ON THE PRACTICAL APPLICATION OF VORTEX BREAKDOWN THEORY TO AXIALLY-SYMMETRICAL AND 3-DIMENSIONAL COMPRESSIBLE FLOWS

A perfect-fluid theory for axially symmetrical vortex breakdown flows by Keller et al. [Z. Angew. Math. Phys. 36, 854 (1985); 39, 404 (1988) ] is extended to three-dimensional compressible flows. In a first step , an approximate theory for thin vortex cores is compared to the exact theory for axially symmetrical flows of inviscid, incompressible flui ds. In subsequent steps, the approximation for thin vortex cores is ex tended to flows of compressible fluids that are not axially symmetrica l. Finally, the various types of vortex breakdown flows and the shear layer instabilities at the surface of vortex breakdown bubbles are bri efly discussed.