Classically studied coherent structures only paint a partial picture of wall-bounded turbulence

  • Hoyas, Sergio (Universitat Politècnica de Valencia)
  • Cremades, Andres (Universitat Politècnica de Valencia)
  • Vinuesa, Ricardo (University of Michigan)

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Turbulent flows have been studied for more than a century; however, the mechanisms governing turbulence and energy transfer remain poorly understood for many scientifically and industrially relevant configurations. This lack of understanding has important practical implications, as near-wall turbulence accounts for a significant fraction of global energy consumption. The intrinsic difficulty of turbulence stems from the nonlinear and multiscale nature of the Navier–Stokes equations, which makes direct numerical simulation of realistic engineering flows computationally intractable. As a result, alternative approaches aimed at understanding, modeling, and controlling turbulence have been developed. Among these, the analysis of coherent structures and their nonlinear interactions has emerged as a promising strategy. Classical coherent structures—such as streamwise streaks, Reynolds-stress events, and vortical structures—have been identified based on different physical criteria. Although their relevance in wall-bounded turbulence is well documented, an objective and unified assessment of their relative importance across wall-normal locations is still lacking. This work [1,2] addresses this limitation by introducing a data-driven framework to identify and rank dynamically relevant regions of turbulent flows without relying on any a priori definition of coherent structures. The proposed methodology combines deep learning with explainable artificial intelligence techniques. A U-net-based surrogate model is trained to predict turbulent flow fields from a large database of instantaneous snapshots with high accuracy. The contribution of each grid point to the model predictions is then quantified using gradient-based Shapley additive explanations, extending cooperative game theory concepts to continuous, high-dimensional systems. These importance measures are used to define novel importance-based structures, referred to as SHAP structures, whose spatial organization and physical properties are analyzed. The results demonstrate that the proposed approach provides an objective, physics-agnostic identification of dynamically relevant regions in turbulent flows, offering new insights into turbulence organization and opening new perspectives for turbulence modeling and flow control strategies. REFERENCES [1] Cremades et al., Nature Communications, vol. 15, 3864, 2024. [2] Cremades et al., Nature Communications, vol. 16, 10189, 2025.