This is a study of sufficient conditions for the stability of rotating flows and swirling flows of perfect conducting fluid with circular magnetic fields. Miles’ theorem [1] and Howard’s semicircle theorem [2] on the stability of stratified shear flows are extended to rotating flows with discontinuous swirl velocity. Some stronger sufficient conditions for stability are established. Some sufficient conditions for the stability and instability of the perfect conductive fluids subjected to a transverse circular magnetic field are also studied.

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