Critical Layers and Protoplanetary Disk Turbulence

Critical layers and protoplanetary disk turbulence

Authors:

Umurhan et al

Abstract:

A linear analysis of the zombie vortex instability is performed in a stratified shearing sheet setting for three model barotropic shear flows: the vorticity step, the shear layer and the asymmetric jet. The examination assumes that both disk-normal gravity and stratification is constant. The aim is to better understand the instability of so-called Z-modes and the subsequent nonlinear self-reproduction process discussed in the literature. We report several results: The instability is the result of a resonant interaction between a Rossby wave and a gravity wave. The associated critical layer is the location where the Doppler shifted frequency of a distant Rossby wave equals the local Brunt-Vaisala frequency. For the shear flow model we confirm the minimum required Rossby number (Ro) for instability to be 0.2. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The zombie vortex instability as well as the Rossby wave instability are examined for the first time in a jet model, finding that the instability can occur for Ro= 0.05. For all model flows considered, nonlinear vorticity forcing due to unstable Z-modes is shown to result in the creation of a jet flow at the critical layer. The jet-flow emerges as the result of the competition between the vertical lifting of perturbation radial vorticity and the radial transport of vertical perturbation vorticity wherein the former mechanism usually dominates the latter. We confirm that nonlinear forcing results in a self-replicating/self-reproducing pattern of creation and destruction: parent jets spawn and grow child jets at associated critical layers and once the child jet grows strong enough it subsequently creates a next generation of jets associated with its critical layer while simultaneously destroying itself due to the Rossby wave instability.