Hydromagnetic stability of stratified compressible fluid between two rotating cylinders

The stability of a perfectly conducting nonisothermal compressible fluid between two coaxial cylinders in the presence of a magnetic field is studied. In the case of axisymmetric disturbances, it is observed that the magnetic field (which increase with distance from the axis of rotation) has destabilizing influence, but the rate of increase of instability is reduced when the effect of compressibility is also considered. It is observed that nonisothermal compressible fluids have more stabilizing influence than isothermal compressible fluids. However the system can be made stable by rapid rotation of the fluid when the magnetic-field gradient is moderate. The analysis of nonaxisymmetric disturbances shows that all unstable modes propagate against the basic rotation. It is shown that the system is more unstable for nonisothermal compressible fluids.