Prog. Theor. Phys. Suppl. **138** (2000) 674-683.
## Numerical studies of pattern formation in three-dimensional magnetoconvection

N.O. Weiss(1),
A.M.Rucklidge(1),
M.R.E. Proctor(1),
P.C. Matthews(1,2) and
D.P. Brownjohn(1)

(1) Department of Applied Mathematics and Theoretical Physics,

University of Cambridge, Cambridge, CB3 9EW, UK

(2) School of Mathematical Sciences, University of Nottingham,

University Park, Nottingham, NG7 2RD, UK

**Abstract.**
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.

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