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Travelling and Standing Waves in Magnetoconvection
P. C. Matthews and A. M. Rucklidge
Proceedings: Mathematical and Physical Sciences
Vol. 441, No. 1913 (Jun. 8, 1993), pp. 649-658
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52327
Page Count: 10
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The problem of Boussinesq magnetoconvection with periodic boundary conditions is studied using standard perturbation techniques. It is found that either travelling waves or standing waves can be stable at the onset of oscillatory convection, depending on the parameters of the problem. When travelling waves occur, a steady shearing flow is present that is quadratic in the amplitude of the convective flow. The weakly nonlinear predictions are confirmed by comparison with numerical solutions of the full partial differential equations at Rayleigh numbers 10% above critical. Modulated waves (through which stability is transferred between travelling and standing waves) are found near the boundary between the regions in parameter space where travelling waves and standing waves are preferred.
Proceedings: Mathematical and Physical Sciences © 1993 Royal Society