Coherent Structures in the Breakdown Bubble of a Vortex Flow

Helical structures downstream of the breakdown bubble of the Grabowski vortex profile at Keynolds numbers of Re <= 500 have been extensively studied through stability analyses in the literature. However, the low-frequency coherent structures inside the bubble, which have been observed in experiments, were not predicted by the stability approach. In the present work, asymptotic stabilities of the Grabowski vortex flow at Re <= 1000 are carried out to compare against previous works, and then the linear optimal inflow perturbation and the corresponding outcome are studied to unveil the dynamics inside the bubble. It is found that low-frequency inflow perturbations penetrate the bubble and are amplified to coherent structures, whereas high-frequency perturbations are convected around the border of the bubble. These linearized results agree well with previous experimental observations and are validated by direct numerical simulations.