Issue |
A&A
Volume 444, Number 1, December II 2005
|
|
---|---|---|
Page(s) | 25 - 44 | |
Section | Astrophysical processes | |
DOI | https://doi.org/10.1051/0004-6361:20053683 | |
Published online | 21 November 2005 |
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
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.
Key words: accretion, accretion disks / hydrodynamics / instabilities / turbulence
© ESO, 2005
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