Title: Discovery of a physically interpretable data-driven wind-turbine wake model Show Chinese title

Title: 具有物理可解释性的数据驱动型风力涡轮机尾流模型的发现

Abstract: This study presents a compact data-driven Reynolds-averaged Navier-Stokes (RANS) model for wind turbine wake prediction, built as an enhancement of the standard $k$-$\varepsilon$ formulation. Several candidate models were discovered using the symbolic regression framework Sparse Regression of Turbulent Stress Anisotropy (SpaRTA), trained on a single Large Eddy Simulation (LES) dataset of a standalone wind turbine. The leading model was selected by prioritizing simplicity while maintaining reasonable accuracy, resulting in a novel linear eddy viscosity model. This selected leading model reduces eddy viscosity in high-shear regions$\unicode{x2014}$particularly in the wake$\unicode{x2014}$to limit turbulence mixing and delay wake recovery. This addresses a common shortcoming of the standard $k$-$\varepsilon$ model, which tends to overpredict mixing, leading to unrealistically fast wake recovery. Moreover, the formulation of the leading model closely resembles that of the established $k$-$\varepsilon$-$f_P$ model. Consistent with this resemblance, the leading and $k$-$\varepsilon$-$f_P$ models show nearly identical performance in predicting velocity fields and power output, but they differ in their predictions of turbulent kinetic energy. In addition, the generalization capability of the leading model was assessed using three unseen six-turbine configurations with varying spacing and alignment. Despite being trained solely on a standalone turbine case, the model produced results comparable to LES data. These findings demonstrate that data-driven methods can yield interpretable, physically consistent RANS models that are competitive with traditional modeling approaches while maintaining simplicity and achieving generalizability. Show Chinese abstract

Abstract: 本研究提出了一种基于数据驱动的紧凑型雷诺平均纳维-斯托克斯 (RANS) 模型，用于预测风力涡轮机尾流，该模型是对标准 $k$-$\varepsilon$ 公式的增强。 我们利用符号回归框架“湍流应力各向异性稀疏回归”(SpaRTA) 发现了多个候选模型，并基于单个独立风力涡轮机的大涡模拟 (LES) 数据集进行了训练。 我们通过优先考虑简单性并保持合理精度来选择领先模型，最终形成了一种新颖的线性涡粘性模型。 该领先模型降低了高剪切区域$\unicode{x2014}$（尤其是在尾流$\unicode{x2014}$）的涡粘性，从而限制了湍流混合并延迟了尾流恢复。 这解决了标准 $k$-$\varepsilon$ 模型的一个常见缺陷，即该模型倾向于过度预测混合，导致不现实的过快尾流恢复速度。 此外，主导模型的表述与已确立的$k$-$\varepsilon$-$f_P$模型的形式非常相似。与此相似性一致，主导模型和$k$-$\varepsilon$-$f_P$模型在预测速度场和功率输出方面表现出几乎相同的性能，但在湍流动能的预测上有所不同。此外，使用三种未见过的六台风机配置（具有不同的间距和排列）评估了主导模型的泛化能力。尽管该模型仅针对单台风机案例进行了训练，但它产生的结果与大涡模拟（LES）数据相当。这些发现表明，数据驱动的方法可以产生可解释且物理上一致的雷诺平均纳维-斯托克斯（RANS）模型，这些模型在保持简单性和实现泛化的同时，能够与传统的建模方法竞争。