ANGULAR-MOMENTUM TRANSPORT IN ACCRETION DISKS VIA CONVECTION

In this paper, we investigate, by three-dimensional hydrodynamical sim ulations, the role that vertical convective motions play in providing angular momentum transport in a Keplerian disk. We begin by deriving s imple and general analytic constraints upon the correlated radial and azimuthal velocity fluctuation tensor, critical to the direction of en ergy and angular momentum transport. When azimuthal pressure gradients are small, as is often the case for incompressible turbulence in a sh earing disk, the constraints are particularly straightforward and stri king: they imply there can be no net outward transport in a steady flo w. (More precisely, any steady transport that is present must be due t o the explicit forcing by azimuthal pressure gradients.) Furthermore, numerical simulations show inward transport even in disks characterize d by solid body rotation, which are quite far from axisymmetric. If th e kinetic energy of rotational velocity fluctuations increases with ti me because of coupling with the mean flow (as in an instability), the relationship suggests (and our numerical simulations confirm) that in a Keplerian disk the Reynolds stress is negative, i.e., that the angul ar momentum and energy transport is inward. The analogous relationship for shearing but nonrotating (Cartesian) flow displays the opposite s ign for the fluctuation tensor, i.e., an increase in the ''streamwise' ' velocity fluctuations is associated with outward (from higher moment um to smaller momentum) transport. Although Cartesian shear flows are known to be extremely sensitive to disruption by nonlinear secondary i nstabilities, hydrodynamical calculations presented here demonstrate t hat Keplerian disk flows show no such inclination. We suggest that the key to understanding this critical difference is the very different n ature of the interaction between the mean flow and the transport in ea ch system. We provide a physical interpretation of our findings in ter ms of the role epicyclic oscillations play in mediating angular moment um transport. We base our convection simulations upon a reproducible a nalytic expression for the vertical profile of an unstable equilibrium state in a stratified disk. The nonlinear evolution of the convective cells is then followed after the initial profile is perturbed. Convec tion can be sustained only if an ad hoc source of heating is added to the disk midplane. The net transport associated with steady convection is small and on average inward. A comparison between the volume-avera ged Reynolds stress and the time rate of change of the azimuthal kinet ic energy associated with fluctuations in the rotational velocity show s remarkable agreement with our simple analytic predictions. Taken as a whole, these results offer little hope that convection-or any other form of incompressible hydrodynamic turbulence-is likely to be a signi ficant source of angular momentum transport in nonmagnetic disks. Cohe rent pressure forcing by, e.g., spiral density waves, remains a viable option.