On convection in a horizontal magnetic field with periodic boundary conditions

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Abstract
The effect of an imposed horizontal magnetic field on two-dimensional convection in a plane layer heated from below is studied in the presence of periodic boundary conditions in the horizontal. An amplitude equation describing the transitions between travelling and standing waves and steady convection near a particular multiple bifurcation is derived. When the first instability is oscillatory, two solution branches bifurcate simultaneously from the conduction solution, corresponding to travelling and standing waves. The branch of travelling waves is stable throughout and terminates on the steady state branch in a steady state bifurcation as the Rayleigh number is increased. Beyond this point stable overturning convection is found. Standing waves are unstable. The results are indicative of the larger amplitude behavior of the system.

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