A hydrodynamic shear instability in stratified disks

Abstract

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 d ln Ω/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.

Experimental Analysis of the Stratorotational Instability in a Cylindrical Couette Flow

“…We have observed the new Strato-rotational Instability in the form of non-axisymmetric oscillating modes. Our results validate the theoretical results of Molemaker et al [11], Yavneh et al [12], Shalybkov and Rüdiger [13] and Dubrulle et al [14]. In particular, instability thresholds, axial and azimuthal wavenumbers and temporal frequencies of the helicoidal travelling modes (m = 0) have been measured for a fixed Froude number F r = 0.5, an aspect ratio η = 0.80 and for different Reynolds numbers.…”

“…Moreover, and contrary to the classical Taylor vortices of the centrifugal instability, the most unstable modes should be non-axisymmetric. This theoretical analysis has then been continued in an astrophysical context by Shalybkov and Rüdiger [13] and extended to the stability of accretion disk Keplerian flows by Dubrulle et al [14] who gave to this new instability its now accepted appellation Strato-Rotational Instability (SRI). To the best of our knowledge, and despite explicit calls recently published [11,13], no experimental validation of these theoretical predictions has yet been provided, apart from a short comment made by Withjack and Chen [4] in 1974 and a stability curve that was determined by Boubnov and Hopfinger in 1997 [15].…”

The strato-rotational instability of Taylor–Couette and Keplerian flows

“…This corresponds to the local approximation of the Keplerian flow for which both flows possess the same shearto-rotation ratio Ω /Om (Ω being the angular velocity) equal to −3/2. The stability properties of the flow in this small-gap limit have been obtained in Yavneh et al (2001) and Dubrulle et al (2005b). We shall see that they sensibly differ from those obtained for an unbounded Keplerian flow.…”

Stability and turbulent transport in Taylor–Couette flow from analysis of experimental data

“…A vertical stable stratification added onto the flow plays the same role as a vertical magnetic field at low P m. In the inviscid limit, its presence changes the Rayleigh criteria into r 2 ∂ r Ω 2 > 0 [40,41]) . This means that all anti-cyclonic flows are potentially linearly unstable.…”

“…This means that all anti-cyclonic flows are potentially linearly unstable. The role of dissipation on the instability has been studied numerically [41,42]) and experimentally [43,44]. It was found that stratification stabilizes the flow in the GSPC regime, while it destabilizes it in the GSBC anti-cyclonic regime.…”