Henry, D. and Juel, A. and Ben Hadid, H. and Kaddeche, S.
(2008)
*Directional effect of a magnetic field on oscillatory
low-Prandtl-number convection.*
Physics of Fluids, 20 (034104).
ISSN 1070-6631

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## Abstract

The directional effect of a magnetic field on the onset of oscillatory convection is studied numerically in a confined three-dimensional cavity of relative dimensions 4:2:1 length:width:height filled with mercury and subject to a horizontal temperature gradient. The magnetic field suppresses the oscillations most effectively when it is applied in the vertical direction, and is the least efficient when applied in the longitudinal direction parallel to the temperature gradient. In all cases, however, exponential growths of the critical Grashof number, Grc Gr, ratio of buoyancy to viscous dissipation forces with the Hartmann number Ha, ratio of magnetic to viscous dissipation forces are obtained. Insight into the damping mechanism is gained from the fluctuating kinetic energy budget associated with the time-periodic disturbances at threshold. The kinetic energy produced by the vertical shear of the longitudinal basic flow dominates the oscillatory transition, and when a magnetic field is applied, it increases in order to balance the stabilizing magnetic energy. Moreover, subtle changes in the spatial distribution of this shear energy are at the origin of the exponential growth of Grc. The destabilizing effect of the velocity fluctuations strongly decreases when Ha is increased due to the decay of the velocity fluctuations in the bulk accompanied by the appearance of steep gradients localized in the Hartmann layers, so that an increase of the shear of the basic flow at Grc is required in order to sustain the instability. This yields an increase in Grc, which is reinforced by the fact that the shear of the basic flow naturally decreases at constant Gr with the increase of Ha, particularly when the magnetic field is applied in the vertical direction. For transverse and longitudinal fields, the decay of the velocity fluctuations is combined with an increase of the shear energy term due to a sustained growth in stabilizing magnetic energy with Ha

Item Type: | Article |
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Subjects: | PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 06 Nov 2008 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1172 |

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