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Baroclinic Critical Layers and Zombie Vortex Instability in Stratified Rotational Shear Flow

Abstract

Without instabilities, the gas in the protoplanetary disk around a forming protostar remains in orbit rather than falling onto the protostar and completing its formation into a star. Moreover without instabilities in the fluid flow of the gas, the dust grains within the disk's gas cannot accumulate, agglomerate, and form planets. Keplerian disks are linearly stable by Rayleigh’s theorem because the angular momentum of the disk increase

s with increasing radius. This has led to the belief that there exists a large region in protoplanetary disks, known as the dead zone, which is stable to pure hydrodynamic disturbances. The dead zone is also believed to be stable against magneto-rotational instability (MRI) because the disks' cool temperatures inhibit ionization and therefore prevent the MRI.

A recent study shows the existence of a new hydrodynamic instability called the Zombie Vortex Instability (ZVI), where successive generations of self replicating vortices (\textit{zombie vortices}) may fill the disk with turbulence and destabilize it. The instability is triggered by finite amplitude perturbations, including weak Kolmogorov noise, in stratified (with Brunt-Vasala frequency N) flows, rotating with angular velocity and shear.

So far there are no observational evidences of the Zombie Vortex Instability and there are very few laboratory experiments of stratified plane Couette flow with background rotation in the literature.

We perform systematic simulations exploring existence of Zombie Vortex Instability in terms of control parameters (Reynolds number, shear, rotation and stratification). We present a parameter map showing two regimes where ZVI occurs, and interpret the physics that determines the boundaries of the two regimes. We also discuss the effects of viscosity and the existence of a threshold for $Re$. Our study on viscous effect, parameter map and its underlying physics provide guidance for designing practical laboratory experiments in which ZVI could be observed.

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