Recently work has revealed that novel vortices in stratified shear flows can replicate themselves through the excitation of critical layers (Marcus et al., Phys. Rev. Lett. 2013, 111(8): 084501). Such vortices are referred to ‘zombie vortices,’ and their replication process is suggested to be a promising explanation for the accretion of protoplanetary disks. The critical levels that accomplish the self-replication are ‘baroclinic’ critical levels, located where the Doppler-shifted phase velocity matches the internal gravity wave velocity. In this talk, we will study the dynamics of baroclinic critical layers theoretically via matched asymptotic analysis.
We first study the linear and nonlinear evolution of the baroclinic critical layers under a steady forcing. We show that the linear critical layer is characterised by secular growth of the wave amplitude, and when it becomes nonlinear, the mean flow distortion of vorticity is the dominant characteristic. We then show that such a mean-flow defect is susceptible to a `secondary instability,’ which makes the critical layer roll up into billows and has the ability to excite new baroclinic critical layers. Our study could provide a theoretical understanding for the self-replicating zombie vortices.