Simulation of vortex bursting

The 3-D, incompressible, time-dependent Navier-Stokes equations in primitive variables are used to simulate bursting of a line vortex embedded in a unbounded uniform flow. The entire study is divided into three parts. First, the steady axisymmetric vortex behavior with various swirl level is studied. At low swirl level, the vortex flow remains parallel and can be described by the quasi parallel equations. At higher swirl levels, the flow develops large amplitude waves. When the amplitude of these waves is large enough, recirculation bubbles will occur on the vortex axis. The flow within the recirculation bubbles is found to nearly obey the Prandtl-Batchelor\u27s conditions. Secondly, the spatial and temporal evolution of axisymmetric vortex breakdown is investigated. When the swirl and Reynolds number are small, asymptotically steady flows develops, with steady recirculation bubbles at the higher swirl. When the swirl and Reynolds number are high enough, ring vortices are shed periodically from the primary (mostly steady) bubble, much as would happen from a bluff body. A steady/unsteady boundary dividing asymptotically steady and unsteady flow is constructed in the swirl parameter vs Reynolds number plane. It appears that the high Reynolds number limit of the boundary is at the swirl level corresponding to Benjamin\u27s vortex criticality condition. As Reynolds number decreases, the swirl level required to induce unsteady flow increases. The Strouhal number of the shed vortices is about.2, independent to both the swirl parameter and Reynolds number. Lastly, 3-D stability of the steady and unsteady axisymmetric flows, at some selected swirl parameter and at a constant Reynolds number, is examined. A small, but finite, first harmonic perturbation is introduced and the behavior of the flow is simulated by solving the full 3-D Navier-Stokes equations. At low swirl level, where quasi parallel is valid, the flow is found to be stable to 3-D perturbations. At higher swirl, where the quasi parallel approximation fails and the axisymmetric flow is wavy but has no bubble, the flow evolves into a spiral type of vortex breakdown. At even higher swirl, where recirculation bubbles occur, the first recirculation bubble is found to be stable to 3-D perturbations, but not the second one. Asymmetric amplification is concentrated at the second bubble. Hence, the flow has the appearance of bubble breakdown upstream and a downstream spiral breakdown. When the axisymmetric solution exhibits regular vortex shedding behavior, the shed ring vortices are found to be stretched and spiraling around an almost axisymmetric core. The flow appears to have a front end axisymmetric bubble, followed by a spiraling tail. When spiraling occurs, the first harmonic component dominates the asymmetric motion