TY  - JOUR
A1  - Donner, Reik Volker
A1  - Seehafer, Norbert
A1  - Sanjuan, Miguel Angel Fernandez
A1  - Feudel, Fred
T1  - Low-dimensional dynamo modelling and symmetry-breaking bifurcations
T2  - Physica. D, Nonlinear phenomena
N2  - 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
Y1  - 2006
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/12313
UR  - http://www.sciencedirect.com/science/journal/01672789
SN  - 0167-2789
VL  - 223
IS  - 2
SP  - 151
EP  - 162
PB  - Elsevier
CY  - Amsterdam
ER  -