标题： 基于预解式的湍流尾流估计 显示英文标题

标题： Resolvent-based estimation of a turbulent wake

摘要： 我们提出了一种基于求解器的框架，用于估计跨流周期性NACA0012翼型在马赫数0.3、雷诺数23,000和攻角6度时尾流中的湍流速度脉动。 在Jung等人方法的基础上（J. Fluid Mech. 2025, vol. 0, A1），我们将该方法扩展到更复杂的湍流尾流区域，这涉及三个主要挑战：（1）线性化纳维-斯托克斯算子中的全局不稳定模态，（2）多尺度湍流结构，以及（3）高维数据集。 为解决这些挑战，我们采用了一种数据驱动的方法，从通过大涡模拟获得的交叉谱密度中构建因果求解器估计核。 这些核使用维纳-霍普夫方法推导得出，该方法最优地施加因果性，从而提高实时估计的准确性。 该框架捕捉了相干结构的频谱特征，并包含了作用于线性系统的非线性强迫项的彩色统计特性。 为了处理高维估计问题的计算需求，我们利用了在同一框架内开发的并行算法。 我们进一步通过分析单传感器估计误差与目标流动量的相关性来研究传感器布置。 结果表明，使用翼型表面有限的剪切应力测量值，可以准确地对跨流平均、跨流傅里叶变换和中间截面流动的流向速度进行因果估计。 本研究强调了基于求解器的框架在可压缩、湍流环境中高效估计的潜力。 显示英文摘要

摘要： We present a resolvent-based framework for estimating turbulent velocity fluctuations in the wake of a spanwise-periodic NACA0012 airfoil at Mach 0.3, Reynolds number 23,000, and an angle of attack of 6 degrees. Building on the methodology of Jung et al. (J. Fluid Mech. 2025, vol. 0, A1), we extend the approach to the more complex regime of a turbulent wake, which involves three primary challenges: (1) globally unstable modes in the linearized Navier-Stokes operator, (2) multi-scale turbulent structures, and (3) high-dimensional datasets. To address these challenges, we employ a data-driven approach that constructs causal resolvent-based estimation kernels from cross-spectral densities obtained via large-eddy simulations. These kernels are derived using the Wiener-Hopf method, which optimally enforces causality, thereby enhancing real-time estimation accuracy. The framework captures the spectral signatures of coherent structures and incorporates the colored statistics of nonlinear forcing terms acting on the linear system. To handle the computational demands of the high-dimensional estimation problem, we utilize parallel algorithms developed within the same framework. We further investigate sensor placement by analyzing single-sensor estimation error and coherence with target flow quantities. Results demonstrate accurate causal estimation of streamwise velocity for the spanwise-averaged, spanwise-Fourier-transformed, and mid-span flow using limited shear-stress measurements on the surface of the airfoil. This study underscores the potential of the resolvent-based framework for efficient estimation in compressible, turbulent environments.