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Convection in a rotating cylindrical annulus in the presence of a magnetic field. (English) Zbl 0902.76037

Summary: The effect of radial and azimuthal components of a magnetic field on the convection columns in the fluid filled gap between two cylinders rotating rigidly about their common vertical axis is investigated numerically. The inner cylinder is cooled, the outer one heated such that the buoyancy force driving the convection is provided by the centrifugal force. But the analysis applies also to the planetary case where the effective components of gravity and of the temperature gradient are reversed. Because of conical end surfaces of the annular gap, the convection columns drift relative to the rotating frame of reference. The magnetic field exerts a stabilizing influence on the onset of convection and on the onset of secondary instabilities, leading to stationary mean flow convection or to time-dependent vacillating convection. Of particular interest are the cases of merging stability regions when double minima of a neutral curve exist.

MSC:

76E15 Absolute and convective instability and stability in hydrodynamic stability
76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
80A20 Heat and mass transfer, heat flow (MSC2010)
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