Force- and Loss-Free Transitions Between Vortex Flow States

It is suggested that a certain kind of vortex breakdown can be interpreted as a two-stage transition. The analysis is based on an extension of a variational principle proposed by Benjamin. Complete numerical results are presented which show loss-free transitions (including their internal structure) in a Rankine vortex. Moreover, an apparent paradox is resolved which is associated with the fact that a vortex flow in a diffuser approaches the critical state.