Data-driven definition of coherent structures in turbulent channels

The ability of explainable deep learning to detect patterns in turbulent flows has recently been demonstrated. In a recent work (Cremades et al., Nature Communications 15, 3864, 2024), the impact of the Reynolds-stress structures on the evolution of the flow was presented, and their importance for flow predictions was assessed. The present contribution extends the previous results to obtain the importance of every single grid point of a three-dimensional turbulent channel at a friction Reynolds number of 125. First, the evolution of the flow is modeled through deep learning. In particular, a U-net architecture is employed. This deep neural network is able to exploit the existing flow patterns to produce high-quality predictions of the flow (with less than 1% relative error). Then, the importance of each grid point (SHAP value) is evaluated using the expected-gradients method. Finally, new coherent structures based on the impact of each grid point on the prediction of the flow are defined (QSHAP). The new structures are compared against other coherent structures, such as Reynolds-stress structures, streaks, and vortices. The QSHAP structures are strongly related to the Reynolds stresses and streaks in different wall-normal locations. The present methodology opens new opportunities for the analysis of turbulence, and can be extended to the analysis other relevant quantities such as the wall-shear stress or the turbulent kinetic energy. Furthermore, this work paves the way to novel control strategies targeting the most relevant regions of the flow, identified by the SHAP methodology.