A minimal model for vertical shear instability in protoplanetary accretion disks

Yellin-Bergovoy, Ron; Umurhan, O. M.; Heifetz, Eyal

doi:10.1080/03091929.2021.1941921

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…We argue by analogy to submesoscale atmospheric and oceanic dynamics that dynamical activity in these settled particle layers is driven by the twin action of the SymI and KH roll-up. We suspect that the significance of the SymI in characterizing the VSI (Yellin-Bergovoy et al 2021) and the vertical shearing streaming instability (VSSI; Lin 2021) also applies to the turbulent development of the midplane dynamics we report here-especially for simulations showing sustained turbulent activity in which the SI emerges either weakly or not at all. Indeed, analysis of the St = 0.04 simulation after it achieves a quasi-steady shear-driven turbulent state shows that the effective Richardson numbers are near or larger than 1/4, an important feature also observed in the simulations reported in Gerbig et al (2020).…”

Section: Motivationmentioning

confidence: 79%

“…We note that it has recently been argued that the vertical shear instability (VSI; Nelson et al 2013) is the disk analog of the SymI (sometimes referred to as "sloping convection" in the geophysical fluid dynamics literature; Yellin-Bergovoy et al 2021). Indeed, a latitudinal temperature gradient gives rise to a radial variation in planetary zonal flow, while a similar vertical variation of Keplerian flow emerges from a radial temperature gradient that leads to the VSI.…”

Section: Disk Analog Of Symmetric Instabilitymentioning

confidence: 83%

“…In both scenarios, therefore, there is a misalignment between the density and azimuthal/zonal flow isolines. For further exposition see Yellin-Bergovoy et al (2021).…”

Section: Disk Analog Of Symmetric Instabilitymentioning

confidence: 99%

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Turbulence in Particle-laden Midplane Layers of Planet-forming Disks

Sengupta

Umurhan

2023

ApJ

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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, where H is 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 ≤ 2 / Ri − 2 · Ω , 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 2563 resolution simulations are not statistically converged and that corresponding 5123 simulations 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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Section: Motivationmentioning

confidence: 79%

Section: Disk Analog Of Symmetric Instabilitymentioning

confidence: 83%

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Turbulence in Particle-laden Midplane Layers of Planet-forming Disks

Sengupta

Umurhan

2023

ApJ

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“…Whether the VSI is truly quasi-2D in dynamical character or, perhaps, dynamically more akin to flows exhibiting a splitcascade remains to be determined only once higher-resolution simulations are conducted that capture its fastest growing linear modes with lengthscale l max . For the VSI Umurhan et al 2016;Yellin-Bergovoy et al 2021), which needs at least 20-40 grid point resolution across l max to numerically resolve any potential downscale energy cascade (for instance, see the relative high-resolution but radially restricted VSI simulations of Richard et al 2016).…”

Section: Vsi and Other Forms Of Turbulencementioning

confidence: 99%

Formation of the First Planetesimals via the Streaming Instability in Globally Turbulent Protoplanetary Disks?

Estrada

Umurhan

2023

ApJ

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Using self-consistent models of turbulent particle growth in an evolving protoplanetary nebula of solar composition, we find that recently proposed local metallicity and Stokes number criteria necessary for the streaming instability to generate gravitationally bound particle overdensities are generally not approached anywhere in the disk during the first million years, an epoch in which meteoritic and observational evidence strongly suggests that the formation of the first planetesimals and perhaps giant planet core accretion are already occurring.

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Vertical shear instability with partially reflecting boundary conditions

Wu,

Yu,

Cui

2024

Monthly Notices of the Royal Astronomical Society

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The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary disks. Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disk surfaces. VSI depends critically on the boundary behaviors of waves at the disk surfaces. We extend earlier studies by performing a comprehensive numerical analysis of VSI with partially reflecting BCs for both the axisymmetric and non-axisymmetric unstable VSI modes. We find that the growth rates of the unstable modes diminish when the outgoing component of the flow is greater than the incoming one for high-order body modes. When the outgoing wave component dominates, the growth of VSI is notably suppressed. We find that the non-axisymmetric modes are unstable and they grow at a rate that decreases with the azimuthal wavenumber. The different BCs at the lower and upper disk surfaces naturally lead to non-symmetric modes relative to the disk midplane. The potential implications of our studies for further understanding planetary formation and evolution in protoplanetary disks (PPDs) are also briefly discussed.

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A minimal model for vertical shear instability in protoplanetary accretion disks

Cited by 6 publications

References 26 publications

Turbulence in Particle-laden Midplane Layers of Planet-forming Disks

Turbulence in Particle-laden Midplane Layers of Planet-forming Disks

Formation of the First Planetesimals via the Streaming Instability in Globally Turbulent Protoplanetary Disks?

Vertical shear instability with partially reflecting boundary conditions

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