Interfacial conditions for a cylindrical vortex sheet or a cylindrical fluid layer with radius-dependent density, velocity and magnetic fields are derived for isentropic compressible swirling flows subjected to arbitrary disturbances. Surface tension is included for possible immiscible fluids. These conditions are valid for both spatially and temporally growing waves and for flow profiles with or without discontinuities. The deformation of the sheet or the layer affects the flow in two ways: perturbing the total pressure field and disturbing the centrifugal force field created by the azimuthal components of the velocity and the magnetic flux. The latter seems to be straightforward, but is easily overlooked as in some of the previous analyses. We will show that failure to consider such a perturbation to a stable centrifugal force field will lead to the improper destabilization of certain modes with smaller axial and azimuthal wavenumbers.

The interfacial conditions and their corresponding stability characteristics are further examined for a general class of incompressible flows subject to temporal perturbations. Unlike the single role of destabilization played by the velocity in two-dimensional stratified flows or axisymmetric jet flows, the rotating velocity in vortex motions plays a dual role in flow stability: the angular-velocity gradient generates tangential shear, and the angular velocity itself creates a centrifugal force field. While the former always destabilizes the flow, the latter can either stabilize or destabilize the flow depending on whether the resultant force is centrifugally stable or unstable. These characteristics are demonstrated by examining three general types of perturbations.