In this paper we consider the problem proposed by A.N. Kolmogorov to study the reasons of turbulence. We consider the action of the external periodic field along one of the coordinates on a viscous and inviscid conductive media in the two-dimensional case. We propose a numerical study of this problem based on the solution of the systems of the Euler and mainly the Navier-Stokes equations. The calculations show that under certain conditions periodic vortex structures may appear in the liquid, similar to the “parquet” mode in the Kolmogorov task, with the subsequent development of the self-similar regime.