Experiments and numerical simulations have shown that turbulence in transitional wall-bounded shear flows frequently takes the form of long oblique bands if the domains are sufficiently large to accommodate them. These turbulent bands have been observed in plane Couette flow, plane Poiseuille flow, counter-rotating Taylor–Couette flow, torsional Couette flow, and annular pipe flow. At their upper Reynolds number threshold, laminar regions carve out gaps in otherwise uniform turbulence, ultimately forming regular turbulent–laminar patterns with a large spatial wavelength. At the lower threshold, isolated turbulent bands sparsely populate otherwise laminar domains, and complete laminarization takes place via their disappearance. We review results for plane Couette flow, plane Poiseuille flow, and free-slip Waleffe flow, focusing on thresholds, wavelengths, and mean flows, with many of the results coming from numerical simulations in tilted rectangular domains that form the minimal flow unit for the turbulent–laminar bands.

中文翻译：

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壁限剪切流中的模式

实验和数值模拟表明，如果域足够大以容纳它们，过渡壁边界剪切流中的湍流经常采用长斜带的形式。这些湍流带已在平面 Couette 流、平面 Poiseuille 流、反向旋转 Taylor-Couette 流、扭转 Couette 流和环形管流中观察到。在雷诺数上限时，层流区域在原本均匀的湍流中形成间隙，最终形成具有大空间波长的规则湍流层流模式。在较低的阈值处，孤立的湍流带稀疏地填充在其他层流域中，并且通过它们的消失发生了完全的层流化。我们回顾了平面 Couette 流、平面 Poiseuille 流和自由滑移 Waleffe 流的结果，重点关注阈值，