Magnetoconvection

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Abstract
Cowling investigated the effect of an imposed magnetic field on convection in order to explain the origin of sunspots. After summarizing the classical linear theory of Boussinesq magnetoconvection, this review proceeds to more recent nonlinear results. Weakly nonlinear theory is used to establish the relevant bifurcation structure, which involves steady, oscillatory and chaotic solutions. Behaviour found in numerical experiments can then be related to these analytical results. Thereafter, attention is focused on the astrophysically relevant problem of fully compressible magnetoconvection. Steady two-dimensional nonlinear solutions show two important effects: stratification introduces an asymmetry between rising and falling fluid, while compressibility leads to evacuated magnetic flux sheets. Time-dependent behaviour includes transitions between standing waves and travelling waves, as well as changes in horizontal scale, leading to the development of more complicated spatial structures. Work on three-dimensional models, which is now in progress, will lead to a better understanding of the structure of a sunspot.

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