Abstract: In recent years there has been a great deal of interests in the stability of swirlingflows. It is because of not only the significance to the enhancement of supersonic mixing butalso the important applications to many practical flows such as the trailing-line vortices behindan aircraft. The absolute/convective instability of incompressible swirling flows and the temporalinstability of compressible swirling flows have been fully explored, whereas the absolute/convectiveinstability of compressible swirling fl...