Interest in magnetoconvection arose initially from astrophysics, following the discovery of strong magnetic fields in sunspots, and the realization that their relative coolness (and hence their darkness) was a consequence of magnetic interference with convection. As theoretical studies progressed from linear to nonlinear investigations, and ultimately to massive numerical experiments, it became clear not only that magnetoconvection poses in itself a fascinating challenge to applied mathematicians but also that it serves as a prototype of double-diffusive behaviour in fluid dynamics, oceanography and laboratory experiments.

In this opening chapter we first summarize the development of our subject and then provide a brief survey of the chapters that follow in the book. Although we shall focus our attention on idealized configurations that are mathematically tractable, we also discuss more complex behaviour in the real world.

Background and motivation

The original motivation for our subject came from astrophysics. Stars like the Sun, with deep outer convection zones, are magnetically active. Their magnetic fields are maintained by hydromagnetic dynamo action, resulting from interactions between convection, rotation and magnetic fields in their interiors – just as the geomagnetic field is maintained by a dynamo in the Earth's liquid core. The most prominent magnetic features on the Sun are sunspots, like that shown in Figure 1.1. Although such a spot covers less than of the solar disc, there are other more active stars with huge spots that spread over significant fractions of their surfaces (Thomas and Weiss 2008).