The classical instability of a differentially rotating fluid takes place according to Rayleigh's criterion, i.e. when there is a radially outward decrease of angular momentum (per unit mass). In 1978, however, I showed that a tiny radial decrease of angular velocity is enough to give instability if a small azimuthal magnetic field is present.
This rather unusual instability arises when the magnetic energy is small compared with the rotational energy, provided that the electrical conductivity of the fluid or gas is not too weak. Non-axisymmetric waves then grow and propagate around the rotation axis, and the fastest-growing modes amplify very fast indeed, at a rate determined solely by the differential rotation.
Phil. Trans. Roy. Soc. A Vol 289, pp 459-500, 1978
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