On the survival of zombie vortices in protoplanetary discs

On the survival of zombie vortices in protoplanetary discs

Authors:

Lesur et al

Abstract:

Recently it has been proposed that the zombie vortex instability (ZVI) could precipitate hydrodynamical activity and angular momentum transport in unmagnetized regions of protoplanetary discs, also known as ‘dead zones’. In this Letter we scrutinize, with high-resolution 3D spectral simulations, the onset and survival of this instability in the presence of viscous and thermal physics. First, we find that the ZVI is strongly dependent on the nature of the viscous operator. Although the ZVI is easily obtained with hyperdiffusion, it is difficult to sustain with physical (second order) diffusion operators up to Reynolds numbers as high as 107. This sensitivity is probably due to the ZVI's reliance on critical layers, whose characteristic length-scale, structure, and dynamics are controlled by viscous diffusion. Second, we observe that the ZVI is sensitive to radiative processes, and indeed only operates when the Peclet number is greater than a critical value ∼104, or when the cooling time is longer than ∼10Ω−1. As a consequence, the ZVI struggles to appear at R ≳ 0.3 au in standard 0.01 M⊙ T Tauri disc models, though younger more massive discs provide a more hospitable environment. Together these results question the prevalence of the ZVI in protoplanetary discs.

Thresholds to Trigger Instability and the Properties of Zombie Turbulence in the Dead Zones of Protoplanetary Disks

Zombie Vortex Instability. II. Thresholds to Trigger Instability and the Properties of Zombie Turbulence in the Dead Zones of Protoplanetary Disks

Authors:

marcus et al

Abstract:

In Zombie Vortex Instability (ZVI), perturbations excite critical layers in stratified, rotating shear flow (as in protoplanetary disks), causing them to generate vortex layers, which roll-up into anticyclonic zombie vortices and cyclonic vortex sheets. The process is self-sustaining as zombie vortices perturb new critical layers, spawning a next generation of zombie vortices. Here, we focus on two issues: the minimum threshold of perturbations that trigger self-sustaining vortex generation, and the properties of the late-time zombie turbulence on large and small scales. The critical parameter that determines whether ZVI is triggered is the magnitude of the vorticity on the small scales (and not velocity), the minimum Rossby number needed for instability is Rocrit∼0.2 for β≡N/Ω=2, where N is the Brunt-V\"ais\"al\"a frequency. While the threshold is set by vorticity, it is useful to infer a criterion on the Mach number, for Kolmogorov noise, the critical Mach number scales with Reynolds number: Macrit∼RocritRe−1/2. In protoplanetary disks, this is Macrit∼10−6. On large scales, zombie turbulence is characterized by anticyclones and cyclonic sheets with typical Rossby number ∼0.3. The spacing of the cyclonic sheets and anticyclones appears to have a "memory" of the spacing of the critical layers. On the small scales, zombie turbulence has no memory of the initial conditions and has a Kolmogorov-like energy spectrum. While our earlier work was in the limit of uniform stratification, we have demonstrated that ZVI works for non-uniform Brunt-V\"ais\"al\"a frequency profiles that may be found in protoplanetary disks.

Undead Zones in Protoplanetary Disks

Zombie Vortex Instability I: The "Dead" Zones of Protoplanetary Disks are Not Dead

Authors:

Marcus et al

Abstract:

There has been considerable interest in purely hydrodynamic instabilities in the dead zones of protoplanetary disks (PPDs) as a mechanism for driving angular momentum transport and as a source of vortices to incubate planetesimal formation. We present a series of numerical simulations with both a pseudo-spectral anelastic code and the fully compressible Godunov finite-volume code Athena, showing that stably stratified flows in a shearing, rotating box are violently unstable and produce space-filling, sustained turbulence dominated by large vortices with Rossby numbers of order 0.2-0.3. This Zombie Vortex Instability (ZVI) is observed in both codes and is triggered by initial Kolmogorov turbulence with Mach numbers less than 0.01. ZVI is robust and requires no special tuning of cooling times, boundary conditions, or initial radial entropy or vortensity gradients. ZVI has not been seen in previous studies of flows in a rotating, shearing box because those calculations frequently lacked vertical density stratification and/or sufficient numerical resolution. Although we do not observe appreciable angular momentum transport from ZVI in small domains, we hypothesize that ZVI in larger domains with the fully compressible equations may lead to significant angular transport via spiral density waves launched by vortices. In a companion paper, we derive the instability criterion for ZVI; although ZVI is a subcritical instability, rather than a linear one, we show that initial Kolmogorov noise with Mach number no greater than 10^{-6} will trigger ZVI.