HYDROMAGNETIC STABILITY OF A STREAMINGCOMPRESSIBLE GAS CYLINDER IN A LIQUID FOR( m=0)MODE

Document Type : Original Article

Authors

1 Professor, Mathematics Department, Faculty of Science, Ain Shams University, Cairo,Egypt.

2 Engineer, Engineering Physics and Mathematics Department, Faculty of Engineering, Ain Shams University , Cairo, Egypt.

Abstract

ABSTRACT
The hydromagnetic instability of compressible hollow jet involved with surface tension is
discussed in the axisymmetric mode for all short and long wavelengths. The dispersion
relation is derived and discussed analytically and numerically. The axial magnetic fields
inside the gas and liquid regions have stabilizing effects for all short and long wavelengths.
This is physically interpreted that the axial field exerts a strong effect which causes the
bending and twisting of the magnetic lines of force. The compressibility effects need careful
treating. Here the incompressible fluid result is obtained as a tends to ∞ ( a is the sound speed
in the fluid). For finite value of a (i.e. compressible fluid), the temporal amplification is
larger than that in the incompressible case. So the compressibility has a strong destabilizing
tendency and increase the unstable domains. The streaming is destabilizing for all short and
long wavelengths. The capillary force is destabilizing for small wave numbers while it is
stabilizing for all the rest wavelengths. Whatever the stabilizing effect of the electromagnetic
force is strong enough, the capillary, streaming and compressible instability could not be
suppressed and the model will be always unstabl

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