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Journal Articles Astronomy and Astrophysics - A&A Year : 2005

An hydrodynamic shear instability in stratified disks

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Abstract

We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity Omega decreases outwards with radius r. At not too small stratification, its growth rate is a fraction of Omega. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when d ln Omega / d ln r =-3/2 (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.
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Dates and versions

hal-03732602 , version 1 (27-10-2022)

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B. Dubrulle, L. Marié, Ch. Normand, D. C. Richard, Franck Hersant, et al.. An hydrodynamic shear instability in stratified disks. Astronomy and Astrophysics - A&A, 2005, 429, pp.1-13. ⟨10.1051/0004-6361:200400065⟩. ⟨hal-03732602⟩
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