Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T21:14:32.366Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

REFERENCES

Alfvén, H. 1942 a Ark. Mat. Astron. Fys. 29B, 1.Google Scholar
Alfvén, H. 1942 b Nature, 150, 405.CrossRefGoogle Scholar
Alfvén, H. 1950 Cosmical Electrodynamics. Oxford University Press.Google Scholar
Namikawa, T. & Hamabata, H. 1987 Phys. Lett. 126A, 195.CrossRefGoogle Scholar
Namikawa, T. & Hamabata, H. 1988 Phys. Fluids, 31, 887.CrossRefGoogle Scholar
Parker, E. N. 1984 Geophys. Astrophys. Fluid Dyn. 29, 1.CrossRefGoogle Scholar
Walén, C. 1944 a Ark. Mat. Astron. Fys. 30 A, 1.Google Scholar
Walén, C. 1944 b Ark. Mat. Astron. Fys. 31 B, 1.Google Scholar