论文标题
基于大涡模拟的激光雷达测量的湍流电场的重建
Reconstruction of turbulent flow fields from lidar measurements based on large-eddy simulation
论文作者
论文摘要
我们使用大涡模拟（LES）和4D-VAR数据同化算法研究了大气边界层中湍流场中湍流场的重建。这导致了一个优化问题，其中测量和模拟之间的误差在观察时间范围内最小化。为了利用湍流的空间连贯性，我们在目标函数中使用二次正则化，该函数基于两点协方差矩阵。此外，为了改善调理并消除连续性限制，该问题被转化为karhunen-loève。为了进行优化，我们使用了准Newton Limited-Memory BFGS算法与梯度的伴随方法相结合。我们还将基于泰勒的冷冻湍流（TFT）模型的重建视为比较点。为了评估该方法，我们从压力驱动边界层的细网格LES构建了一系列虚拟LiDAR测量值。重建在更粗的网格和较小的域上使用LES，并将结果与细网格参考进行比较。考虑了两种激光扫描模式：一种经典的计划位置指示剂模式，该模式在水平平面中刷了LIDAR光束，以及基于Lissajous曲线的3D图案。我们发现，归一化误差在扫描区域中的15％至25％（通过背景方差归一化），并且在距离该扫描区域以外的相关长度比例的距离上增加到$ 100 \％$。此外，根据扫描模式和位置，LES的表现优于TFT 30％至70％。
We investigate the reconstruction of a turbulent flow field in the atmospheric boundary layer from a time series of lidar measurements, using Large-Eddy Simulations (LES) and a 4D-Var data assimilation algorithm. This leads to an optimisation problem in which the error between measurements and simulations is minimised over an observation time horizon. To exploit the spatial coherence of the turbulence, we use a quadratic regularisation in the objective function, that is based on the two-point covariance matrix. Moreover, to improve conditioning, and remove continuity constraints, the problem is transformed into a Karhunen-Loève basis. For the optimisation, we use a quasi-Newton limited-memory BFGS algorithm combined with an adjoint approach for the gradient. We also consider reconstruction based on a Taylor's frozen turbulence (TFT) model as point of comparison. To evaluate the approach, we construct a series of virtual lidar measurements from a fine-grid LES of a pressure-driven boundary-layer. The reconstruction uses LES on a coarser mesh and smaller domain, and results are compared to the fine-grid reference. Two lidar scanning modes are considered: a classical plan-position-indicator mode, which swipes the lidar beam in a horizontal plane, and a 3D pattern that is based on a Lissajous curve. We find that normalised errors lie between 15% and 25% (error variance normalised by background variance) in the scanning region, and increase to $100\%$ over a distance that is comparable to the correlation length scale outside this scanning region. Moreover, LES outperforms TFT by 30% to 70% depending on scanning mode and location.
