Maintenance of Oscillations in Three-Dimensional Traveling Waves in Plane Poiseuille Flows / *V. O. Pimanov.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. № 4. P. 47-53
[Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 91-96].

Two solutions of three-dimensional Navier–Stokes equations are studied numerically. These solutions describe the fluid motion in a plane channel, are of the traveling-wave form, and are periodic in the streamwise and spanwise directions. It is shown that, in each solution, the oscillations arise as a result of linear instability in the streamwise averaged velocity field. This instability is due to the existence of streamwise streaks known as the regions where the velocity is higher or lower than the mean velocity. A mechanism for the maintenance of streamwise vortices causing the formation of streaks is revealed. The obtained results confirm and extend the existing knowledge about the mechanism for the formation of near-wall turbulent structures.

*Key words*:
Navier–Stokes equations, direct numerical simulations, plane channel, turbulent flow,
near-wall streaks, streamwise vortices.