Simulations of vertical shear instability in accretion discs

Arlt, R.; Урпин, В. А.

doi:10.1051/0004-6361:20035896

Cited by 55 publications

(57 citation statements)

References 25 publications

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“…How robust is the VSI to different radial boundary conditions, and how do these vouch for the true conditions of protoplanetary disk dead zones? As observed by Urpin (2003) and Arlt & Urpin (2004), the local growth rates of the VSI scale approximately by Ω 0 . While it has not yet been theoretically established to what degree the VSI is active in disk regions that also support the MRI, it is worthwhile noting that the growth rate of the VSI (when active in the absence of the MRI) is a factor of slower than the MRI underscoring the differing timescales of the two instabilities.…”

Section: Discussionsupporting

confidence: 57%

“…The vertical shear instability (VSI; Urpin 2003; Urpin & Brandenburg 1998;Arlt & Urpin 2004;Nelson et al 2013;McNally & Pessah 2015;Stoll & Kley 2015), also known as the Goldreich Schubert Fricke instability (Goldreich & Schubert 1967;Fricke 1968) is a linear instability of axisymmetric inertial modes that relies on the vertical shear of the basic near-Keplerian flow state. This instability may be active in non-magnetized parts of protoplanetary accretion disks and is perhaps discernible in their dead zones (Turner et al 2014).…”

Section: Introductionmentioning

confidence: 99%

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Linear analysis of the vertical shear instability: outstanding issues and improved solutions

Umurhan

Nelson

Gressel

2016

A&A

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Context. The vertical shear instability is one of several known mechanisms that are potentially active in the so-called dead zones of protoplanetary accretion disks. A recent analysis of the instability mechanism indicates that a subset of unstable modes shows unbounded growth -both as resolution is increased and when the nominal lid of the atmosphere is extended. This trend suggests that, possibly, the model system is ill-posed. Aims. This research note both examines the energy content of these modes and questions the legitimacy of assuming separable solutions for a problem whose linear operator is fundamentally inseparable. Methods. The reduced equations governing the instability are revisited and the generated solutions are examined using both the previously assumed separable forms and an improved non-separable solution form that is introduced in this paper. Results. Reconsidering the solutions of the reduced equations by using the separable form shows that, while the low-order body modes have converged eigenvalues and eigenfunctions (for both variations in the model atmosphere's vertical boundaries and radial numerical resolution). It is also confirmed that the corresponding high-order body modes and the surface modes indeed show unbounded growth rates. The energy contained in both the higher order body modes and surface modes diminishes precipitously due to the disk's Gaussian density profile. Most of the energy of the instability is contained in the low-order modes. An inseparable solution form is introduced to filter out the inconsequential surface modes, leaving only body modes (both low-and high-order ones). The analysis predicts a fastest growing mode with a specific radial length scale. The growth rates associated with the fundamental corrugation and breathing modes match the growth and length scales observed in previous nonlinear studies of the instability. Conclusions. Linear stability analysis of the vertical shear instability should be done assuming non-separable solutions, especially for settings involving boundaries in the radial direction. We also conclude that the surface modes are relatively inconsequential because of the little energy they contain, and are artifacts of imposing specific kinematic vertical boundary conditions in isothermals disk models.

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Section: Discussionsupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Linear analysis of the vertical shear instability: outstanding issues and improved solutions

Umurhan

Nelson

Gressel

2016

A&A

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“…The first authors analysed the instability for globally isothermal discs and found that the instability in this case could only be triggered by applying finite initial perturbation because the equilibrium state of the disc (being strictly isothermal) did not contain a shear in Ω. The maximum values of α obtained by Arlt & Urpin (2004) were around 6 × 10 −6 , but the turbulence was decaying in the long run. Nelson et al (2013) extended these simulations and performed high resolution simulations of the VSI for so-called locally isothermal discs that contain a radial temperature gradient, but are vertically isothermal.…”

Section: Introductionmentioning

confidence: 99%

Vertical shear instability in accretion disc models with radiation transport

Stoll

Kley

2014

A&A

135

180

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Context. The origin of turbulence in accretion discs is still not fully understood. While the magneto-rotational instability is thought to operate in sufficiently ionised discs, its role in the poorly ionised protoplanetary disc is questionable. Recently, the vertical shear instability (VSI) has been suggested as a possible alternative. Aims. Our goal is to study the characteristics of this instability and the efficiency of angular momentum transport, in extended discs, under the influence of radiative transport and irradiation from the central star. Methods. We use multi-dimensional hydrodynamic simulations to model a larger section of an accretion disc. First we study inviscid and weakly viscous discs using a fixed radial temperature profile in two and three spatial dimensions. The simulations are then extended to include radiative transport and irradiation from the central star.Results. In agreement with previous studies, for the isothermal disc we find a sustained unstable state with a weak positive angular momentum transport of the order of α ≈ 10 −4 . Under the inclusion of radiative transport the disc cools off and the turbulence terminates. For discs irradiated from the central star we again find a persistent instability with a similar α value as for the isothermal case. Conclusions. We find that the VSI can indeed generate sustained turbulence in discs, albeit at a relatively low level with α about few times 10 −4 .

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“…Local stability analyzes (Klahr 2004;Johnson & Gammie 2005a) find transient instability in this context, but shearing box simulations indicate that this does not drive turbulence (Johnson & Gammie 2005b). Urpin (2003) discusses an instability related to vertical shear and heat transport of the Goldreich-Schubert type (Goldreich & Schubert 1967); however, this instability produces only a rather weak radial transport (Arlt & Urpin 2004). More recently, Dubrulle et al (2005b) and Shalybkov & Ruediger (2005) have discussed an instability arising when both the fluid differential rotation and vertical stratification are stabilizing according to the Høiland criterion.…”

Section: Introductionmentioning

confidence: 99%

On the relevance of subcritical hydrodynamic turbulence to accretion disk transport

Lesur

Longaretti

2005

A&A

153

202

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Hydrodynamic unstratified Keplerian flows are known to be linearly stable at all Reynolds numbers, but may nevertheless become turbulent through nonlinear mechanisms. However, in the last ten years, conflicting points of view have appeared on this issue. We have revisited the problem through numerical simulations in the shearing sheet limit. It turns out that the effect of the Coriolis force in stabilizing the flow depends on whether the flow is cyclonic (cooperating shear and rotation vorticities) or anticyclonic (competing shear and rotation vorticities); Keplerian flows are anticyclonic. We have obtained the following results: i/ The Coriolis force does not quench turbulence in subcritical flows; however, turbulence is more efficient, and much more easily found, in cyclonic flows than in anticyclonic ones. ii/ The Reynolds number/rotation/resolution relation has been quantified in this problem. In particular we find that the resolution demand, when moving away from the marginal stability boundary, is much more severe for anticyclonic flows than for cyclonic ones. Presently available computer resources do not allow numerical codes to reach the Keplerian regime. iii/ The efficiency of turbulent transport is directly correlated to the Reynolds number of transition to turbulence Rg, in such a way that the Shakura-Sunyaev parameter α ∼ 1/Rg. This correlation is nearly independent of the flow cyclonicity. The correlation is expected on the basis of generic physical arguments. iv/ Even the most optimistic extrapolations of our numerical data show that subcritical turbulent transport would be too inefficient in Keplerian flows by several orders of magnitude for astrophysical purposes. Vertical boundary conditions may play a role in this issue although no significant effect was found in our preliminary tests. v/ Our results suggest that the data obtained for Keplerian-like flows in a Taylor-Couette settings are largely affected by secondary flows, such as Ekman circulation.

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Simulations of vertical shear instability in accretion discs

Cited by 55 publications

References 25 publications

Linear analysis of the vertical shear instability: outstanding issues and improved solutions

Linear analysis of the vertical shear instability: outstanding issues and improved solutions

Vertical shear instability in accretion disc models with radiation transport

On the relevance of subcritical hydrodynamic turbulence to accretion disk transport

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