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Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a non-uniform magnetic field

Published online by Cambridge University Press:  13 March 2009

Hiromitsu Hamabata  and
Tomikazu Namikawa
Hiromitsu Hamabata
Affiliation:
Department of Physics, Faculty of Science, Osaka City University, Osaka 558, Japan
Tomikazu Namikawa
Affiliation:
Department of Physics, Faculty of Science, Osaka City University, Osaka 558, Japan
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Abstract

Exact wave solutions of the nonlinear magnetohydrodynamic equations for a highly conducting incompressible fluid within an axisymmetric container are obtained. It is shown that there are four types of exact wave solutions with large amplitude in a non-uniform magnetic field. These solutions are very useful because they can be expressed in terms of arbitrary scalar functions and they are applicable to astrophysical and laboratory plasmas as well as the earth's core. The solutions also include as special cases the nonlinear Alfvén waves in a uniform magnetic field and in a circular magnetic field found respectively by Walén (1944) and by Namikawa & Hamabata (1987, 1988).

Type
Research Article
Information
Journal of Plasma Physics , Volume 42 , Issue 2 , October 1989 , pp. 247 - 256
Copyright
Copyright © Cambridge University Press 1989

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References

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