Maintenance of oscillations in three-dimensional traveling waves in plane Poiseuille flows

Two solutions of the three-dimensional Navier–Stokes equations are studied numerically. The solutions describe the fluid motion in a plane channel. They are traveling waves that are periodic in streamwise and spanwise directions. We show that, in each solution, oscillations arise as a result of a linear instability of the streamwise averaged velocity field. We associate the instability with the existence of streamwise streaks that are domains with relatively high and low fluid velocity. We present the streamwise vortices generation mechanism and show that the vortices maintain the streaks. The obtained results confirm and refine the existing notions about the generation of the near-wall turbulent structures.