ИСТИНА

The behaviour of hydrodynamical fluctuations in gaseous component of young protoplanetary disks is of primary importance for planetary system formation and evolution. It is also related to the major problem of the enhanced angular momentum transfer and nature of the effective viscosity in protoplanetary disks and, more generally, in Keplerian disks. Having a significant gradient of angular velocity, these disks are capable of a substantial transient effects in dynamics of perturbations. In our study we consider such effects employing a variational formulation of the optimisation problem what allows one to obtain an optimal initial perturbations that exhibit the highest possible growth at a specified time interval. In particular, we use our method to study the transient dynamics in a shearing sheet approximation. It is shown that the most rapidly growing shearing harmonic has azimuthal wavelength of order of the disc thickness. Moreover, its initial shape is always nearly identical to vortical perturbation having the same potential vorticity. We also extend our study to a global spatial scale taking into account the background vorticity gradient and the disc cylindrical geometry. It is shown that global vortices 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 disk boundary. We estimate that if disc is already in a turbulent state with small effective viscosity, these large scale vortices have the most favorable 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. Thus, we conclude that transiently growing vortical structures on scales above the disc thickness should provide an additional angular momentum transfer in discs and should affect their variability properties as well.