Vortex breakdown state selection as a meta-stable process

Abstract

Previous studies of unconfined swirling jets showed that both bubble and conical states of vortex breakdown can occur over a range of Reynolds numbers. State selection was postulated to be metastable, with small changes to initial conditions causing a discontinuous change to the final state for a particular final Reynolds-swirl number pair. Axisymmetric numerical simulations using a spectral element method of a swirling jet started from zero initial flow conditions show that the bubble state prevails at lower swirl ratios while the cone state dominates at higher swirl ratios. However, simulations where the jet evolution was started from a developed bubble state maintained that same state well into the region where previous simulations resulted in conical breakdown. These results give some indication of the inherent stability of the bubble state relative to the cone state. They also extend the work of Billant, Chomaz, and Huerre [ J. Fluid Mech. , 376:183--219, 1998] who observed the cone state from startup at swirl ratios slightly greater than the critical swirl ratio. In these simulations, perturbations cause the cone to be swept downstream only reappearing as a bubble with favourable perturbations.