  We study linear transient dynamics in a thin Keplerian disc employing a
method based on variational formulation of optimisation problem. It is shown
that in a shearing sheet approximation due to a prominent excitation of density
waves by vortices the most rapidly growing shearing harmonic has azimuthal
wavelength, $\lambda_y$, of order of the disc thickness, $H$, and its initial
shape is always nearly identical to a vortex having the same potential
vorticity. Also, in the limit $\lambda_y\gg H$ the optimal growth $G\propto
(\Omega/\kappa)^4$, where $\Omega$ and $\kappa$ stand for local rotational and
epicyclic frequencies, respectively, what suggests that transient growth of
large scale vortices can be much stronger in areas with non-Keplerian rotation,
e.g. in the inner parts of relativistic discs around the black holes. We
estimate that if disc is already in a turbulent state with effective viscosity
given by the Shakura parameter $\alpha<1$, the considered large scale vortices
with wavelengths $H/\alpha>\lambda_y>H$ have the most favourable conditions to
be transiently amplified before they are damped. At the same time, turbulence
is a natural source of the potential vorticity for this transient activity. We
extend our study to a global spatial scale showing that global perturbations
with azimuthal wavelengths more than an order of magnitude greater than the
disc thickness still are able to attain the growth of dozens of times in a few
Keplerian periods at the inner boundary of disc.
