Destabilization of rotating flows with positive shear by azimuthal magnetic fields

According to Rayleigh's criterion, rotating flows are linearly stable when their specific angular momentum increases radially outward. The celebrated magnetorotational instability opens a way to destabilize those flows, as long as the angular velocity is decreasing outward. Using a local approximation we demonstrate that even flows with very steep positive shear can be destabilized by azimuthal magnetic fields which are current free within the fluid. We illustrate the transition of this instability to a rotationally enhanced kink-type instability in the case of a homogeneous current in the fluid, and discuss the prospects for observing it in a magnetized Taylor-Couette flow.