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The stability of MHD Taylor-Couette flow

The linear marginal instability of an MHD Taylor-Couette flow of infinite vertical extension is considered. For hydrodynamically unstable flows the minimum Reynolds number exists even without a magnetic field, but there are also solutions with smaller Reynolds numbers for certain (weak) magnetic fields. The magnetic field can, therefore, destabilize the rotating flow. This instability, however, can only exist for not too small magnetic Prandtl numbers. Also the situation for nonaxisymmetric disturbances is considered. Without magnetic fields such modes possess higher Reynolds numbers than the axisymmetric modes. The situation is changed in the MHD regime. For modest magnetic fields the excitation of modes with m=1 is easier than the excitation of modes with m=0 if critical magnetic amplitudes are exceeded.