The Effect of Non-normality of the Navier-Stokes Operator on the Dynamics of an Axisymmetric Swirling Flow

Abstract

We consider in detail the effect of non-normality of the Navier-Stokes operator on the time evolution of an axisymmetric swirling flow. The eigenvalue analysis and transient growth analysis have been employed to obtain the least stable eigenmode and the global optimal perturbation respectively, which are both taken as the initial disturbances. Three stages of dynamic process have been observed for the dynamics of the optimal perturbation. In the linear stage the result of the amplification of perturbation energy is consistent with that revealed by transient growth theory. Having come into the nonlinear stage, the perturbation energy growth is suppressed by the interaction with the Oseen vortex core. Finally, the phenomena of secondary energy growth is also observed. Compared with the results obtained by applying the least stable eigenmode as the initial disturbance, the nonlinear behavior of the optimal perturbation features radial fluid motion and the rapid production of small eddies. The effect of perturbation amplitude on the nonlinear evolution of flows is also investigated.