New insights into experimental stratified flows obtained through physics-informed neural networks

Abstract We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data of stratified flows. A fully connected deep neural network is trained using time-resolved experimental data in a salt-stratified inclined duct experiment, consisting of three-component velocity fields and density fields measured simultaneously in three dimensions at Reynolds number $= O(10^3)$ and at Prandtl or Schmidt number $=700$. The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions at the duct walls. These physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices of Holmboe waves; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed asymmetric Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of stratified turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

摘要：我们开发了一种物理信息神经网络（PINN），以显著增强分层流的最先进实验数据。在一个盐分层倾斜管道实验中，利用时间分辨实验数据对一个全连接深度神经网络进行训练，该实验包含在雷诺数$= O(10^3)$以及普朗特数或施密特数$=700$时在三维空间中同时测量的三分量速度场和密度场。PINN强制满足不可压缩性、动量和浮力的控制方程以及管道壁的边界条件。这些受物理约束的增强数据以更高的时空分辨率输出，并展示了五个关键结果：（i）消除测量噪声；（ii）校正由扫描测量技术引起的失真；（iii）识别出霍尔姆博波中微弱但具有动力学重要性的三维涡旋；（iv）修正湍流能量收支和混合效率；（v）预测潜在压力场及其在观测到的不对称霍尔姆博波动力学中的作用。这些结果在拓展实验范围方面迈出了重要的一步，特别是在分层湍流的背景下，其中准确计算三维梯度和解析小尺度仍然是长期的挑战。