一种用物理激励参数统计表征湍流数据的方法，如质心速度图所示
A method to statistically characterize turbulent data with physically motivated parameters, illustrated on a centroid velocity map
摘要：
我们研究了最近提出的3D可压缩MHD湍流模型（Chevillard等，2010; Durrive等，2021）作为统计学表征2D和3D湍流数据的工具的潜力。该模型由十几个自由（直观的，物理动机的）参数参数化，这些参数控制场（密度，速度和磁场）的统计数据。目前的研究是一个概念的研究证明：（一）我们限制自己的不可压缩流体动力学模型的一部分，（二）我们认为作为数据质心速度地图，（三）我们让只有三个自由参数变化（即相关长度，赫斯特参数和非线性参数）。在这个框架内，我们证明，给定一个质心速度图，我们可以找到一个自动的方式（即通过马尔可夫链蒙特卡罗分析）的参数值，使模型类似于给定的地图，即再现其统计相当不错。因此，由于这种方法，人们可以统计地描述各种紊流数据，并进行比较。换句话说，我们展示了如何将此模型用作比较观测或模拟数据集的度量。此外，由于该模型在数值上特别快（比我们用来生成参考数据的数值模拟快近500倍），因此可以用作替代模型。最后，通过这一过程，我们也开始了第一次系统的探索这个模型的参数空间。这样做，我们展示了参数如何影响质心速度图的视觉和统计特性，并展示了各种参数之间的相关性，为模型提供了新的见解。
英文摘要：
We investigate the potential of a recently proposed model for 3D compressible MHD turbulence (Chevillard et al. 2010; Durrive et al. 2021) to be used as a tool to characterize statistically 2D and 3D turbulent data. This model is parametrized by a dozen of free (intuitive, physically motivated) parameters, which control the statistics of the fields (density, velocity and magnetic fields). The present study is a proof of concept study: (i) we restrict ourselves to the incompressible hydrodynamical part of the model, (ii) we consider as data centroid velocity maps, and (iii) we let only three of the free parameters vary (namely the correlation length, the Hurst parameter and the intermittency parameter). Within this framework, we demonstrate that, given a centroid velocity map, we can find in an automated manner (i.e. by a Markov Chain Monte Carlo analysis) values of the parameters such that the model resembles the given map, i.e. which reproduces its statistics fairly well. Hence, thanks to this procedure, one may characterize statistically, and thus compare, various turbulent data. In other words, we show how this model may be used as a metric to compare observational or simulated data sets. In addition, because this model is numerically particularly fast (nearly 500 times faster than the numerical simulation we use to generate our reference data) it may be used as a surrogate model. Finally, by this process we also initiate the first systematic exploration of the parameter space of this model. Doing so, we show how the parameters impact the visual and the statistical properties of centroid velocity maps, and exhibit the correlations between the various parameters, providing new insight into the model.
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