arXiv 2202.131292022-02-26physics.flu-dyncs.CEcs.LG

Rayleigh-Bénard对流中局部湍流热通量的直接数据驱动预报

Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection

Technische Universität Ilmenau（伊尔默瑙工业大学）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；New York University（纽约大学）

Sandeep Pandey, Philipp Teutsch, Patrick Mäder, Jörg Schumacher

备注：: 14 pages, 13 figures
发表信息：: Physics of Fluids 34.4 (2022): 045106
DOI：: 10.1063/5.0087977

摘要：

提出了一种卷积自编码器-递归神经网络机器学习组合模型，用于分析和预测普朗特数${\rm Pr}=7$和瑞利数${\rm Ra}=10^7$下二维湍流Rayleigh-Bénard对流中局部对流热通量场的动力学和低阶统计量.两个递归神经网络应用于减少的潜在数据空间，水库计算模型的回声状态网络和一个经常性的门控单元的形式的流数据的时间推进。因此，本工作利用三种不同的机器学习算法的模块化组合，以建立一个完全数据驱动和简化的模型，在复杂的热驱动流的湍流传热的动力学。具有12个隐藏层的卷积自动编码器能够将湍流数据的维数降低到其原始大小的约0.2%。我们的结果表明，一个相当好的精度在一阶和二阶统计的对流热通量。该算法还能够再现间歇性羽流混合动力学的热边界层的上边缘与一些偏差。这同样适用于局部对流热通量的概率密度函数与差异的远尾。此外，我们证明了噪声弹性的框架，这表明本模型可能适用于作为一个简化的动力学模型，提供运输通量及其变化的粗网格单元的大规模计算模型，如全球大气和海洋环流模型。

英文摘要：

A combined convolutional autoencoder-recurrent neural network machine learning model is presented to analyse and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh-Bénard convection flow at Prandtl number ${\rm Pr}=7$ and Rayleigh number ${\rm Ra}=10^7$. Two recurrent neural networks are applied for the temporal advancement of flow data in the reduced latent data space, a reservoir computing model in the form of an echo state network and a recurrent gated unit. Thereby, the present work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2 \% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework which suggests the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to the coarse grid cells of larger-scale computational models, such as global circulation models for the atmosphere and ocean.

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