Placidi M, Ganapathisubramani B
1City, University of London, London, EC1V 0HB UK.
2University of Southampton, Southampton, SO17 1BJ UK.
Boundary Layer Meteorol. 2018;167(1):99-121. doi: 10.1007/s10546-017-0317-3. Epub 2017 Nov 4.
Wind-tunnel experiments were carried out on fully-rough boundary layers with large roughness ( , where is the height of the roughness elements and is the boundary-layer thickness). Twelve different surface conditions were created by using LEGO™ bricks of uniform height. Six cases are tested for a fixed plan solidity ( ) with variations in frontal density ( ), while the other six cases have varying for fixed . Particle image velocimetry and floating-element drag-balance measurements were performed. The current results complement those contained in Placidi and Ganapathisubramani (J Fluid Mech 782:541-566, 2015), extending the previous analysis to the turbulence statistics and spatial structure. Results indicate that mean velocity profiles in defect form agree with Townsend's similarity hypothesis with varying , however, the agreement is worse for cases with varying . The streamwise and wall-normal turbulent stresses, as well as the Reynolds shear stresses, show a lack of similarity across most examined cases. This suggests that the critical height of the roughness for which outer-layer similarity holds depends not only on the height of the roughness, but also on the local wall morphology. A new criterion based on shelter solidity, defined as the sheltered plan area per unit wall-parallel area, which is similar to the 'effective shelter area' in Raupach and Shaw (Boundary-Layer Meteorol 22:79-90, 1982), is found to capture the departure of the turbulence statistics from outer-layer similarity. Despite this lack of similarity reported in the turbulence statistics, proper orthogonal decomposition analysis, as well as two-point spatial correlations, show that some form of universal flow structure is present, as all cases exhibit virtually identical proper orthogonal decomposition mode shapes and correlation fields. Finally, reduced models based on proper orthogonal decomposition reveal that the small scales of the turbulence play a significant role in assessing outer-layer similarity.
在具有大粗糙度（ ，其中 是粗糙度元件的高度， 是边界层厚度）的充分粗糙边界层上进行了风洞实验。通过使用高度均匀的乐高积木创造了十二种不同的表面条件。对于固定的平面实度（ ），测试了六种情况，其迎流密度（ ）有所变化，而另外六种情况则在固定 时 有所变化。进行了粒子图像测速和浮动元件阻力平衡测量。当前结果补充了普拉西迪和加纳帕蒂苏布拉马尼（《流体力学杂志》782:541 - 566，2015）中的结果，将先前的分析扩展到了湍流统计和空间结构。结果表明，缺陷形式的平均速度剖面在 变化时与汤森德相似性假设相符，然而，在 变化的情况下一致性较差。流向和壁法向湍流应力以及雷诺剪应力在大多数研究案例中缺乏相似性。这表明外层相似性成立的粗糙度临界高度不仅取决于粗糙度的高度，还取决于局部壁面形态。发现了一种基于遮蔽实度的新准则，定义为单位壁面平行面积的遮蔽平面面积，它类似于劳帕克和肖（《边界层气象学》22:79 - 90，1982）中的“有效遮蔽面积”，该准则能够捕捉湍流统计与外层相似性的偏差。尽管在湍流统计中报告了这种缺乏相似性的情况，但适当正交分解分析以及两点空间相关性表明存在某种形式的通用流动结构，因为所有案例都呈现出几乎相同的适当正交分解模态形状和相关场。最后，基于适当正交分解的简化模型表明，湍流的小尺度在评估外层相似性方面起着重要作用。
