Abstract
The onset of instability of MHD Couette flow due to non-axisymmetric, oscillatory disturbances is investigated. For counter-rotating cylinders, the existence is discovered of two threshold magnetic fields. Below the first threshold, non-axisymmetric, oscillatory modes are responsible for the onset of instability in analogy with the hydrodynamic case. For values of the magnetic field between the two thresholds, the critical modes are axisymmetric and stationary. Beyond the second threshold, in the region of high magnetic field, the critical modes are again non-axisymmetric and oscillatory. For the case of a stationary inner cylinder, only the large magnetic threshold exists. For co-rotating cylinders, the assumptions are verified under which the exact solution was obtained by Hassard, Chang and Ludford (1972).
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