Ph. Roberts et Ca. Jones, The onset of magnetoconvection at large Prandtl number in a rotating layeri. Finite magnetic diffusion, GEOPH ASTRO, 92(3-4), 2000, pp. 289-325
This paper develops further a convection model that has been studied severa
l times previously as a very crude idealization of planetary core dynamics.
A plane layer of electrically-conducting fluid rotates about the vertical
in the presence of a magnetic field. Such a field can be created spontaneou
sly, as in the Childress-Soward dynamo, but here it is uniform, horizontal
and externally-applied. The Prandtl number of the fluid is large, but the E
kman, Elsasser and Rayleigh numbers are of order unity, as is the ratio of
thermal to magnetic diffusivity. Attention is focused on the onset of conve
ction as the temperature difference applied across the layer is increased,
and on the preferred mode, i.e., the planform and time-dependence of small
amplitude convection. The case of main interest is the layer confined betwe
en electrically-insulating no-slip walls, but the analysis is guided by a p
arallel study based on illustrative boundary conditions that are mathematic
ally simpler.