On the Phenomenology of Hydrodynamic Shear Turbulence

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

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Boundary-layer turbulence as a kangaroo process

A nonlocal mixing-length theory of turbulence transport by finite size eddies is developed by means of a novel evaluation of the Reynolds stress. The analysis involves the contruct of a sample path space and a stochastic closure hypothesis. The simplifying property of exhange (strong eddies) is satisfied by an analytical sampling rate model. A nonlinear scaling relation maps the path space onto the semi-infinite boundary layer. The underlying near-wall behavior of fluctuating velocities perfectly agrees with recent direct numerical simulations. The resulting integro-differential equation for the mixing of scalar densities represents fully developed boundary-layer turbulence as a nondiffusive (Kubo-Anderson or kangaroo) type of stochastic process. The model involves a scaling exponent (with → in the diffusion limit). For the (partly analytical) solution for the mean velocity profile, excellent agreement with the experimental data yields 0.58. © 1995 The American Physical Society