Drift-wave turbulence produces anomalous transport via cross-correlations between fluctuations. This transport has profound implications for confinement, structure formation, and virtually all aspects of the non-linear turbulent dynamics. In this work, we use a data-driven method based on deep learning in order to study turbulent transport in the 2D Hasegawa–Wakatani system and infer a reduced mean-field model from numerical solution. In addition to the usual turbulent diffusion, we find an effect which couples the particle flux to the local gradient of vorticity, which tends to modulate the density profile. The direct coupling to the shear is relatively weak. In addition, the deep learning method finds a model for spontaneous zonal flow generation by negative viscosity, stabilized by non-linear and hyperviscous terms. We compare these results to analytic calculations using quasilinear theory and wave kinetics, finding qualitative agreement, though the calculations miss certain higher-order effects. A simplified, 1-D model for the evolution of the profile, flow, and intensity based on the deep learning results is solved numerically and compared to previous models for staircasing based on bistability. We see that the physics uncovered by the deep learning method provided simple explanations for the formation of zonal structures in the density, flow, and turbulence fields. We highlight the important role of symmetry in the deep learning method and speculate on the portability of the method to other applications.
漂移波湍流通过涨落之间的互相关产生反常输运。这种输运对约束、结构形成以及非线性湍流动力学的几乎所有方面都具有深远影响。在本工作中，我们采用一种基于深度学习的数据驱动方法，研究二维Hasegawa–Wakatani系统中的湍流输运，并从数值解中推断出一个约化的平均场模型。除了通常的湍流扩散之外，我们发现了一个将粒子通量与局部涡度梯度耦合的效应，该效应倾向于调制密度分布。对剪切率的直接耦合相对较弱。此外，深度学习方法还发现了一个通过负黏性、并由非线性和超黏性项稳定的自发带状流产生模型。我们将这些结果与基于准线性理论和波动力学的解析计算进行比较，发现定性一致，尽管解析计算遗漏了某些高阶效应。基于深度学习结果，我们求解了一个描述密度分布、流场和强度演化的简化一维模型，并将其与基于双稳态的阶梯结构模型进行了对比。我们发现，深度学习方法所揭示的物理机制为密度、流场和湍流场中带状结构的形成提供了简单解释。我们强调了对称性在深度学习方法中的重要作用，并探讨了该方法推广到其他应用的可行性。