This article introduces a new Neural Network stochastic model to generate a
1-dimensional stochastic field with turbulent velocity statistics. Both the
model architecture and training procedure ground on the Kolmogorov and Obukhov
statistical theories of fully developed turbulence, so guaranteeing
descriptions of 1) energy distribution, 2) energy cascade and 3) intermittency
across scales in agreement with experimental observations. The model is a
Generative Adversarial Network with multiple multiscale optimization criteria.
First, we use three physics-based criteria: the variance, skewness and flatness
of the increments of the generated field that retrieve respectively the
turbulent energy distribution, energy cascade and intermittency across scales.
Second, the Generative Adversarial Network criterion, based on reproducing
statistical distributions, is used on segments of different length of the
generated field. Furthermore, to mimic multiscale decompositions frequently
used in turbulence's studies, the model architecture is fully convolutional
with kernel sizes varying along the multiple layers of the model. To train our
model we use turbulent velocity signals from grid turbulence at Modane wind
tunnel.

本文介绍了一种新的神经网络随机模型，用于生成具有湍流速度统计的一维随机场。该模型的结构和训练程序基于克尔莫戈洛夫和奥布科夫的完全发展湍流统计理论，因此可以保证与实验观测一致的能量分布、能量级联和尺度间歇性的描述。该模型是一个具有多尺度优化准则的生成对抗网络，首先使用三个基于物理的准则：生成场增量的方差、偏度和平坦度，分别检索湍流能量分布、能量级联和尺度间歇性。其次，基于重现统计分布的生成对抗网络准则，用于不同长度的生成场的段落上。此外，为了模仿湍流研究中经常使用的多尺度分解，模型结构完全卷积，模型的多个层的内核大小变化。为了训练我们的模型，我们使用摩登风洞的网格湍流的湍流速度信号。