ABSTRACT
In this chapter we introduce basic concepts concerning the dynamics of rotating fluids. The effect of rapid rotation on a flow can significantly alter its nature. These effects are particularly important for planetary applications. In Section 3.1 we introduce steady boundary layers and shear flows, which occur in rotating fluids, and show how these layers can have a strong influence on the mainstream flow outside them. In Section 3.2, we consider the combined influence of rotation and magnetic field on these layers. Time dependent effects, particularly waves propagating in rotating and electrically conducting fluids, are considered in Section 3.3. Finally, in Section 3.4, we address the particular case of thermal Rossby wave, which is the preferred mode of convection in a rapidly rotating sphere such as planetary interiors. We shall devote Section 3.4.2 to a description of the simpler rotating cylindrical annulus model, since it offers the simplest access to the spherical problem. The basic equations for the spherical problem are introduced in Section 3.4.3 and the onset of columnar convection in spherical shells is discussed in Section 3.4.4. In Section 3.4.5 the onset of inertial mode convection is described which prevails at very low Prandtl numbers. In Section 3.4.6 the properties of finite amplitude convection are outlined for moderately low Prandtl numbers Pr, while convection at higher values of Pr is considered in Section 3.4.7. In Section 3.4.8 equatorially attached convection is considered which evolves from inertial mode convection. The problem of penetrative convection is addressed in Section 3.4.9 where also some aspects of convection in the presence of thermal as well as chemical buoyancy are discussed. The chapter concludes with some remarks on applications among which the dynamo action of convection is of special importance.
