湍流数据同化技术及应用

近年来数据同化（DA）被引入湍流动力学研究中，通过融合实验测量和数值计算，提高了实验测量的精度和广度，改善了数值模拟的预测性能。实验观测、预测模型和同化算法是数据同化的三要素，湍流研究中的实验观测包括热线风速仪、粒子图像测速法（PIV）、压力传感器等局部测量数据，预测模型主要指流动控制方程及湍流封闭方程，而同化算法包括贝叶斯推断、集合卡尔曼滤波（EnKF）、伴随等。稳态数据同化一般结合雷诺平均Navier-Stokes （RANS）模型方程，从重新标定模型常数、修正涡黏模型方程形式误差、修正雷诺应力项等方面着手。非稳态的数据同化一般包括四维变分（4DVar）等时间连续的数据同化方式以及顺序数据同化。4DVar通过时间正向和逆向积分迭代，存储量和计算量都非常大。顺序数据同化不需要时间逆向积分，可以在若干时刻对实验观测进行间断地植入，正向求解整个系统。另外，随着人工智能的飞速发展，湍流数据同化研究也向智能化迈进。对于纯数据驱动的湍流机器学习，其缺乏物理本质的约束，而基于物理信息的机器学习在物理本质上与数据同化是一致的。

Turbulent flow data assimilation and its applications

Data Assimilation (DA) has been introduced into the turbulence dynamics community in recent years. Coupling experimental measurements and numerical simulation, it improves the accuracy and scope of measurements and reduces the uncertainty of simulations. Experimental observations, predictive models and assimilation algorithms are three essential factors in DA. Observations in turbulent flows usually involve hot wire anemometer, Particle Image Velocimetry (PIV), pressure sensors and other measurement techniques. The predictive model refers specifically to flow governing equations and turbulence closures. The assimilation algorithm ranges from Bayesian inference, Ensemble Karman Filter (EnKF), to adjoint formulations. DA for steady-state flows has a combination of Reynolds-Averaged Navier-Stokes (RANS) turbulence models, aiming at model constant recalibration, equation form-error correction and Reynolds stress term reproduction, whilst the unsteady DA has two main categories, i.e., four-dimensional variational DA (4DVar) and sequential DA. Employing the forward and backward integration, 4DVar requires large storage space and high computational cost. Free from backward integration, sequential DA can intermittently couple with the observational data at selected instances in a forward direction. Additionally, fast development of machine learning and artificial intelligence pushes turbulence research towards the direction of intelligence. While the pure data-driven machine learning lacks physical constraints, the physical-informed machine learning is in consistent with DA in the essence of physics.