167-2789 |
Title of parent work (English): | Physica. D, Nonlinear phenomena |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Date of first publication: | 2006/11/15 |
Publication year: | 2006 |
Release date: | 2017/03/24 |
Volume: | 223 |
Issue: | 2 |
First page: | 151 |
Last Page: | 162 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |