Stability of rimming flows

Necessary and sufficient conditions for the stability of the inviscid profile, subject to infinitesimal axisymmetric disturbances were studied. A generalization of Rayleigh's criterion was found, taking into account the presence of an interface. Centrifugally stable profiles could be destabilized through a combination of capillary and Rayleigh-Taylor effects on the interface. As for the viscous profile, rigid body rotation, a sufficient condition was established for its stability to infinitesimal axisymmetric disturbances (a generalization of Synge's criterion). This turned out to be the stability condition of the generalized Rayleigh's criterion applied to the viscous profile. Viscosity did not destabilize the flow. The characteristic equation was derived for the instability of the rigid body rotation for some limiting cases.