Examination of group-velocity criterion for breakdown of vortex flow in a divergent duct

A group-velocity criterion for vortex breakdown implied by wave trapping theory is applied to vortex flows in a slightly divergent duct that exhibits breakdown. The group velocities for both symmetric (n = 0) and nonsymmetric (n = plus or - 1) modes of wave propagation are calculated for the experimental data. It is found that the flow ahead of the breakdown region is always supercritical and stable to these modes of disturbances. However, the flow field behind the breakdown region may be either supercritical or subcritical to the modes n = 0 and n = 1, and always supercritical to mode n = -1. The flow field behind this breakdown region is unstable to the asymmetric mode disturbance (n = 1) for a finite range of wavenumbers. The calculated frequencies of the unstable disturbances are in good agreement with the frequencies obtained from the experimental measurements.