Onset of spiral vortex breakdown in supersonic flows

The onset of vortex breakdown in supersonic flows remains an unsolved problem in physics. In this study, a sufficient condition for spiral vortex breakdown to occur in supersonic flows was derived from the conserved total enthalpy at the vortex axis under complete supersonic inflow conditions. The theoretical threshold was simply determined by the relationship between the magnitudes of the kinetic and internal energies (i.e. axial velocity squared and static temperature, respectively) downstream. In addition, it was found that the squared velocity and static temperature in the sufficient condition were closely related to a rapid reduction in the helicity, which indicated that vortex breakdown occurred. Numerical simulations confirmed that the theoretical threshold corresponds to the onset of spiral vortex breakdowns in supersonic flows.