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Exact nonlinear helical oscillations in magnetohydrodynamics

Published online by Cambridge University Press:  19 April 2006

H. Murata
H. Murata
Affiliation:
Department of Physics, Hyogo College of Medicine, Nishinomiya, 663, Japan
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Abstract

An exact solution of the nonlinear magnetohydrodynamic equations for a viscous incompressible fluid of finite conductivity is obtained, which represents a circularly polarized structure with time dependent amplitude in a uniform magnetic field. There is a phase difference of ½π between the spatial structures of the velocity and the magnetic field of the disturbance. In the inviscid perfectly conducting limit, this solution represents a standing helical oscillation which is a circularly polarized standing Alfvén wave of arbitrary amplitude, and the sum of the kinetic and magnetic energy densities of the oscillation are constant in the absence of any input of energy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 1 , 11 September 1980 , pp. 31 - 34
Copyright
© 1980 Cambridge University Press

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References

Alfvén, H. 1950 Cosmical Electrodynamics. Oxford University Press.
Moffatt, H. K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.