The Effect of Non-Normality of Navier-Stokes Operator Mechanism on Dynamics of an Axisymmetric Swirling Flow

Abstract

The effect of non-normality of the Navier-Stokes operator on the dynamics of an axisymmetric swirling flow, namely, the Oseen vortex, has been investigated. The eigenvalue analysis and transient growth analysis have been employed in order to obtain the least stable eigenmode and the global optimal perturbation, which are both considered as the initial perturbation. Three stages of dynamic process have been put into evidence for the evolution of the optimal perturbation. The early (linear) stage is characterized by the amplification of radial perturbation, consistent with the prediction of transient growth theory. Having come into the nonlinear stage, the perturbation energy growth is suppressed by the interaction between the vortex ring and the Oseen vortex core. Finally, the phenomena of secondary energy growth are 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, which are both thought to be beneficial to fluid entrainment or mixing. The effect of perturbation amplitude on the nonlinear evolution of flows is also studied.