Lagrangian stochastic models are widely used to predict and analyze turbulent dispersion in complex environments, such as in various terrestrial and marine canopy flows. However, due to a lack of empirical data, it is still not understood how particular features of highly inhomogeneous canopy flows affect the Lagrangian statistics. In this work, we study Lagrangian short-time statistics by analyzing empirical Lagrangian trajectories in subvolumes of space that are small in comparison with the canopy height. For the analysis we used 3D Lagrangian trajectories measured in a dense canopy flow model in a wind-tunnel, using an extended version of real-time 3D particle tracking velocimetry. One of our key results is that the random turbulent fluctuations due to the intense dissipation were more dominant than the flow's inhomogeneity in affecting the short-time Lagrangian statistics. This amounts to a so-called quasihomogeneous regime of Lagrangian statistics at small scales. Using the Lagrangian dataset, we calculate the Lagrangian autocorrelation function and the second-order Lagrangian structure-function and extract associated parameters, namely, a Lagrangian velocity decorrelation timescale, $T_i$, and the Kolmogorov constant, $C_0$. We demonstrate that in the quasihomogeneous regime, both these functions are well represented using a second-order Lagrangian stochastic model that was designed for homogeneous flows. Furthermore, we show that the spatial variations of the Lagrangian separation of scales, $T_i/{\tau }_{\eta }$, and the Kolmogorov constant, $C_0$, cannot be explained by the variation of the Reynolds number, ${\text{Re}}_{\lambda }$, in space, and that $T_i/{\tau }_{\eta }$ was small as compared with homogeneous turbulence predictions at similar ${\text{Re}}_{\lambda }$. We thus hypothesize that these characteristics occurred due to the injection of kinetic energy at small scales due to the so-called “wake-production” process, and we show empirical results supporting our hypothesis. These findings shed light on key features of Lagrangian statistics in flows with intense dissipation, and have direct implications for modeling short term dispersion in such complex environments.

中文翻译：

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拉格朗日框架中的湍流与障碍物相互作用：冠层流中的随机建模应用

拉格朗日随机模型被广泛用于预测和分析复杂环境中的湍流扩散，例如各种陆地和海洋冠层流。但是，由于缺乏经验数据，仍然不了解高度不均匀的冠层流量的特定特征如何影响拉格朗日统计。在这项工作中，我们通过分析与树冠高度相比较小的空间子体积中的经验拉格朗日轨迹来研究拉格朗日短时统计。对于分析，我们使用了实时3D粒子跟踪测速仪的扩展版本，在风洞中的密集冠层流模型中测量了3D拉格朗日轨迹。我们的主要结果之一是，由于强烈耗散而引起的随机湍流涨落比气流的影响更大。在影响短时拉格朗日统计上的不均匀性。这相当于小规模拉格朗日统计的所谓准同质状态。使用拉格朗日数据集，我们计算了拉格朗日自相关函数和二阶拉格朗日结构函数，并提取了相关参数，即拉格朗日速度去相关时标，${Ť}_{\mathrm{一世}}$，以及Kolmogorov常数， $C_0$。我们证明，在准均质状态下，这两种功能都可以使用为均质流设计的二阶拉格朗日随机模型很好地表示。此外，我们证明了拉格朗日尺度分离的空间变化，${Ť}_{\mathrm{一世}}/{\tau }_{\eta }$，以及Kolmogorov常数， $C_0$，无法用雷诺数的变化来解释， ${\text{回覆}}_{\lambda }$，在太空中 ${Ť}_{\mathrm{一世}}/{\tau }_{\eta }$ 与类似情况下的均匀湍流预测相比较小 ${\text{回覆}}_{\lambda }$。因此，我们假设这些特征是由于所谓的“唤醒生产”过程而在小范围内注入动能而产生的，并且我们显示了支持我们的假设的经验结果。这些发现揭示了拉格朗日统计在强耗散流动中的关键特征，并且对在这种复杂环境中对短期弥散进行建模具有直接意义。