Large Hydromagnetic Axisymmetric Instability of a Streaming Gas Cylinder Surrounded by Bounded Fluid with Non Uniform Field
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Abstract
The magnetohydrodynamic axisymmetric instability of a streaming gas jet surrounded by bounded °uid with non-uniform ¯eld has been developed. The problem is formulated, solved and the boundary conditions are applied across the interfaces. The eigenvalue relation is derived and discussed analytically and the results are con¯rmed numerically. Some reported works are recovered as limiting cases from the present general results. The streaming has a destabilizing e?ect for all short and long wavelengths. The capillary force is stabilizing for short wavelengths but it is destabilizing for long wave- lengths. The axial magnetic ¯elds interior the gas and °uid media are stabilizing. The transverse ¯eld is destabilizing for all wavelengths. The radii ratio of the gas and °uid cylinders plays an important role for stabilizing the model and made it more realistic one than the full liquid jet or/and the ordinary hollow jet. The numerical analysis clarify the stable and unstable domains based on di?erent values of the various parameters of the problem.
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