Kinematic dynamo properties of a quasigeostrophic flow in a rotating sphere.

The problem of convection in rapidly rotating spherical shells is central to the study of planetary core dynamics. In the limit of large rotation this problem is mainly two-dimensional and can be simplified by the use of a quasigeostrophic approximation, without loss of the essential features in the flow. This allows the simulation to reach regimes of small Ekman and large Reynolds number, which are appropriate for planetary cores. A magnetohydrodynamic study of this parameter regime is crucial for the understanding of planetary dynamos, especially weak-field dynamos which are expected to operate on a quasigeostrophic flow state. We present a first study of the kinematic dynamo properties of quasigeostrophic flows. They contains vertical helicity and dissymmetry between cyclones and anticyclones, two factors favouring a strong alpha effect to convert toroidal magnetic field into poloidal field. Previous studies of slightly ageostrophic convection at more moderate parameter values have shown that the second dynamo effect, which converts back poloidal field into toroidal field is mainly another alpha. We show that in the quasigeostrophic limit, this second effect cannot be an alpha and has therefore to be an omega effect. Quasigeostrophic flows contain strong zonal winds created by potential vorticity mixing, and can naturally produce this omega effect. The efficiency of both dynamo effects is studied versus flow parameters. We then anticipate where in the parameter space dynamo action should be easier to create and present preliminary results of kinematic dynamo calculations, done in the case of a thermally forced flow and in the case of the flow produced by a differentially rotating inner core.