Necessary conditions for the stability of a general class of compressible vortex flows are obtained using the method of generalized progressing wave expansion. The vortex motion and the density are assumed to vary in both the radial and axial directions. These conditions, representing a generalized state of statically stable distribution for the steady flow, require that the flow be stable in the centrifugal force field created by the rotation of the fluids, in the gravitational force field arisen from the density variation, and in the pressure field constraining the variation of density and forces in both the radial and axial directions. These results also suggest the likely behavior of Richardson criteria for stability of the flow yet to be derived.

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