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The amplification of a weak applied magnetic field by turbulence in fluids of moderate conductivity

Published online by Cambridge University Press:  28 March 2006

Keith Moffatt
Keith Moffatt
Affiliation:
Trinity College, Cambridge
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Abstract

The effect of turbulence on an applied magnetic field is considered in the case when the magnetic Reynolds number Rm is large compared with unity but small compared with the ordinary Reynolds number R of the turbulence. When the applied field is sufficiently weak, it is argued that its effect on the velocity field is negligible. The equation for the field is then linear and its spectrum may be obtained throughout the equlibrium range of wave-numbers. It appears that the spectrum increases as $k^{\frac {1}{3}}$ up to a wave-number kc marking the threshold of conduction effects, and falls off as $k^{-\frac {11}{3}}$ beyond kc. The net effect of the turbulence is expressed in terms of an eddy conductivity equal to $R_m^{- \frac {5}{2}}$ times the electrical conductivity of the fluid. The effect of magnetic forces when these are not negligible is also tentatively considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 11 , Issue 4 , December 1961 , pp. 625 - 635
Copyright
© 1961 Cambridge University Press

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References

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