The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: the dependence on the prandlt numbers |
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Authors: | O M Podvigina |
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Institution: | 1.International Institute of Earthquake Prediction Theory and Mathematical Geophysics,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | The onset of Boussinesq convection in a horizontal layer of an electrically conducting incompressible fluid is considered.
The layer rotating about a vertical axis is heated from below; a vertical magnetic field is imposed. Rigid electrically insulating
boundaries are assumed. The loss of stability of the trivial steady state, which occurs as the Rayleigh numbers increase,
can be accompanied by the development of a monotonic or an oscillatory instability, depending on the parameter values of the
problem at hand (the Taylor number, the Chandrasekhar number, the kinematic and the magnetic Prandtl numbers). When the instability
is monotonic, the emerging convective rolls themselves are also unstable if the Taylor number is sufficiently large (the so-called
Küppers-Lortz instability takes place). In the present work it is studied how the critical value of the Rayleigh number, the
type of the trivial steady state instability, and the critical value of the Taylor number for the Küppers-Lortz instability
depend on the kinematic and the magnetic Prandtl numbers. We consider the values of the Prandtl number not exceeding 1, which
is typical for the outer core of the Earth. |
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Keywords: | |
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