Rossby wave instability in 3D discs

Méheut, H.; Yu, Cong; Lai, Dong

doi:10.1111/j.1365-2966.2012.20789.x

Cited by 61 publications

(73 citation statements)

References 48 publications

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“…Recently published studies (Lin 2012;Meheut et al 2012) indicate and confirm that the Rossby wave instability both endures in three-dimensional settings and appears to be dominated by the (largely) two-dimensional dynamical process originally characterizing the effect. A reduced shallow-water system that is nonasymptotic will aid in better understanding the development of this instability as well as others that may be concurrently present in these flow configurations.…”

Section: Summary and Discussionmentioning

confidence: 87%

Potential vorticity dynamics in the framework of disk shallow-water theory

Umurhan¹

2012

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Context. We consider potential vorticity dynamics for astrophysical disks. Aims. The aim of this work is to extend exploration of shear instabilities in cold astrophysical disks that are three-dimensional and whose mean states are baroclinic. In particular, we seek to demonstrate the potential existence of traditional baroclinic instabilities in meteorological studies. We show this in a simplified two-layer Philips disk model of a midplane symmetric disk. Methods. We analyze the dynamical normal-mode response of thin annular disks with two strongly localized potential vorticity gradients, one in each of two disk layers. Each disk layer is of constant but differing densities. The resulting mean azimuthal velocity profile shows a variation in the vertical direction, implying that the system is baroclinic in the mean state. The stability of the system is treated in the context of disk shallow-water theory, wherein azimuthal disturbances are much longer than the corresponding radial or vertical scales. The normal-mode problem is solved numerically using two different methods. Results. The results of a symmetric single-layer barotropic model is considered and it is found that instability persists for models in which the potential vorticity profiles are not symmetric, consistent with previous results. The instaiblity is interpreted in terms of interacting Rossby waves. For a two-layer system, in which the flow is fundamentally baroclinic, we report here that instability takes on the form of mixed barotropic-baroclinic type: instability occurs, but it qualitatively follows the pattern of instability found in the barotropic models. Instability arises because of the phase locking and interaction of the Rossby waves between the two layers. The strength of the instability weakens as the density contrast between layers increases. Conclusions. Baroclinic instability is feasible for astrophysical disks but has the character of mixed barotropic-baroclinic type. The instability as explored in this study could be present in protoplanetary disks with weak vertical density stratification.

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Section: Summary and Discussionmentioning

confidence: 87%

Potential vorticity dynamics in the framework of disk shallow-water theory

Umurhan¹

2012

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“…One intriguing characteristic of these vortices is that the vertical displacements of gas in the vortices centres over the whole vertical scale height of the disk. This was first obtained in numerical simulations (Meheut et al 2010) and then confirmed analytically (Meheut et al 2012b;Lin 2012). These structures are of particular interest for the study of the dust concentration.…”

Section: Introductionmentioning

confidence: 98%

“…We used the Lax-Friedrich scheme (see Tóth 1996) with a Koren limiter (Koren 1993). A global simulation of the disk is needed to fully capture the RWI, but as the instability is symmetric about the midplane of the disk we only need to compute the upper half of it (Meheut et al 2010(Meheut et al , 2012b. For those reasons, the disk is simulated on a cylindrical grid with r [1, 6 AU], ϕ [0, 2π], and z [0, 0.5 AU].…”

Section: Methodsmentioning

confidence: 99%

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Dust-trapping Rossby vortices in protoplanetary disks

Méheut¹,

Méliani²,

Varnière³

et al. 2012

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111

109

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Context. One of the most challenging steps in planet formation theory is the one leading to the formation of planetesimals of kilometre size. A promising scenario involves the existence of vortices able to concentrate a large amount of dust and grains in their centres. Up to now this scenario has mostly been studied in 2D razor thin disks. A 3D study including, simultaneously, the formation and resulting dust concentration of the vortices with vertical settling, is still missing. Aims. The Rossby wave instability self-consistently forms 3D vortices, which have the unique quality of presenting a large-scale vertical velocity in their centre. Here we aim to study how this newly discovered effect can alter the dynamic evolution of the dust. Methods. We performed global 3D simulations of the RWI in a radially and vertically stratified disk using the code MPI-AMRVAC. After the growth phase of the instability, the gas and solid phases are modelled by a bi-fluid approach, where the dust is considered as a fluid without pressure. Both the drag force of the gas on the dust and the back reaction of the dust on the gas are included. Multiple grain sizes from 1 mm to 5 cm are used with a constant density distribution. Results. We obtain in a short timescale a high concentration of the largest grains in the vortices. Indeed, in 3 rotations the dust-to-gas density ratio grows from 10 −2 to unity leading to a concentration of mass up to that of Mars in one vortex. The presence of the radial drift is also at the origin of a dust pile-up at the radius of the vortices. Lastly, the vertical velocity of the gas in the vortex causes the sedimentation process to be reversed, the mm size dust is lifted and higher concentrations are obtained in the upper layer than in the midplane. Conclusions. The Rossby wave instability is a promising mechanism for planetesimal formation, and the results presented here can be of particular interest in the context of future observations of protoplanetary disks.

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“…The vertical structure of the modes has recently be studied in more detail (Meheut et al 2012;Lin 2012) with dedicated tools as those presented in Zhang & Lai (2006).…”

Section: Outlooksmentioning

confidence: 99%

Formation and long-term evolution of 3D vortices in protoplanetary discs

Méheut¹,

Keppens²,

Casse³

et al. 2012

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Context. In the context of planet formation, anticyclonic vortices have recently received much attention for the role they can play in planetesimal formation. Radial migration of intermediate-size solids towards the central star may prevent them from growing to larger solid grains. On the other hand, vortices can trap the dust and accelerate this growth, counteracting fast radial transport. Several effects have been shown to affect this scenario, such as vortex migration or decay. Aims. We aim to study the formation of vortices by the Rossby wave instability and their long-term evolution in a full threedimensional (3D) protoplanetary disc. Methods. We used a robust numerical scheme combined with adaptive mesh refinement in cylindrical coordinates, which allowed us to affordably compute long-term 3D evolutions. We considered a full disc radially and vertically stratified, in which vortices can be formed by the Rossby wave instability. Results. We show that the 3D Rossby vortices grow and survive over hundreds of years without migration. The localised overdensity that initiated the instability and vortex formation survives the growth of the Rossby wave instability for very long times. When the vortices are no longer sustained by the Rossby wave instability, their shape changes towards more elliptical vortices. This allows them to survive shear-driven destruction, but they may be prone to elliptical instability and slow decay. Conclusions. When the conditions for growing Rossby-wave-related instabilities are maintained in the disc, large-scale vortices can survive over very long timescales and may be able to concentrate solids.

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Rossby wave instability in 3D discs

Cited by 61 publications

References 48 publications

Potential vorticity dynamics in the framework of disk shallow-water theory

Potential vorticity dynamics in the framework of disk shallow-water theory

Dust-trapping Rossby vortices in protoplanetary disks

Formation and long-term evolution of 3D vortices in protoplanetary discs

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