  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; ii/ 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 $\alpha\sim
1/Rg$. 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. 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.
