Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T06:38:48.544Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian approach to the mean-field electrodynamics for turbulent fluids with arbitrary conductivities

Published online by Cambridge University Press:  26 April 2006

L. L. Kichatinov
L. L. Kichatinov
Affiliation:
Siberian Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, PO Box 4, Irkutsk 33, USSR
Get access Rights & Permissions [Opens in a new window]

Abstract

A modification is made to the traditional Lagrangian approach to the derivation of the mean EMF of turbulent fluids which allows for finite conductivities. Consideration is confined to the case of homogeneous, isotropic but generally mirrornon-invariant and compressible turbulence. The eddy magnetic diffusivity and the coefficient α of the alpha-effect are expressed in terms of statistical moments of displacements of adjacent particles which undergo convective transport and microscopic diffusion in a turbulent flow. These expressions, being valid for arbitrary conductivities, reproduce known results in the cases of both very large and very small magnetic Reynolds numbers. Difficulties and advantages of the use of the results obtained for evaluations of the mean EMF are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 115 - 126
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1950 The application of the similarity theory of turbulence to atmospheric diffusion. Q. J. R. Met. Soc. 76, 133–146.Google Scholar
Drummond, I. T. & Horgan, R. R. 1986 Numerical simulation of the α-effect and turbulent magnetic diffusion with molecular diffusivity. J. Fluid Mech. 163, 425–438.Google Scholar
Kliatskin, V. I. 1980 Stochastic Equations and Waves in Randomly Inhomogeneous Media. Moscow: Nauka (in Russian).
Kraichnan, R. H. 1976 Diffusion of passive-scalar and magnetic fields by helical turbulence. J. Fluid Mech. 77, 753–768.Google Scholar
Krause, F. & Rädler, K.-H. 1981 Mean-Field Magnetohydrodynamics and Dynamo Theory. Pergamon.
Moffatt, H. K. 1974 The mean electromotive force generated by turbulence in the limit of perfect conductivity. J. Fluid Mech. 65, 1–10.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.
Molchanov, I. T., Ruzmaikin, A. A. & Sokoloff, D. D. 1984 A dynamo theorem. Geophys. Astrophys. Fluid Dyn. 30, 241–259.Google Scholar
Rüdiger, G. 1975 The influence of the uniform magnetic field of arbitrary strength on turbulence. Astron. Nachr. 295, 275–283.Google Scholar
Vainshtein, S. I. & Kichatinov, L. L. 1986 The dynamics of magnetic fields in highly conducting turbulent medium and the generalized Kolmogorov-Fokker-Planck equations. J. Fluid Mech. 168, 73–87.Google Scholar
Zeldovich, Ya. B., Ruzmaikin, A. A. & Sokoloff, D. D. 1983 Magnetic Fields in Astrophysics. Gordon and Breach.