In this chapter we introduce the effects of rotation into the study of magnetoconvection. While these effects can safely be neglected when discussing the dynamics of the solar photosphere, since typical timescales are much less than a solar day, the large-scale motions occurring deeper in the solar convection zone and in the Earth's liquid core are strongly affected by rotation. Indeed, rotation would appear to be a crucial ingredient in the dynamo mechanisms that are responsible for the geomagnetic field and the solar magnetic cycle. A full discussion of dynamo theory is outside the scope of this book (though see, for example, Dormy and Soward 2007) but we shall discuss dynamo models in which convection plays a prominent role. As such, we shall depart later in this chapter from consideration of convective flows in simple planar models and in addition discuss what happens in spherical geometries.

A necessary preliminary to understanding the complex interaction of magnetic fields with rotating convection is a discussion of the rotating, nonmagnetic case. This is first done in a Cartesian geometry. Then the effect of a vertical magnetic field is introduced. We restrict ourselves to the problem of convection in a layer rotating about a vertical axis. Then we can discuss the effects of a vertical magnetic field (this makes comparison with previous chapters easier, but such a configuration is not one that can readily be recognized in nature).