Stability of swirling gas flows

The stability of inviscid swirling gas flows to small nonaxisymmetric perturbations is considered. For small Brunt-Vaisala frequencies, the problem reduces to the classical Sturm-Liouville form and the oscillation theorem can be applied. The resulting necessary and sufficient stability condition is compared to various criteria in the literature and a limited numerical study of isothermal rigidly rotating Poiseuille flow. For given azimuthal and axial wavenumbers, it is found numerically that the higher inertial modes become unstable for successively lower Rossby numbers and that this sequence of critical values approaches the theoretical value from above.