Initiation of breakdown in slender compressible vortices

The onset of vortex breakdown in compressible flows is investigated analytically for the case in which the flow is axially symmetric, the vortex is isolated, its axis is parallel to the main flow, and the vortex radius is small compared to the breakdown length. The conservation equations for mass, momentum, and energy are formulated and solved numerically using a finite-difference scheme, as described by Krause (1985); numerical results are presented in graphs and briefly characterized.