Solar and stellar convection zones

Abstract

There are several important astrophysical questions that might be answered by numerical modelling. These involve the kinematic effects of motion on magnetic fields, the dynamics of magnetoconvection, the stucture and scale of convection and the global dynamo problem. This review will focus on detailed modelling of nonlinear compressible convection in a strong vertical magnetic field. Techniques range from heuristic models, which may be relatively primitive, through idealized numerical experiments to large scale simulations and each approach has its proponents. Early studies of nonlinear convection relied on the Boussinesq or anelastic approximations but recently there have been systematic investigations of fully compressible two- and three-dimensional convection as well as ambitious simulations. Detailed studies of two-dimensional behaviour reveal complicated bifurcation structures, involving changes of scale and transitions from steady to oscillatory solutions and from standing waves to travelling waves. Such behaviour is sensitive to assumptions built into the numerical model. Models of large-scale behaviour throughout the convection zone of a star like the sun show that dynamo action can occur but are still far from being able to reproduce the observed patterns of differential rotation or magnetic activity.