On the relevance of subcritical hydrodynamic turbulence to accretion disk transport

Laboratoire d'Astrophysique, Observatoire de Grenoble, BP 53, 38041 Grenoble Cedex 9, France e-mail: [geoffroy.lesur;pierre-yves.longaretti]@obs.ujf-grenoble.fr

Received: 22 June 2005
Accepted: 13 September 2005

Abstract

Hydrodynamic unstratified Keplerian flows are known to be linearly stable at all Reynolds numbers, but may nevertheless become turbulent through nonlinear mechanisms. However, in the last ten years, conflicting points of view have appeared on this issue. We have revisited the problem through numerical simulations in the shearing sheet limit. It turns out that the effect of the Coriolis force in stabilizing the flow depends on whether the flow is cyclonic (cooperating shear and rotation vorticities) or anticyclonic (competing shear and rotation vorticities); Keplerian flows are anticyclonic. We have obtained the following results:
i/ The Coriolis force does not quench turbulence in subcritical flows; however, turbulence is more efficient, and much more easily found, in cyclonic flows than in anticyclonic ones.
ii/ The Reynolds number/rotation/resolution relation has been quantified in this problem. In particular we find that the resolution demand, when moving away from the marginal stability boundary, is much more severe for anticyclonic flows than for cyclonic ones. Presently available computer resources do not allow numerical codes to reach the Keplerian regime.
iii/ The efficiency of turbulent transport is directly correlated to the Reynolds number of transition to turbulence Rg, in such a way that the Shakura-Sunyaev parameter . This correlation is nearly independent of the flow cyclonicity. The correlation is expected on the basis of generic physical arguments.
iv/ Even the most optimistic extrapolations of our numerical data show that subcritical turbulent transport would be too inefficient in Keplerian flows by several orders of magnitude for astrophysical purposes. Vertical boundary conditions may play a role in this issue although no significant effect was found in our preliminary tests.
v/ Our results suggest that the data obtained for Keplerian-like flows in a Taylor-Couette settings are largely affected by secondary flows, such as Ekman circulation.