An hydrodynamic shear instability in stratified disks

Type Article
Date 2005-01
Language English
Author(s) Dubrulle B1, Marie Louis1, Normand C2, Richard D1, 3, Hersant F4, 5, Zahn Jp3
Affiliation(s) 1 : CEA Saclay, GIT, SPEC, DRECAM,DSM,CNRS,URA 2464, F-91191 Gif Sur Yvette, France.
2 : CEA Saclay, SPHT, DSM, CNRS,URA 2306, F-91191 Gif Sur Yvette, France.
3 : Observ Paris, LUTH, F-92195 Meudon, France.
4 : Inst Theoret Astrophys, D-6900 Heidelberg, Germany.
5 : Observ Paris, LESIA, F-92195 Meudon, France.
Source Astronomy & Astrophysics (0004-6361) (EDP Sciences), 2005-01 , Vol. 429 , N. 1 , P. 1-13
DOI 10.1051/0004-6361:200400065
WOS© Times Cited 93
Keyword(s) accretion, accretion disks, hydrodynamic, instabilities, turbulence
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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