Maintenance of oscillations in three-dimensional traveling waves in plane Poiseuille flows. (English. Russian original) Zbl 1405.35142

Mosc. Univ. Mech. Bull. 73, No. 4, 91-96 (2018); translation from Vestn. Mosk. Univ., Ser. I 73, No. 4, 47-53 (2018).
Summary: 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.


35Q30 Navier-Stokes equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35C07 Traveling wave solutions
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