Numerical investigation of a swirling flow under the optimal perturbation

The nonlinear evolution of 3-D instability of a viscous swirling flow, namely, the Oseen vortex, is addressed by direct numerical simulation with a Reynolds number equal to 5000. The global optimal perturbation is considered as the initial perturbation. In axisymmetric cases, three flow regimes are found: (1) the linear growth; (2) the decay of perturbation energy; (3) secondary energy growth. The linear energy growth, which is characterized by the amplification of radial perturbations, is arrested by the interaction between the vortex ring and the Oseen vortex core. The development of the vortex structure is also investigated for non-symmetric flows.