Negative Reynolds stress generation by accretion disc convection

Abstract

A B S T R A C TThe phenomenon of negative viscosity-alpha in convectively unstable Keplerian accretion discs is discussed. The convection is considered as a random flow with an axisymmetric mesoscale pattern. Its correlation tensor is computed with a time-averaging procedure using Kley's 2D hydrocode. There is a distinct anisotropy between the turbulence intensities in the radial and azimuthal directions, i.e. the radial velocity rms dominates the azimuthal one. As a consequence, an extra term in the expression for the turbulent transport of angular momentum appears which does not vanish for rigid rotation ('L-effect'). It is negative ('inwards transport') and even seems to dominate the positive contribution of the eddy viscosity representing outwards transport of angular momentum. For a turbulence model close to that of the mixing-length theory, the rotational influence on the anisotropy of the turbulence intensities, ku 0 2 R l 2 ku 0 2 f l, and the covariance ku 0 R u 0 f l -representing the angular momentum transport -is computed and compared with the accretion disc simulations. Indeed, the negative angular momentum transport can be explained with the observed dominance of the radial turbulence intensity. If, on the other hand, in turbulence fields the azimuthal intensity would dominate or the turbulence is even isotropic, then we always find a positive transport of the angular momentum.

The eddy heat-flux in rotating turbulent convection

“…Canuto, Minotti & Schilling (1994) demonstrated for their rather general model how the global rotation influences the formation of anisotropy between the components of the turbulence intensity. If in the equatorial plane without rotation both the turbulent intensities u ′2 r and u ′2 φ strongly differ then the rotation is smoothing the differences and may even completely suppress them (Rüdiger, Tschäpe & Kitchatinov 2002). For faster rotation there is thus a clear tendency for a return-to-isotropy.…”

Excitation of spiral density waves by convection in accretion discs

“…However, the non‐linear development of these axisymmetric [two‐dimensional (2D)] convective modes turned out to lead to inward (i.e. towards the central star) transport of angular momentum (Kley, Papaloizou & Lin 1993; Rüdiger, Tschäpe & Kitchatinov 2002), which is obviously not what is required for the accretion of matter from the disc on to the central star.…”

“…Ruden et al (1988) carried out a linear analysis of axisymmetric convective modes in discs and, although linear axisymmetric modes do not produce torques themselves to transport angular momentum, these authors also estimated -from the radial wavelengths and growth rates of the most unstable axisymmetric modes -a Shakura-Sunyaev α ∼ 10 −3 − 10 −2 , which might be in the case of non-linear axisymmetric or non-axisymmetric vertical convection. However, the non-linear development of these axisymmetric (two-dimensional) convective modes turned out to lead to inward (i.e., towards the central star) transport of angular momentum (Kley et al 1993;Rüdiger et al 2002), which is obviously not what is required for the accretion of matter from the disc onto the central star.…”

Angular Momentum Transport in Convectively Unstable Shear Flows

“…Convection is commonly not considered as a viable angular momentum transport mechanism in accretion disks since several studies have indicated that the transport owing to convection occurs inward (e.g. Cabot & Pollack 1992;Ryu & Goodman 1992;Stone & Balbus 1996;Cabot 1996;Rüdiger et al 2002). Furthermore, in an influential paper, Stone & Balbus (1996, hereafter SB96) presented numerical simulations of hydrodynamic convection where the transport was indeed found to be small and directed inward on average.…”