Critical layers and protoplanetary disk turbulence

Abstract

A linear analysis of the zombie vortex instability is performed in a stratified shearing sheet setting for three model barotropic shear flows. The linear analysis is done by utilizing a Green's function formulation to resolve the critical layers of the associated normal-mode problem. The instability is the result of a resonant interaction between a Rossby wave and a gravity wave which we refer to as Z-modes. The associated critical layer is the location where the Doppler shifted frequency of a distant Rossby wave equals the local Brunt-Vaisala frequency. The minimum required Rossby number for instability, Ro= 0.2, is confirmed for parameter values reported in the literature. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The zombie vortex instability is examined in a jet model, finding that the instability can occur for Ro= 0.05. Nonlinear vorticity forcing due to unstable Z-modes is shown to result in the creation of a jet flow at the critical layer emerging as the result of the competition between the vertical lifting of perturbation radial vorticity and the radial transport of perturbation vertical vorticity. We find that the picture of this instability leading to a form of nonlinearly driven self-replicating pattern of creation and destruction is warranted: a parent jet spawns a growing child jet at associated critical layers. A mature child jet creates a next generation of child jets at associated critical layers while simultaneously destroying its parent jet via the Rossby wave instability.

Accepted to ApJ (25 pages). Results of previously appearing versions unchanged. Changes and additions include: updated references and nomenclature, viscous solutions added, higher resolution solutions displayed, expanded discussion, and shortened abstract

References in corpus (10)

• Convective Overstability in radially stratified accretion disks under thermal relaxation
• Vertical shear instability in accretion disc models with radiation transport
• Convective overstability in accretion disks: 3D linear analysis and nonlinear saturation
• Baroclinic Vorticity Production in Protoplanetary Disks; Part II: Vortex Growth and Longevity
• On the vertical-shear instability in astrophysical discs
• Vortex formation in protoplanetary discs induced by the vertical shear instability
• Rossby Wave Instability in three dimensional discs
• On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
• Gap formation and stability in non-isothermal protoplanetary discs
• A shallow-water theory for annular sections of Keplerian Disks

Cited by in corpus (14)

• Resonant Drag Instabilities in protoplanetary disks: the streaming instability and new, faster-growing instabilities
• Radiation Hydrodynamical Turbulence In Protoplanetary Disks: Numerical Models and Observational Constraints
• The initial conditions for planet formation: Turbulence driven by hydrodynamical instabilities in disks around young stars
• Gas and dust dynamics in starlight-heated protoplanetary disks
• A thermodynamic view of dusty protoplanetary disks
• Mapping the Conditions for Hydrodynamic Instability on Steady State Accretion Models of Protoplanetary Disks
• Dust settling against hydrodynamic turbulence in protoplanetary discs
• Efficiency of thermal relaxation by radiative processes in protoplanetary discs: constraints on hydrodynamic turbulence
• Requirements for gravitational collapse in planetesimal formation --- the impact of scales set by Kelvin-Helmholtz and nonlinear streaming instability
• Global Simulations of the Vertical Shear Instability with Non-ideal Magnetohydrodynamical Effects
• Zombie Vortex Instability. III. Persistence with Nonuniform Stratification and Radiative Damping
• On the Vertical Shear Instability in Magnetized Protoplanetary Disks
• Vortex survival in 3D self-gravitating accretion discs
• History of the Solar Nebula from Meteorite Paleomagnetism