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Generation of magnetic fields by convection

Published online by Cambridge University Press:  29 March 2006

F. H. Busse
F. H. Busse
Affiliation:
Department of Planetary and Space Science, University of California, Los Angeles
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Abstract

The nonlinear hydromagnetic dynamo problem is investigated for the case of convection in a layer of an electrically conducting fluid heated from below. It is shown that two-dimensional convection rolls in conjunction with a longitudinal mean flow are capable of amplifying a magnetic field in the form of a wave propagating in the longitudinal direction. The action of the Lorentz forces causes a reduction of the amplitude of convection with the consequence that the energy of the magnetic field cannot grow beyond an equilibrium value which is determined as a function of the parameters of the problem. The analysis is based on an expansion in powers of the longitudinal wavenumber β of the magnetic field and applies in the case of large values of the magnetic Prandtl number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 3 , 20 February 1973 , pp. 529 - 544
Copyright
© 1973 Cambridge University Press

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References

Bullard, E. C. & Gellacan, H. 1954 Phil. Trans. Roy. SOC. A 247, 213.
Busse, F. H. 1967 J. Math. Phys. 46, 140.
Busse, F. H. 1971 J. Geophys. 37, 153.
Childress, S. & Soward, A. M. 1972 Phys. Rev. Lett. 29, 837.
Elsasser, W. M. 1946 Phys. Rev. 69, 106.
Gage, K. S. & Reid, W. H. 1968 J. Pluid Mech. 33, 21–32.
Goldstein, R. J. & Graham, D. J. 1969 Phys. Fluids, 12, 1133.
Moffatt, H. K. 1970 J. Pluid Mech. 44, 705.
Moffatt, H. K. 1972 Lecture Notes in Physics, vol. 12, p. 266. Springer.
Parher, E. N. 1955 Astrophys. J. 122, 293.
Roberts, G. O. 1972 Phil. Trans. Roy. Soc. A 271, 411.
Roberts, P. H. 1971 In Mathematical Problems in Geophysical Sciences, Lectures in Applied Mathematics, vol. 14 (ed. W. H. Reid). Providence: American Mathematical Society.
Schluter, A., Lortz, D. & Busse, F. H. 1965 J. Fluid Mech. 28, 223.
Steenbeck, M., Krause, F. & Radler, K. H. 1966 2. Naturf. 21a, 369.