Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it to the canonical problem of fluid dynamics: three dimensional homogeneous and isotropic turbulence. By doing numerical experiments we perform a systematic assessment of how well the technique reconstructs large- and small-scales features of the flow with respect to the quantity and the quality/type of data supplied to it. The types of data used are: (i) field values on a fixed number of spatial locations (Eulerian nudging), (ii) Fourier coefficients of the fields on a fixed range of wavenumbers (Fourier nudging), or (iii) field values along a set of moving probes inside the flow (Lagrangian nudging). We present state-of-the-art quantitative measurements of the scale-by-scale {} and a detailed discussion of the probability distribution function of the reconstruction error, by comparing the nudged field and the {} point-by-point. Furthermore, we show that for more complex flow configurations, like the case of anisotropic rotating turbulence, the presence of cyclonic and anticyclonic structures leads to unexpectedly better performances of the algorithm. We discuss potential further applications of nudging to a series of applied flow configurations, including the problem of field-reconstruction in thermal Rayleigh-B'enard convection and in magnetohydrodynamics (MHD), and to the determination of optimal parametrisation for small-scale turbulent modeling. Our study fixes the standard requirements for future applications of nudging to complex turbulent flows.

中文翻译：

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与大数据同步：对Navier-Stokes方程进行推导，以对湍流进行数据同化

推挤是一种重要的数据同化技术，其中使用局部场测量值来控制动力学系统的演化和/或重构所供应流的整个相空间配置。在这里，我们将其应用于流体动力学的经典问题：三维均匀湍流和各向同性湍流。通过进行数值实验，我们就该技术相对于提供给它的数据的数量和质量/类型如何重构流量的大小特征进行了系统的评估。所使用的数据类型为：（i）在固定数量的空间位置上的场值（欧拉微动），（ii）在固定波数范围上的场的傅立叶系数（傅里叶微动），或（iii）沿流动内部的一组活动探针（拉格朗日推力）。通过比较微调字段和{}逐点，我们提出了按比例缩放{}的最新定量测量方法，并详细讨论了重建误差的概率分布函数。此外，我们表明，对于更复杂的流动配置（如各向异性旋转湍流的情况），旋风和反旋风结构的存在会导致算法出乎意料的更好性能。我们讨论了微调对一系列应用的流动配置的潜在进一步应用，包括热瑞利-贝纳德对流和磁流体动力学（MHD）中的场重构问题，以及为小规模湍流建模确定最佳参数化的问题。 。