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Onset of wall-attached convection in a rotating fluid layer in the presence of a vertical magnetic field

Published online by Cambridge University Press:  26 March 2008

J. J. SÁNCHEZ-ÁLVAREZ ,
E. CRESPO DEL ARCO  and
F. H. BUSSE
J. J. SÁNCHEZ-ÁLVAREZ
Affiliation:
ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040 Madrid, Spain
E. CRESPO DEL ARCO
Affiliation:
UNED, Departamento de Física Fundamental, Apdo. 60.141, 28080 Madrid, Spain
F. H. BUSSE
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
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Abstract

A horizontal fluid layer heated from below and rotating about a vertical axis in the presence of a vertical magnetic field is considered. From earlier work it is known that the onset of convection in a rotating layer usually occurs in the form of travelling waves attached to the vertical sidewalls of the layer. It is found that this behaviour persists when a vertical magnetic field is applied. When the Elsasser number Λ is kept constant and the sidewall is thermally insulating the critical Rayleigh number Rc increases in proportion to the rotation rate described by the square root of the Taylor number, τ. This asymptotic relationship is found for an electrically highly conducting sidewall as well as for an electrically insulating one. At fixed rotation rate for Q≫τ, Rc grows in proportion to Q when the sidewall is electrically highly conducting, and in proportion to Q3/4 when the sidewall is electrically insulating. Here Q is the Chandrasekhar number which is a measure of the magnetic energy density, and a thermally insulating sidewall has been assumed. Of particular interest is the possibility that the magnetic field counteracts the stabilizing influence of rotation on the onset of sidewall convection in the case of thermally insulating sidewalls. When the sidewall is thermally highly conducting, Rc for the sidewall mode grows in proportion to τ4/3. This asymptotic behaviour is found for both cases of electrical boundary conditions, but it no longer precedes the onset of bulk convection for Λ ≳ 1.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 427 - 443
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Bodenschatz, E., Pesch, W. & Ahlers, G. 2000 Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 32, 709–778.Google Scholar
Buell, J. C. & Catton, I. 1983 Effect of rotation on the stability of a bounded cylindrical layer of fluid heated from below. Phys. Fluids 26, 892–896.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and hydromagnetic stability. Dover. (Referred to herein as CH61.)Google Scholar
Goldstein, H. F., Knobloch, E., Mercader, I. & Net, M. 1993 Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers. J. Fluid Mech. 248, 583–604.CrossRefGoogle Scholar
Herrmann, J. & Busse, F. H. 1993 Asymptotic theory of wall-attached convection in a rotating fluid layer. J. Fluid Mech. 255, 183–194. (Referred to herein as HB93.)CrossRefGoogle Scholar
Kuo, E. Y. & Cross, M. C. 1993 Traveling-wave wall states in rotating Rayleigh-Bénard convection. Phys. Rev. E 47, R2245–R2248.Google Scholar
Marqués, F., Mercader, I., Batiste, O. & Lopez, J. M. 2007 Centrifugal effects in rotating convection: axisymmetric states and three-dimensional instabilities. J. Fluid Mech. 580, 303–318.Google Scholar
Sánchez-Álvarez, J. J., Serre, E., Crespo del Arco, E. & Busse, F. H. 2005 Square patterns in rotating Rayleigh-Bénard convection. Phys. Rev. E 72, 036307.Google Scholar
Zhong, F., Ecke, R. E. & Steinberg, V. 1991 Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection. Phys. Rev. Lett. 67, 2473–2477.Google Scholar