Rotational stabilization of pinch instabilities in Taylor-Couette flow.

The axisymmetric linear stability of dissipative Taylor-Couette flow with an azimuthal magnetic field is considered. The magnetic field can be unstable without a rotation. This is the well-known pinch type instability. The stable rotation stabilizes the unstable azimuthal magnetic field. The dissipative flow stability can be classified according to Michael's stability condition for an ideal flow. The dissipative effects stabilize the flow and an ideally unstable flow becomes really unstable only when both the angular velocity and the magnetic field exceed some critical values.