On the relevance of subcritical hydrodynamic turbulence to accretion disk transport

By G. Lesur, Pierre-Yves Longaretti. 2005

134 citations recorded by the source corpus.

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 $\alpha\sim 1/Rg$. 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.

Subfields: Computational Mechanics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/00b76b3b12b9697ea26f0ccba80e153b8a2ff042

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Global and Planetary Change

Citations in the corpus

MHD simulations of the magnetorotational instability in a shearing box with zero net flux II. The effect of transport coefficients (2007, methodology): “This code has been successfully used for pure HD (Lesur & Longaretti 2005) and MHD-MRI (Lesur & Longaretti 2007) problems.”
Dynamics of Protoplanetary Disks (2010, background): “For shear-driven instabilities, theoretical arguments (e.g Lesur & Longaretti 2005) and, to a limited extent, laboratory experiments (Ji et al. 2006), have largely excluded the existence of instabilities that would yield efficient angular momentum transport.”
The subcritical baroclinic instability in local accretion disc models (2009, methodology): “…transient growths could lead to a nonlinear instability explaining the result of Klahr & Bodenheimer (2003), but it is still unclear whether transient growths are relevant for nonlinear instabilities (see e.g. Lesur & Longaretti 2005, and reference therein for a complete discussion of this point).”
MORPHOLOGICAL QUENCHING OF STAR FORMATION: MAKING EARLY-TYPE GALAXIES RED (2009, background): “Mechanism (ii) does not occur in our simulations since the critical Reynolds number above which rotational shear instabilities might be able to grow is largely beyond reach (Ji et al. 2006; Lesur & Longaretti 2005).”
On internal wave breaking and tidal dissipation near the centre of a solar-type star (2010, methodology): “In the paper we only analyse the SNOOPY results, since they are at a much higher resolution, but here describe our problem set-up in ZEUS, for completeness.”