Axisymmetric and Non-Axisymmetric Initiation of Vortex Breakdown

The onset of axisymmetric (bubble) and non-axisymmetric (spiral) modes of breakdown is stud-ied numerically for swirling pipe ows. We nd that the onset of axisymmetric vortex breakdown occurs when the vortex attains local criticality. A transient simulation of the evolution of vortex breakdown revealed that downstream-running waves are trapped approximately at the location of ow criticality. These trapped waves are slowly amplied and eventually result in the bubble breakdown region with reversed ow and enlarged core size. Non-axisymmetric disturbance were found to decay on columnar base ows; however, for base ows with bubble breakdown, non-axisymmetric disturbances were amplied. These amplied disturbances resulted in the formation of spiral breakdown. If the base ow inlet swirl was only slightly larger than that leading to ax-isymmetric breakdown, a nearly columnar solution was obtained, suggesting that weak asymmetry may help to stabilize the columnar solution branch. The numerical simulations also revealed that most of the energy in spiral breakdown is contained in the rst few non-axisymmetric modes of variation.