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On the Rayleigh-Taylor problem in magneto-hydrodynamics with finite resistivity

Published online by Cambridge University Press:  28 March 2006

J. D. Jukes
J. D. Jukes
Affiliation:
Culham Laboratory, Atomic Energy Research Establishment, Harwell
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Abstract

In order to elucidate the importance of the infinite conductivity assumption in MHD a simple problem has been studied. This is a Rayleigh-Taylor problem of two superposed fluids under gravity partially stabilized by a uniform, horizontal magnetic field. It is found that the inclusion of a small, but finite resistivity introduces new and unexpected solutions. For instance, moderately long, stabilized’ waves are now found to grow aperiodically and unexpectedly rapidly at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$). Other modes are found to be periodic and damped at a rate ∝ ($\rm {resistivity}^{\frac{1}{3}$).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 16 , Issue 2 , June 1963 , pp. 177 - 186
Copyright
© 1963 Cambridge University Press

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References

Bickerton, R. J., Aitken, K., Hardcastle, R., Jukes, J. D., Reynolds, P. & Spalding, I. 1961 Pinch Stability–Theory and Experiment. Paper 10/68. Proc. Int. Conf. Plasma Physics, Salzburg.Google Scholar
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Tayler, R. J. 1960 Stability of twisted magnetic fields in a fluid of finite electrical conductivity. Rev. Mod. Phys. 32, 907.Google Scholar