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Scholarly Works (2 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2014)

One of the most important problems in astrophysics is how angular momentum is transported in protoplanetary disks (PPDs - disks containing gas and dust orbit around newly-forming protostars). Collisional viscosity is believed to be insufficient for angular momentum transport. Therefore, turbulence enhanced transport are proposed. In addition, long-lived coherent vortices are also speculated to exist in PPDs, which could play an important role in completing star formation and building planets. Without instabilities, turbulence and vortices cannot form. In weak magnetized PPDs, magneto-rotational instability (MRI) operates to generate turbulence. However, regions known as ``dead zone", are cool and unionized to have MRI. This has led to intense theoretical and computational search for pure hydrodynamic instabilities.

A new hydrodynamic, finite amplitude instability has been discovered in linearly stable, rotating, stably-stratified, shear flows. The instability starts from a new family of critical layers - baroclinic critical layers. These critical layers, which are linear, neutrally stable eigenmodes in stratified shear flows, have singularity in their vertical velocities. Under the effect of rotation, these critical layers produce vortex layers. Vortex layers intensify by drawing energy from the background shear flows, and subsequently roll up to create new vortices, which in turn excite new critical layers. The whole process self-replicates until the whole domain is filled with large-volume, large amplitude vortices. Because this instability can occur in the dead zones of protoplanetary disks we refer it as zombie instability and these new class of vortices that self-replicate as zombie vortices. High resolution numerical simulations show this instability can be triggered by a variety of weak perturbations including small volume compact single vortex, a pair of vortices and noise. The threshold of the instability is determined by the Rossby number or vorticity of the initial perturbations. Energy analysis based on the zonal non-zonal decomposition of the energy shows energy that supplies the instability is extracted from the zonal flows. Vortex is responsible for the energy extraction process. Instability saturates when the all the space are taken by zombie vortices. The separation distance between zombie vortices is approximately the distance from critical layers with lowest stream-wise wave number to the perturbations. The flows at late time are determined only by the background parameters not their initial perturbations. Zombie instability is also discussed in a broader picture to show the dead zones of PPDs are not dead. Our numerical simulation suggest although zombie instability is a finite-amplitude instability, due to the large Reynolds number of the disk flows, it is effectively a linear instability. How zombie instability might lead to sufficient angular momentum transport is also discussed. Finally, we speculate there might not be a laminar Keplerian disks at all. The disk flows are essentially turbulence from the collapsing of gas cloud with possibility turbulent flows filled with zombie vortices. A newly developed semi-analytic method for flows with strong background shear is also presented to be an alternative to widely used shearing sheet method in the astrophysical community. The semi-analytic method is used for simulating internal inertial-gravity waves in rotating, stratified flows with and without shear. The method can also be generalized to systems with linear forcing terms.

    Cover page: Zombie Instability in Rotating, Stably-Stratified Shear Flows and in Protoplanetary Disks
    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2016)
    In Zombie Vortex Instability (ZVI), perturbations excite critical layers in stratified, rotating shear flow (as in protoplanetary disks (PPDs)), 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-Väisälä 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 PPDs, 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 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-Väisälä frequency profiles that may be found in PPDs.
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