Hydromagnetic stability of rotating stratified compressible fluid flows

Abstract

The hydromagnetic stability of a radially stratified compressible fluid rotating between two coaxial cylinders is investigated. The stability with respect to axisymmetric disturbances is examined. The fluid system is found to be thoroughly stable to axisymmetric disturbances provided the fluid rotates very rapidly. The system is shown to be unstable to non-axisymmetric disturbances, and the slow amplifying hydromagnetic wave modes propagate against the basic rotation. The lower and upper bounds of the azimuthal phase speeds of the amplifying waves are determined. A quadrant theorem on the slow waves characteristic of a rapidly rotating fluid is derived. Special attention is given to the effects of compressibility of the fluid. Some results concerning the stabilitiy of an incompressible fluid system are obtained as special cases of the present analysis.