With the recent advances in machine learning, strategies based on data can be used to augment wall modeling in the turbulent boundary layer. Combined with the attached eddy hypothesis, the present work applies extreme gradient boosting (XGBoost) to predict the large-scale wall-attached structures at a range of wall-normal locations based on a near-wall reference position (zR+≈4) spanning a Reynolds-number range Reτ∼O(103)−O(105). The input and output signals are selected as the large-scale structures; here, the input signals are set as in the fixed near-wall reference position by a series of streamwise velocity ({X−N,…,X−1,X0,X1,…,XN}), and the output signal Y0 is set directly above X0. Within each dataset, the large-scale wall-attached structures are identified from the prediction modeled by XGBoost between the turbulence in the upper region and at the near-wall reference position, resulting in a successful prediction of the large-scale structures inclination angles. Along the wall-normal offset Δz and streamwise offset Lx (distance between Xi and X0), the slope of the feature importance (represented by contour levels) is exactly equal to the degree of inclination of large-scale structures, indicating the turbulent inner and outer connection inferred by the machine learning input and output interactions perspective. This study shows that there is a great opportunity in machine learning for wall-bounded turbulence modeling by connecting the flow interactions between near-wall and outer regions.

中文翻译：

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从机器学习的角度检测湍流边界层中的大规模附壁结构倾斜角度

随着机器学习的最新进展，基于数据的策略可用于增强湍流边界层中的壁面建模。结合附着涡假说，本工作应用极端梯度增强（XGBoost）来预测基于跨越a的近壁参考位置（zR+≈4）的一系列壁法向位置处的大型附着结构。雷诺数范围 Reτ∼O(103)−O(105)。输入输出信号均选择大规模结构；这里，输入信号通过一系列流向速度（{X−N，…，X−1，X0，X1，…，XN}）设置为固定近壁参考位置，输出信号Y0为设置在 X0 的正上方。在每个数据集中，通过 XGBoost 建模的上部区域和近壁参考位置的湍流之间的预测来识别大型附壁结构，从而成功预测大型结构倾斜角度。沿壁面法向偏移量 Δz 和流向偏移量 Lx（Xi 和 X0 之间的距离），特征重要性的斜率（用等高线水平表示）恰好等于大尺度结构的倾斜程度，表明湍流的内部和外部通过机器学习输入和输出交互的角度推断出的外部连接。这项研究表明，通过连接近壁和外部区域之间的流动相互作用，机器学习为壁界湍流建模提供了巨大的机会。