Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

Nicholas Dudu, Arturo Rodríguez, Gael Moran, Jose Terrazas, Richard Adansi, V. Kotteda, Christopher Harris, Vinod Kumar
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Abstract

Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.
基于机器学习的深层大气湍流分形和卷积分析
大气湍流研究表明,在从惯性外尺度到耗散内尺度的一系列尺度上存在自相似标度结构。通过使用广泛使用的盒计数法计算可视化湍流图像的分形维数,获得了这种自相似结构的度量。如果盲目使用盒计数法,可能会导致误导的结果,其中对应于上面提到的上下长度尺度的缩放范围的边缘被错误地纳入。此外,湍流中产生的某些非自相似的结构可能会对盒数维度产生虚假的贡献。一个经过适当训练的卷积神经网络可以以适当的方式考虑到上述两个特征,使用比覆盖假定分形集的盒子数量更详细的信息作为输入。给出一个具体的例子,可以分析覆盖物体的覆盖盒簇的形状如何随盒的大小而变化。我们将利用大涡模拟(Large-Eddy Simulations, LES)建立一个衰减各向同性湍流情景的大气湍流数据集,并分析由此产生的特征结构。这些可以包括速度大小的等高线,以及引入模拟流动的被动标量的水平。然后,我们将识别可用于训练网络的结构特征,以获得描述缩放范围的最合适的分形维数,即使该范围是有限的,最小到一个数量级。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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