Transitional separating flow induced by a rectangular plate subjected to uniform incoming flow at Reynolds number (based on the incoming velocity and half plate height) 2000 is investigated using direct numerical simulation. The objective is to unveil the long-lasting mystery of low-frequency flapping motion (FM) in flow separation. At a fixed streamwise-vertical plane or from the perspective of previous experimental studies using pointwise or planar measurements, FM manifests as a low-frequency periodic switching between low and high velocities covering the entire separation bubble. The results indicate that in three-dimensional space, FM reflects an intricate evolution of streamwise elongated streaky structures under the influence of separated shear layer and mean flow reversal. The FM is an absolute instability, and is initiated through a lift-up mechanism boosted by mean flow deceleration near the crest of the separating streamline. At this particular location, the shear bends the vortex filament abruptly, so that one end is vertically struck into the first half of the separation bubble, whereas the other end is extended in the streamwise direction in the second half of the separation bubble. These two ends of vortex filament are mutually sustained and also stretched by the vertical acceleration and streamwise acceleration in the first and second halves of the separation bubble, respectively. This process periodically switches the low-velocity (or high-velocity) streaky structure to a high-velocity (or low-velocity) streaky structure encompassing the entire separation bubble, and thus flaps the separated shear layer up and down in the vertical direction. A ‘large vortex’ shedding manifests when the streaky structure switches signs. This large vortex is fundamentally different from the spanwise vortex shedding residing in the shear layer originated from the Kelvin–Helmholtz instability and successive vortex amalgamation. It is also believed that the three-dimensional evolution of streaky structures in the form of FM is applicable for both geometry- and pressure-induced separating flows.

中文翻译：

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流动分离中的低频扑动运动研究

使用直接数值模拟研究了由矩形板在雷诺数（基于进入速度和半板高度）2000 下受到均匀流入流引起的过渡分离流。目的是揭开流体分离中低频扑动运动 (FM) 的长期谜团。在固定的流向垂直平面上或从以前使用点状或平面测量的实验研究的角度来看，FM表现为覆盖整个分离泡的低速和高速之间的低频周期性切换。结果表明，在三维空间中，FM反映了在分离剪切层和平均流反转影响下流向拉长条纹结构的复杂演化。 FM 是一种绝对不稳定性，是通过分离流线顶部附近的平均流量减速推动的提升机构启动的。在该特定位置处，剪切力使涡流丝突然弯曲，使得一端垂直地撞击到分离泡的第一半部中，而另一端在分离泡的第二半部中沿流向延伸。涡丝的两端相互支撑，并分别受到分离气泡第一半部和第二半部的垂直加速度和流向加速度的拉伸。该过程周期性地将低速（或高速）条纹结构切换为包围整个分离泡的高速（或低速）条纹结构，从而使分离的剪切层在垂直方向上上下拍动。当条纹结构转换符号时，就会出现“大漩涡”脱落。这种大涡与剪切层中源自开尔文-亥姆霍兹不稳定性和连续涡合并的展向涡脱落有着根本的不同。人们还认为，FM 形式的条纹结构的三维演化适用于几何引起的分离流和压力引起的分离流。