Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

Abstract

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4

arXiv commentAccepted for publication in ApJ. Some minor changes due to referee report, most notably that the clumping mechanism has been identified as the streaming instability of Youdin & Goodman (2005). Movies of the simulations are still available at http://www.mpia.de/homes/johansen/research_en.php

References in corpus (23)

• Streaming Instabilities in Protoplanetary Disks
• Dust coagulation in protoplanetary disks: a rapid depletion of small grains
• Planetesimal Formation by Gravitational Instability
• Turbulence in Accretion Disks. Vorticity Generation and Angular Momentum Transport via the Global Baroclinic Instability
• Local Magnetohydrodynamical Models of Layered Accretion Disks
• The ionization fraction in alpha-models of protoplanetary disks
• Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
• Magnetic field generation in fully convective rotating spheres
• Dust diffusion in protoplanetary discs by magnetorotational turbulence
• Turbulence and angular momentum transport in a global accretion disk simulation
• Reviving Dead Zones in Accretion Disks by Rossby Vortices at their Boundaries
• Particle Pile-ups and Planetesimal Formation
• Reduction of chemical networks. II. Analysis of the fractional ionisation in protoplanetary discs
• Simulations of dust-trapping vortices in protoplanetary discs
• Growth and saturation of the Kelvin-Helmholtz instability with parallel and anti-parallel magnetic fields
• Formation of Giant Planets by Concurrent Accretion of Solids and Gas inside an Anti-Cyclonic Vortex
• On the accumulation of solid bodies in global turbulent protoplanetary disc models
• Inertial range scaling in numerical turbulence with hyperviscosity
• The effect of the Coriolis force on Kelvin-Helmholtz-driven mixing in protoplanetary disks
• Non-linear dynamics of Kelvin-Helmholtz unstable magnetized jets: three-dimensional effects
• The effect of hyperdiffusivity on turbulent dynamos with helicity
• The effects of the Tidal Force on Shear Instabilities in the Dust Layer of the Solar Nebula
• 2-D models of layered protoplanetary discs: I. The ring instability

Cited by in corpus (86)

• Rapid planetesimal formation in turbulent circumstellar discs
• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
• Asteroids Were Born Big
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration
• Dust and Gas in the disc of HL Tauri: Surface density, dust settling, and dust-to-gas ratio
• Forming Planetesimals in Solar and Extrasolar Nebulae
• Particle Clumping and Planetesimal Formation Depend Strongly on Metallicity
• Breaking the Chains: Hot Super-Earth systems from migration and disruption of compact resonant chains
• Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Linear Evolution and Numerical Methods
• Probing dust grain evolution in IM Lupi's circumstellar disc. Multi-wavelength observations and modelling of the dust disc
• On the migration of protogiant solid cores
• Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks
• Challenges in Planet Formation
• Standing on the shoulders of giants: Trojan Earths and vortex trapping in low mass self-gravitating protoplanetary disks of gas and solids
• Particle Concentration At Planet Induced Gap Edges and Vortices: I. Inviscid 3-D Hydro Disks
• Survival of the mm-cm size grain population observed in protoplanetary disks
• Can dust coagulation trigger streaming instability?
• The Physics of Protoplanetesimal Dust Agglomerates. III. Compaction in Multiple Collisions
• A Well-Posed Kelvin-Helmholtz Instability Test and Comparison
• A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics
• Protoplanetary migration in turbulent isothermal disks
• The initial conditions for planet formation: Turbulence driven by hydrodynamical instabilities in disks around young stars
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? III. Sedimentation driven coagulation inside the snow-line
• A panoptic model for planetesimal formation and pebble delivery
• Planetesimal Population Synthesis: Pebble Flux Regulated Planetesimal Formation
• Vertical Shearing Instabilities in Radially Shearing Disks: The Dustiest Layers of the Protoplanetary Nebula
• A thermodynamic view of dusty protoplanetary disks
• On the accumulation of planetesimals near disc gaps created by protoplanets
• Growth and migration of solids in evolving protostellar disks I: Methods and Analytical tests
• From Grains to Planetesimals: Les Houches Lecture
• Planetesimal formation via sweep-up growth at the inner edge of dead zones
• Dust settling against hydrodynamic turbulence in protoplanetary discs
• Global Modeling of Nebulae with Particle Growth, Drift and Evaporation Fronts. I: Methodology and Typical Results
• Efficient planet formation by pebble accretion in ALMA rings
• Requirements for gravitational collapse in planetesimal formation --- the impact of scales set by Kelvin-Helmholtz and nonlinear streaming instability
• Testing the Jeans, Toomre and Bonnor-Ebert concepts for planetesimal formation: 3D streaming instability simulations of diffusion regulated formation of planetesimals
• Effect of dust radial drift on viscous evolution of gaseous disk
• Dust Settling in Magnetorotationally-Driven Turbulent Discs I: Numerical Methods and Evidence for a Vigorous Streaming Instability
• Macroscopic Dust in Protoplanetary Disks - From Growth to Destruction
• Three-Dimensional Simulations of Kelvin-Helmholtz Instability in Settled Dust Layers in Protoplanetary Disks
• Impacts of dust feedback on a dust ring induced by a planet in a protoplanetary disk
• Recent developments in planet migration theory
• Integration of Particle-Gas Systems with Stiff Mutual Drag Interaction
• Pebble trapping in vortices: three-dimensional simulations
• Forming Planetesimals by Gravitational Instability: I. The Role of the Richardson Number in Triggering the Kelvin-Helmholtz Instability
• Streaming instability in the quasi-global protoplanetary discs
• Colliding Decimetre Dust
• $N$-body Simulation of Planetesimal Formation Through Gravitational Instability of a Dust Layer
• Minimum Dust Abundances for Planetesimal Formation via Secular Gravitational Instabilities
• Planetesimal formation in self-gravitating discs: the effects of particle self-gravity and back-reaction
• Gas accretion damped by dust back-reaction at the snow line
• Numerical determination of the material properties of porous dust cakes
• Effect of dust on Kelvin-Helmholtz instabilities
• Survival of ALMA Rings in the Absence of Pressure Maxima
• Gap and rings carved by vortices in protoplanetary dust
• Planetesimal Initial Mass Functions following Diffusion Regulated Gravitational Collapse
• Induced Turbulence and the Density Structure of the Dust Layer in a Protoplanetary Disk
• The Validity of the Super-Particle Approximation during Planetesimal Formation
• Impact of Local Pressure Enhancements on Dust Concentration inTurbulent Protoplanetary Discs
• Planetesimal formation in self-gravitating discs -- dust trapping by vortices
• The Kelvin-Helmholtz instability in weakly ionised plasmas: Ambipolar dominated and Hall dominated flows
• Dust Settling in Magnetorotationally-Driven Turbulent Discs II: The Pervasiveness of the Streaming Instability and its Consequences
• Radiatively heated, protoplanetary discs with dead zones. I. Dust settling and thermal structure of discs around M stars
• Vortex instabilities triggered by low-mass planets in pebble-rich, inviscid protoplanetary discs
• Dust Concentration at the Boundary Between Steady Super/Sub-Keplerian Flow Created by Inhomogeneous Growth of MRI
• N-Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer in Laminar Gas Disk
• Turbulence in particle laden midplane layers of planet forming disks
• Collisions of solid ice in planetesimal formation
• The Kelvin-Helmholtz instability in weakly ionised plasmas II: multifluid effects in molecular clouds
• The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas
• On the settling of small grains in dusty discs: analysis and formulas
• N-Body Simulation of Planetesimal Formation through Gravitational Instability and Coagulation. II. Accretion Model
• Kelvin-Helmholtz instability and Alfvenic vortex shedding in solar eruptions
• On the pressure of collisionless particle fluids. The case of solids settling in disks
• Effects of Chemistry on Vertical Dust Motion in Early Protoplanetary Disks
• Magnetized Kelvin-Helmholtz instability in the presence of a radiation field
• Morphology and dynamical stability of self-gravitating vortices: Numerical simulations
• Planet Formation
• Photophoretic Levitation and Trapping of Dust in the Inner Regions of Protoplanetary Disks
• The Prospects for Hurricane-like Vortices in Protoplanetary Disks
• The Possibility of the Kelvin-Helmholtz Instability during Sedimentation of Dust Grains in the Protoplanetary Disk
• A Pathway for Collisional Planetesimal Growth in the Ice-Dominant Regions of Protoplanetary Disks
• Nonlinear Evolution of the Unstratified Polydisperse Dust Settling Instability
• Experimental evidence for granular shear-flow instability in the Epstein regime