| The primary goal of this dissertation is to try and improve the fundamental understanding of the mechanism about vortex breakdowns.; Vortex breakdown in spatially growing flows are investigated numerically by simulating the three dimensional incompressible, time-dependent Navier-Stokes equations in cylindrical coordinates. At relatively small values of Reynolds and swirl numbers, axisymmetric vortex breakdown solutions of bubble type are observed and are stable under axisymmetry assumption. This kind of breakdown is found to be strongly related to the upstream propagation of disturbance waves inside the vortex core, thereby lending support to recent attempts to relate vortex breakdown to the emergence of absolute instabilities (Delbende et al. 1998, Rusak et al. 1998).; Carrying the simulations to the 3D simulations, the axisymmetric bubble-type solution becomes unstable, and the transition to a temporally periodic, helical vortex breakdown flow is observed. The finite length region of absolute instability observed around the wake of bubble breakdown, together with the temporal periodicity, indicate the possible existence of a global mode. The transition process of bubble type to spiral type breakdown observed in our simulations also agrees well with Rusak et al.'s theoretical arguments that axisymmetric breakdown represents an important step in the evolution of three-dimensional finite-amplitude disturbances and unsteady three-dimensional breakdown flows. At higher swirl number, a double-helix vortex breakdown is also observed. |
