Transitions to asymmetry in magnetoconvection

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Abstract
In two-dimensional Boussinesq magnetoconvection with symmetrical boundary conditions upward and downward motion are equivalent. Hence there exist symmetric solutions with equivalent flux sheets on either side of each convection roll. Numerical experiments show that this symmetry can be broken for both steady and oscillatory solutions. The underlying bifurcation structure is established by studying a truncated seventeenth-order model system. Steady solutions of this relatively low-order system can be obtained explicitly and their stability can be investigated. Primary bifurcations from the trivial static solution lead to pure single-roll and two-roll solutions, both steady and oscillatory; secondary bifurcations give mixed-mode steady and oscillatory branches while tertiary bifurcations allow behaviour that is more complicated but less robust. Properly interpreted, this detailed study of a particular system provides a better understanding of the behaviour of nonlinear solutions of the full partial differential equations.

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