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Enhanced angular momentum transfer through the boundary layer near thesurface of weakly magnetised accreting star is required in order to explain theobserved accretion timescales in low-mass X-ray binaries, cataclysmic variablesor young stars with massive protoplanetary discs. Accretion disc boundary layeris locally represented by incompressible homogeneous and boundless flow of thecyclonic type, which is linearly stable. Its non-linear instability at theshear rates of order of the rotational frequency remains an issue. We arguethat hydrodynamical subcritical turbulence in such a flow is sustained by thenon-linear feedback from essentially three-dimensional vortices, which aregenerated by quasi-two-dimensional trailing shearing spirals grown to highamplitude via the swing amplification. We refer to those three-dimensionalvortices as cross-rolls, since they are aligned in the shearwise direction incontrast to streamwise rolls generated by the anti-lift-up mechanism inrotating shear flow on the Rayleigh line. Transient growth of cross-rolls isstudied analytically and further confronted with direct numerical simulations(DNS) of dynamics of non-linear erturbations. DNS performed in a tall box showthat transition Reynolds number $R_T$ as function of shear rate accords withthe line of constant maximum transient growth of cross-rolls. The transition inthe tall box has been observed until the shear rate three times higher than therotational frequency, when $R_T\sim 50000$. Assuming that the cross-rolls arealso responsible for turbulence in the Keplerian flow, we estimate $R_T\lesssim10^8$ in this case. The most favourable shear rate to test the existence ofturbulence in the quasi-Keplerian regime may be sub-Keplerian and equalapproximately to $1/2$.

Subcritical transition to turbulence in accretion disc boundary layer