Self-sustaining vortex perturbations in smooth shear flows

The nonlinear dynamics of coherent circular/elliptical cyclonic and anticyclonic vortices in plane flow with constant shear is investigated numerically using a dealiased Fourier pseudospectral code. The flow is asymptotically linearly stable, but is highly non-normal, allowing perturbations to gain energy transiently from the background shear flow. This linear transient growth interplays with nonlinear processes. In certain cases it is shown that the nonlinear feedback is positive, leading to self-sustaining coherent vortices. Self-sustaining coherent vortices exist where the vorticity is parallel to the mean flow vorticity (cyclonic rotation). The required nonlinear feedback is absent for small amplitude anticyclonic vortices. However, elliptical anticyclonic vortices become self-sustaining if the amplitude exceeds a threshold value. The self-sustaining of coherent vortices is similar to the subcritical, so-called bypass, transition to turbulence in shear flows. The common features are: transient linear ...