  Subcritical transition to turbulence in Keplerian accretion disks is still a
controversial issue and some theoretical progress is required in order to
determine whether or not this scenario provides a plausible explanation for the
origin of angular momentum transport in non-magnetized accretion disks.
Motivated by the recent discoveries of exact nonlinear steady self-sustaining
solutions in linearly stable non-rotating shear flows, we attempt to compute
similar solutions in Rayleigh-stable rotating plane Couette flows and to
identify transition mechanisms in such flows by combining nonlinear
continuation methods and asymptotic theory. We obtain exact nonlinear solutions
for Rayleigh-stable cyclonic regimes but show that it is not possible to
compute solutions for Rayleigh-stable anticyclonic regimes, including Keplerian
flow, using similar techniques. We also present asymptotic descriptions of
these various problems at large Reynolds numbers that provide some insight into
the differences between the non-rotating and Rayleigh-stable anticyclonic
regimes and derive some necessary conditions for mechanisms analogous to the
non-rotating self-sustaining process to be present in flows on the Rayleigh
line. Our results demonstrate that subcritical transition mechanisms cannot be
identified in wall-bounded Rayleigh-stable anticyclonic shear flows by
transposing directly the phenomenology of subcritical transition in cyclonic
and non-rotating wall-bounded shear flows. Asymptotic developments, however,
leave open the possibility that nonlinear self-sustaining solutions may exist
in unbounded or periodic flows on the Rayleigh line. These could serve as a
starting point to discover solutions in Rayleigh-stable flows, but the
nonlinear stability of Keplerian accretion disks remains to be determined.
