  Enhanced angular momentum transfer through the boundary layer near the
surface of weakly magnetised accreting star is required in order to explain the
observed accretion timescales in low-mass X-ray binaries, cataclysmic variables
or young stars with massive protoplanetary discs. Accretion disc boundary layer
is locally represented by incompressible homogeneous and boundless flow of the
cyclonic type, which is linearly stable. Its non-linear instability at the
shear rates of order of the rotational frequency remains an issue. We argue
that hydrodynamical subcritical turbulence in such a flow is sustained by the
non-linear feedback from essentially three-dimensional vortices, which are
generated by quasi-two-dimensional trailing shearing spirals grown to high
amplitude via the swing amplification. We refer to those three-dimensional
vortices as cross-rolls, since they are aligned in the shearwise direction in
contrast to streamwise rolls generated by the anti-lift-up mechanism in
rotating shear flow on the Rayleigh line. Transient growth of cross-rolls is
studied analytically and further confronted with direct numerical simulations
(DNS) of dynamics of non-linear erturbations. DNS performed in a tall box show
that transition Reynolds number $R_T$ as function of shear rate accords with
the line of constant maximum transient growth of cross-rolls. The transition in
the tall box has been observed until the shear rate three times higher than the
rotational frequency, when $R_T\sim 50000$. Assuming that the cross-rolls are
also responsible for turbulence in the Keplerian flow, we estimate $R_T\lesssim
10^8$ in this case. The most favourable shear rate to test the existence of
turbulence in the quasi-Keplerian regime may be sub-Keplerian and equal
approximately to $1/2$.
