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.
Keywords:jet shear flows, long-wave approximation, stability, direct Lyapunov method.
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