  The mechanism of transition from laminar state to turbulent state in
Keplerian disks is still unknown. The most popular version today is generation
of turbulence due to magnetorotational instability (MRI). However
magnetohydrodynamic simulations give the value of Shakura-Sunyaev parameter
more then an order of magnitude smaller rather than that found from
observations. One way to solve this problem is the existence of an alternative
or additional mechanism for generating turbulence. It can be the bypass
mechanism, which is responsible for transition to turbulence in Couette and
Poiseuille flows. This mechanism is based on the transient growth of linear
perturbations in the flow with the subsequent transition to the nonlinear
stage. In order to clarify the role of this mechanism in astrophysical disks
first of all it is necessary to calculate the maximal possible growth factor of
linear perturbations in the flow. In this paper the results of such
calculations are presented for perturbations on different scales compared with
the disk thickness. Qualitative description of mechanisms responsible for the
growth will also be presented. It was found that the most rapidly growing shear
harmonics have azimuthal wavelength of the order of the disk thickness. In
addition, their initial form is always similar to the vortex perturbations with
the same potential vorticity. It was shown that the vortices with azimuthal
wavelength more than an order of magnitude in excess of the disc thickness, are
still able to grow by dozens of times.
