A numerical investigation of vortex breakdown has been undertaken in an attempt to understand its properties, and the mechanisms responsible for it. Solutions of the full steady axisymmetric Navier—Stokes equations for breakdown in an unconfined viscous vortex have been obtained for core Reynolds numbers up to 200, for a two-parameter family of assumed upstream velocity distributions. Diffusion and convection of vorticity away from the vortex core, and the strong coupling between the circumferential and axial velocity fields in highly-swirling flows, are shown to lead to stagnation and reversal of the axial flow near the axis. The various theories of vortex breakdown are considered in light of the present numerical solutions.

The method of multiple scales has been used to extend linear-stability theory to nonparallel axisymmetric boundary-layer flow in the neighborhood of the stagnation point on a blunt body of revolution. The extended theory includes nonparallel planar effects as well as the effects of such possibly destabilizing three-dimensional mechanisms as the stretching of vortex filaments in the rapidly diverging boundary-layer flow. These mechanisms have not been previously incorporated into stability theory. Stability predictions based on the extended theory are found to be in close agreement with predictions of parallel-flow stability theory based on the Orr–Sommerfeld equation; axisymmetric and planar nonparallel effects are concluded to be of negligible importance in the axisymmetric stagnation-point boundary layer.

No abstract