Numerical studies of pattern formation in three-dimensional magnetoconvection

A systematic computational survey of magnetoconvection in a square box with periodic lateral boundary conditions is described. This investigation demonstrates the way in which numerical experiments can be combined with techniques of nonlinear dynamics and applied to specific fluid mechanical problems. Considerations of symmetry and associated group theory can be exploited in order to explain the sequence in which the relevant bifurcations must occur. The interaction between magnetic fields and convection was chosen because of its astrophysical importance and because the nonlinear Lorentz force leads to an especially rich and interesting range of behaviour. As the solutions become progressively more nonlinear, there is a transition from an ordered pattern with a simple planform to disordered spatiotemporal behaviour via an intermediate state with intermittent bursts. The solutions are sensitive not only to variations in the key physical parameters (such as diffusivity ratios and field strengths) but also to changes in the aspect ratio of the computational box. In wide boxes a new physical effect - flux separation - appears as a consequence of long wavelength modulation.