A hydrodynamic shear instability in stratified disks

¹ GIT/SPEC/DRECAM/DSM, CNRS, URA 2464, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: bdubrulle@cea.fr
² SPHT/DSM, CNRS, URA 2306 CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
³ LUTH, Observatoire de Paris, 92195 Meudon, France
⁴ Institut für Theoretische Astrophysik, Heidelberg, Germany
⁵ LESIA, Observatoire de Paris, 92195 Meudon, France

Received: 27 November 2002
Accepted: 5 August 2004

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 Ω decreases outwards with radius r. At not too small stratification, its growth rate is a fraction of Ω. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when (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.