Abstract
The problem of the linear stability of steady‐state axisymmetric shear jet flows of a perfectly conducting inviscid incompressible fluid with a free surface in an azimuthal magnetic field is studied. The necessary and sufficient condition for the stability of these flows against small axisymmetric long‐wave perturbations of special form is obtained by the direct Lyapunov method. It is shown that if this stability condition is not satisfied, the steady‐state flows considered are unstable to arbitrary small axisymmetric long‐wave perturbations. A priori exponential estimates are obtained for the growth of small perturbations. Examples are given of the steady‐state flows and small perturbations imposed on them which evolve in time according to the estimates obtained.
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