Journal of Fluid Mechanics (2002), 462:365-382 Cambridge University Press
Copyright © 2002 Cambridge University Press

Magnetorotational instability of dissipative Couette flow

a1 Princeton University Observatory, Princeton, NJ 08544, USA
a2 Princeton Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, NJ 08543, USA


Axisymmetric stability of viscous resistive magnetized Couette flow is re-examined, with the emphasis on flows that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradients of angular velocity and specific angular momentum. In this regime, magnetorotational instabilities (MRI) may occur. Previous work has focused on the Rayleigh-unstable regime. To prepare for an experimental study of MRI, which is of intense astrophysical interest, we solve for global linear modes in a wide gap with realistic dissipation coefficients. Exchange of stability appears to occur through marginal modes. Velocity eigenfunctions of marginal modes are nearly singular at conducting boundaries, but magnetic eigenfunctions are smooth and obey a fourth-order differential equation in the inviscid limit. The viscous marginal system is of tenth order; an eighth-order approximation previously used for Rayleigh-unstable modes does not permit MRI. Peak growth rates are insensitive to boundary conditions. They are predicted with surprising accuracy by WKB methods even for the largest-scale mode. We conclude that MRI is achievable under plausible experimental conditions using easy-to-handle liquid metals such as gallium.

(Received April 19 2001)
(Revised January 21 2002)

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