Viscous, Resistive Magnetohydrodynamic Stability Computed by Spectral Techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydro-dynamic quasiequilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 1983-09, Vol.80 (18), p.5798-5802
Main Authors: Dahlburg, R. B., Zang, T. A., Montgomery, D., Hussaini, M. Y.
Format: Article
Language:English
Subjects:
Aeronautical engineering
Eigenfunctions
Eigenvalues
Hydrodynamics
Magnetic fields
Magnetohydrodynamics
Physical Sciences: Physics
Physics
Plasma Physics
Shear flow
Spectral methods
Viscosity
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Summary:Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydro-dynamic quasiequilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.80.18.5798