Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, ΩL, is the local Keplerian frequency ΩK. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by and , in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where ΩL≥ ΩKand show that, under these conditions, the characteristic length and velocity scales are respectively and , where is twice the Rossby number. It follows that , where is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For , the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation.
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Turbulence in Particle-laden Midplane Layers of Planet-forming Disks
Abstract We examine the settled particle layers of planet-forming disks in which the streaming instability (SI) is thought to be either weak or inactive. A suite of low-to-moderate-resolution 3D simulations in a 0.2H-sized box, whereHis the pressure scale height, are performed using PENCIL for two Stokes numbers, St = 0.04 and 0.2, at 1% disk metallicity. We find that a complex of Ekman-layer jet flows emerge subject to three co-acting linearly growing processes: (1) the Kelvin–Helmholtz instability (KHI), (2) the planet-forming disk analog of the baroclinic Symmetric Instability (SymI), and (3) a later-time weakly acting secondary transition process, possibly a manifestation of the SI, producing a radially propagating pattern state. For St = 0.2 KHI is dominant and manifests as off-midplane axisymmetric rolls, while for St = 0.04 the axisymmetric SymI mainly drives turbulence. SymI is analytically developed in a model disk flow, predicting that it becomes strongly active when the Richardson number (Ri) of the particle–gas midplane layer transitions below 1, exhibiting growth rates , where Ω is the local disk rotation rate. For fairly general situations absent external sources of turbulence it is conjectured that the SI, when and if initiated, emerges out of a turbulent state primarily driven and shaped by at least SymI and/or KHI. We also find that turbulence produced in 2563resolution simulations are not statistically converged and that corresponding 5123simulations may be converged for St = 0.2. Furthermore, we report that our numerical simulations significantly dissipate turbulent kinetic energy on scales less than six to eight grid points.
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- Award ID(s):
- 2007422
- PAR ID:
- 10621853
- Publisher / Repository:
- American Astronomical Society
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 942
- Issue:
- 2
- ISSN:
- 0004-637X
- Page Range / eLocation ID:
- 74
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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