Numerical experiment in the problem of propagation of small perturbations in a round pipe

Flow of viscous incompressible isothermal liquid in round pipe at moderate Reynolds numbers corresponding to laminar and turbulent modes is considered. The problem is solved in a non-stationary formulation, the spatial coordinate system of Euler is used. As a mathematical algorithm, quasi-hydrodynamic (QHD) equations are used. Within the framework of this algorithm, it was first shown that random perturbations of the input speed in the channel attenuate for small Reynolds numbers and lead to the formation of a turbulent mode for large Reynolds numbers.