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The Quarterly Journal of Mechanics and Applied Mathematics 1965 18(4):491-500; doi:10.1093/qjmam/18.4.491
© 1965 by Oxford University Press
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AN EXACT ANALYSIS OF MAGNETOHYDRODYNAMIC STABILITY OF NONDISSIPATIVE COUETTE FLOW{dagger}

TIEN SUN CHANG

( Department of Applied Mathematics and Theoretical Physics University of Cambridge )

An exact solution describing the hydromagnetie stability of nondissipative, conducting Couette flow between two coaxial cylinders under the action of an axial magnetic field is presented.

It is shown that algebraic expressions may be deduced for the determination of the criterion of hydromagnetie stabilization of Couette flow profiles of the form (Ar + B/r), if the critical perturbations are assumed to be due to the axiaymmetrical normal modes. The parameters which determine the criterion are the characteristic Alfvén number, the radius ratio of the cylindrical walls, and adimensionless number characterizing the shape of the velocity profile.


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