Generation of a symmetric magnetic field by thermal convection in a plane rotating layer

V. Zheligovsky^1,2

¹ International Institute of Earthquake Prediction Theory and Mathematical Geophysics 84/32 Profsoyuznaya str., 117997 Moscow, Russia
² Observatoire de la C\^ote d'Azur, CNRS U.M.R. 6529, BP 4229, 06304 Nice Cedex 4, France

Abstract
We investigate numerically magnetic field generation by thermal convection with square periodicity cells in a rotating horizontal layer of an electrically conducting fluid with stress-free electrically perfectly conducting boundaries for Rayleigh numbers in the interval 5100 ≤ \Rn ≤ 5800. Dynamos of three kinds, apparently not encountered before, are presented. (i) Steady and time-periodic regimes, where the flow and magnetic field are symmetric abouta vertical axis. In regimes with this symmetry, the global α-effect is insignificant, and the complex structure of the system of amplitude equations controlling weakly non-linear stability of the system to perturbations with large spatial and temporal scales suggests that the perturbations are likely to exhibit uncommon complex patterns of behaviour, to be studied in the future work. (ii) Periodic in time regimes, where the magnetic field is always concentrated in the interior of the convective layer in contrast to the behaviour first observed by St Pierre (1993) and often perceived as generic for electrically infinitely conducting boundaries. (iii) A dynamo exhibiting chaotic behaviour of heteroclinic nature, where a sample trajectory enjoys excursions between a periodic magnetohydrodynamic regime and rolls. The rolls are amagnetic, but generate magnetic fields kinematically. As a result, magnetic energy reduces almost to zero, while the rolls are approached. Tables 1, Figs 10, Refs 31.