On the stability of circular Rayleigh problem of hydrodynamic stability

Résumé

This study presents a detailed analytical investigation into the stability of incompressible swirling flows. A necessary condition is derived for the emergence of both neutral and unstable disturbance modes within subcritical region. To determine a sufficient condition for the existence of unstable modes, the variational structure of the inviscid stability problem is examined under the assumption of a monotonic axial velocity profile. A Sturm-Liouville framework is then employed to establish the existence of a regular neutral mode. Moreover, it is demonstrated that the total number of linearly unstable modes does not exceed the number of neutral modes admitted by the system.