Instability of rotating magnetic field driven flow in a counter-rotating cylinder

We present experimental and numerical results concerning the instability of a liquid metal flow driven by a rotating magnetic field in a finite rotating cylinder. We observe that counter-rotation of the container with respect to the direction of field rotation may have a pronounced stabilizing or destabilizing action depending on the relative rotation rate. The flow is stabilized if the mechanical counter-rotation is relatively strong. The rotating magnetic field then just slows slightly the core of the flow. As a result, the angular momentum increases with the radial position in a vertical side layer and the Rayleigh stability criterion is satisfied. The flow stays stable so far as it rotates in the direction of the container. A rapid transition takes place almost immediately after reversal of the azimuthal flow direction in a narrow region around the axis of the container. The flow is considerably destabilized at a relatively low counter-rotation of the container. This is observed as a linear instabilit...