Flexible vegetation plays key roles in the natural channel and riparian ecology. This paper investigates the drag coefficient C_df of an emergent flexible vegetation array in a steady nonuniform flow. Laboratory flume tests of five vegetation densities exposed to a constant flow rate were conducted, and the variation in the water surface was accurately measured. The Saint‐Venant equation was applied to explore vegetation hydrodynamics under nonuniform conditions, and a more widely applicable formula for the vegetated drag of nonuniform flow was proposed. Furthermore, the flexible drag coefficient factor α_b was used to represent the flexibility and drag reconfiguration, which were explored from the perspective of material mechanics. The results reveal that the calculated values of C_df exhibit nonmonotonic variation with increasing Reynolds number along the streamwise direction due to the flow nonuniformity. There are two effects of blockage and sheltering in the emergent vegetated patch: The blockage effect increases the drag coefficient, while the sheltering effect—especially at the leading edge and tail of the vegetated patch—reduces the drag of the flexible canopy due to bending deformation. These two effects achieve equilibration in dense flexible canopies. Finally, by relating α_b to flexibility through the slenderness Cauchy number C_YS, a nonmonotonic pattern can be obtained for each test. A fitting formula was proposed based on α_b as a function of C_YS. The results presented in this study can potentially support applications related to the plant flexible dams and vegetated filter strips for river ecosystems.

中文翻译：

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稳态非均匀流动中柔性植被的阻力系数

柔性植被在自然通道和河岸生态中起着关键作用。本文研究了在稳定非均匀流中涌现的柔性植被阵列的阻力系数C _df。对暴露于恒定流量的五种植被密度进行了实验室水槽测试，并精确测量了水面的变化。应用Saint-Venant方程来研究非均匀条件下的植被水动力，并为非均匀流动的植被阻力提出了更广泛适用的公式。此外，柔性阻力系数因子α _b用来表示灵活性和阻力重新配置，这是从材料力学的角度探讨的。结果表明，由于流动不均匀性，C _df的计算值随雷诺数沿流向的增加而呈现非单调变化。涌现的植被斑块有两种阻挡和遮蔽作用：遮蔽作用增加了阻力系数，而遮蔽作用（尤其是在植被斑块的前缘和尾部）减少了挠性树冠由于弯曲变形而产生的阻力。这两个效果可以在密集的柔性顶棚中达到平衡。最后，通过与α _b通过长细柯西数灵活性Ç_YS，可以为每个测试获得非单调模式。提出了一种基于嵌合式α _b作为的函数Ç _YS。这项研究中提出的结果可以潜在地支持与河流生态系统的植物柔性水坝和植被过滤带相关的应用。