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.

中文翻译：

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平面Poiseuille流中三维行波振荡的维持

对三维Navier-Stokes方程的两个解进行了数值研究。这些解决方案描述了平面通道中的流体运动，具有行波形式，并且在流向和跨度方向上是周期性的。结果表明，在每种解决方案中，振荡都是由于流平均速度场中的线性不稳定性而产生的。这种不稳定性是由于存在称为速度高于或低于平均速度的区域的沿流条纹。揭示了一种维持引起条纹的流向涡流的机制。所获得的结果证实并扩展了有关近壁湍流结构形成机理的现有知识。