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Baroclinic Critical Layers and Zombie Vortices in Couette-Taylor Flow

Posted on Jun 17, 2013 in GAFD 2013

Philip Marcus (UC Merced)

We report a new mechanism for creating vortices in a class of flows that are linearly stable and believed, by most researchers, to be also finite-amplitude stable. The vortices should form in stably-stratified Couette flows (both plane and circular), and in protoplanetary disks around forming protostars. Our study was motivated by the fact that protoplanetary disks must have flow instabilities that are capable of transporting angular momentum radially outward so that the protostars can accrete gas and grow into stars. The mechanism that we discovered allows small-amplitude perturbations (i.e., with small volumes and Rossby numbers) to form vortices that are large in volume and amplitude (with a Rossby number of order unity). The mechanism works by exciting neutrally stable baroclinic critical layers, which differ from the usual barotropic critical layers in uni-directional flows (responsible for the much-discussed but rarely-observed Kelvin’s cats-eye vortices). The singularities in the former layers are in their vertical velocities, while the latter are in their stream-wise velocities. The energy of the vortices becomes large, and it is supplied by the kinetic energy of the background shear flow. The vortices we found have an unusual property: a vortex that grows from a single, local perturbation triggers a new generation of vortices to grow at nearby locations. After the second generation of vortices grows large, it triggers a third generation. The triggering of subsequent generations continues ad infinitum so that a front dividing the vortex- dominated flow from the unperturbed flow advances until the entire domain fills with large vortices. The vortices do not advect across the region, the front of the vortex- populated fluid does. The region in protoplanetary disks where we have found this new mechanism is thought to be stable; thus, in the astrophysical literature this region is called the dead zone. Because the vortices we report here arise in the dead zone, grow large, and spawn new generations of vortices that march across the domain, we refer to them as zombie vortices. We consider the mechanism of the zombie vortices’ growth and advance in a proposed lab experiment: circular Couette flow with a vertically stably- stratified Boussinesq fluid (i.e., salt water) with a density that is linear with height. Because this flow is nearly homogenous, the first vortex formed by the initial instability self-replicates in an approximately spatially self-similar manner and fills the domain with a lattice of 3D vortices, which persists, despite the fact that the flow is turbulent.