Zombie vortex instability in the protoplanetary disk: can we find it in the lab?

¹ Aix-Marseille Univ., CNRS, Centrale Marseille, IRPHE, Marseille, France
² Department of Mechanical Engineering, University of California, Berkeley 6121 Etcheverry Hall, Mailstop 1740, Berkeley, CA 94720-1740, USA

Abstract

Without instabilities, the gas in the protoplanetary disk approximately 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 theorem because the angular momentum of the disk increases 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 Marcus et al. (2013) shows the existence of a new hydrodynamic instability called the Zombie Vortex Instability (ZVI), where successive generations of self-replicating vortices (zombie vortices) fill the disk with turbulence and destabilize it. The instability is triggered by finite-amplitude perturbations, including weak Kolmogorov noise, in stratified flows with Brunt-Väisälä frequency N, background rotation Ω and horizontal shear σ. So far there is no observational evidence 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 to determine where the Zombie Vortex Instability exists in terms of the control parameters (Reynolds number Re, σ/f and N/f). 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 effects, parameter map and its underlying! physics provide guidance for designing practical laboratory experiments in which ZVI could be observed.