The Orr mechanism is revisited to understand its precise role in the transition of plane Couette flow. By considering homogeneous shear flow and plane Couette flow, it is identified that the Orr mechanism induces a lift-up effect which significantly amplifies spanwise velocity. An optimal perturbation analysis for an individual velocity component reveals that the amplification of spanwise velocity is most active at the streamwise length comparable to the given spanwise length of the perturbation. The relevance of this mechanism to transition is subsequently examined in plane Couette flow. To this end, a set of initial conditions, which combines the optimal perturbation for spanwise velocity with the one for all the velocity components, is considered by varying their amplitudes. Two representative transition scenarios are found: oblique and streak transitions. In the former, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the latter, its role is limited only to the streak breakdown at the late stage of transition. As such, the oblique transition offers a route to turbulence energetically more efficient than the streak transition, at least for the cases examined in the present paper. Finally, the oblique transition is found to share many physical similarities with the transition by the minimal seed.

中文翻译：

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平行剪切流过渡中的Orr机理

重新审视了Orr机制，以了解其在平面Couette流过渡中的确切作用。通过考虑均匀的剪切流和平面库埃特流，可以确定Orr机构会产生提升作用，从而显着放大翼展速度。对单个速度分量的最佳扰动分析表明，在与给定的扰动的翼展方向长度相当的流向长度上，翼展速度的放大最为活跃。随后在飞机库埃特流中研究了该机制与过渡的相关性。为此，可以通过改变振幅的大小来考虑一组初始条件，该条件将翼展方向速度的最佳摄动与所有速度分量的初始摄动相结合。找到两个代表性的过渡方案：斜和条纹过渡。在前者中，由Orr机制放大的翼展速度扰动既引发了条带放大和击穿，而在后者中，其作用仅限于过渡后期的条带击穿。这样，至少对于本文所研究的情况，倾斜过渡提供了比条纹过渡在能量上更有效的湍流路径。最后，发现斜过渡与最小种子的过渡具有许多物理相似性。至少在本文中研究的情况下，倾斜过渡提供了比条纹过渡更有效的湍流路径。最后，发现斜过渡与最小种子的过渡具有许多物理相似性。至少在本文中研究的情况下，倾斜过渡提供了比条纹过渡更有效的湍流路径。最后，发现斜过渡与最小种子的过渡具有许多物理相似性。