On the Phenomenology of Hydrodynamic Shear Turbulence

Abstract

The question of a purely hydrodynamic origin of turbulence in accretion disks is reexamined, on the basis of a large body of experimental and numerical evidence on various subcritical (i.e., linearly stable) hydrodynamic flows. One of the main points of this paper is that the length scale and velocity fluctuation amplitude which are characteristic of turbulent transport in these flows scale like $Re_m^{-1/2}$, where $Re_m$ is the minimal Reynolds number for the onset of fully developed turbulence. From this scaling, a simple explanation of the dependence of $Re_m$ with relative gap width in subcritical Couette-Taylor flows is developed. It is also argued that flows in the shearing sheet limit should be turbulent, and that the lack of turbulence in all such simulations performed to date is most likely due to a lack of resolution, as a consequence of the effect of the Coriolis force on the large scale fluctuations of turbulent flows. These results imply that accretion flows should be turbulent through hydrodynamic processes. If this is the case, the Shakura-Sunyaev $\alpha$ parameter is constrained to lie in the range $10^{-3}-10^{-1}$ in accretion disks, depending on unknown features of the mechanism which sustains turbulence. Whether the hydrodynamic source of turbulence is more efficient than the MHD one where present is an open question.Comment: 31 pages, 3 figures. Accepted for publication in Ap