Nonlinear oscillatory convection in the presence of a vertical magnetic field

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Abstract
Convection rolls in a fluid layer heated from below become unstable to disturbances in the form of waves travelling along the axis of the rolls when the Rayleigh number exceeds a critical value RII. This transition to a time-dependent form of convection also occurs in the presence of a vertical magnetic field when the fluid is electrically conducting. In this paper the finite-amplitude properties of these waves are investigated for the values 0.1 and 0.025 of the Prandtl number. It is shown that the onset of oscillations reduces the heat transport by convection and that a mean flow in the direction of propagation is associated with the waves. Although the magnetic field has an inhibiting influence on steady convection, the inhibiting influence on the onset of oscillations is even stronger such that in some cases a higher heat transport is obtained in the presence of a magnetic field than in its absence. For similar reasons subcritical finite-amplitude onset of travelling-wave convection occurs for sufficiently large magnetic field strengths. Finally the stability of travelling-wave convection is investigated and the Rayleigh number RIII for the transition to asymmetric wave convection is determined.

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