Corbetta Alessandro, Menkovski Vlado, Benzi Roberto, Toschi Federico
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, Netherlands.
Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands.
Sci Adv. 2021 Mar 17;7(12). doi: 10.1126/sciadv.aba7281. Print 2021 Mar.
Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically nontrivial fluctuations of the velocity field, and it can be quantitatively described only in terms of statistical averages. Strong nonstationarities impede statistical convergence, precluding quantifying turbulence, for example, in terms of turbulence intensity or Reynolds number. Here, we show that by using deep neural networks, we can accurately estimate the Reynolds number within 15% accuracy, from a statistical sample as small as two large-scale eddy turnover times. In contrast, physics-based statistical estimators are limited by the convergence rate of the central limit theorem and provide, for the same statistical sample, at least a hundredfold larger error. Our findings open up previously unexplored perspectives and the possibility to quantitatively define and, therefore, study highly nonstationary turbulent flows as ordinarily found in nature and in industrial processes.
湍流是流体运动中普遍存在的混沌状态，其特征是速度场存在强烈且具有统计学意义的显著波动，并且只能通过统计平均值进行定量描述。强烈的非平稳性阻碍了统计收敛，使得无法对湍流进行量化，例如无法根据湍流强度或雷诺数进行量化。在此，我们表明，通过使用深度神经网络，我们能够从仅两个大尺度涡旋周转时间的小统计样本中，以15%的精度准确估计雷诺数。相比之下，基于物理的统计估计器受中心极限定理收敛速度的限制，对于相同的统计样本，其误差至少大一百倍。我们的研究结果开辟了以前未探索的视角，并提供了定量定义并因此研究自然界和工业过程中常见的高度非平稳湍流的可能性。
