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Magnetohydrodynamic equations under anisotropic conditions

Published online by Cambridge University Press:  01 January 1997

R. KINNEY and
J. C. McWILLIAMS
R. KINNEY
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307, USA and Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, California 90024, USA
J. C. McWILLIAMS
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307, USA and Institute of Geophysics and Planetary Physics, University of California at Los Angeles, Los Angeles, California 90024, USA
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Abstract

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Scaling analysis is used to derive approximations of magnetohydrodynamics with self-consistent leading-order dynamics under general conditions of anisotropy. Both incompressible and weakly compressible limits are considered. The horizontal magnetic and velocity fields obey dynamics given by a reduced closed set of equations, but the vertical components have different decoupled dynamics in the different regimes. Conservation laws are also discussed. It is shown that the reduced equations are not self-consistent unless either the ratio of vertical to horizontal length scales is large or the fluid is gravitationally stratified and the ratio of length scales is small. New equations are derived for a rotating stratified plasma, which are an extension of the quasigeostrophic equations of neutral fluids.

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 57 , Issue 1 , January 1997, pp. 73 - 82
Copyright
1997 Cambridge University Press