Three-dimensional non-linear magnetoconvection in a strongly stratified compressible layer exhibits different patterns as the strength of the imposed magnetic field is reduced. There is a transition from a magnetically dominated regime, with small-scale convection in slender hexagonal cells, to a convectively dominated regime, with clusters of broad rising plumes that confine the magnetic flux to narrow lanes where fields are locally intense. Both patterns can coexist for intermediate field strengths, giving rise to flux separation: clumps of vigorously convecting plumes, from which magnetic flux has been excluded, are segregated from regions with strong fields and small-scale convection. A systematic numerical investigation of these different states shows that flux separation can occur over a significant parameter range and that there is also hysteresis. The results are related to the fine structure of magnetic fields in sunspots and in the quiet Sun.

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ArticleThe interaction between magnetic fields and convection is interesting both because of its astrophysical importance and because the nonlinear Lorentz force leads to an especially rich variety of behaviour. We present several sets of computational results for magnetoconvection in a square box, with periodic lateral boundary conditions, that show transitions from steady convection with an ordered planform through a regime with intermittent bursts to complicated spatiotemporal behaviour. The constraints imposed by the square lattice are relaxed as the aspect ratio is increased. In wide boxes we find a new regime, in which regions with strong fields are separated from regions with vigorous convection. We show also how considerations of symmetry and associated group theory can be used to explain the nature of these transitions and the sequence in which the relevant bifurcations occur.