The use of data-driven methods in fluid mechanics has surged dramatically in recent years due to their capacity to adapt to the complex and multi-scale nature of turbulent flows, as well as to detect patterns in large-scale simulations or experimental tests. In order to interpret the relationships generated in the models during the training process, numerical attributions need to be assigned to the input features. One important example are the additive-feature-attribution methods. These explainability methods link the input features with the model prediction, providing an interpretation based on a linear formulation of the models. The Shapley additive explanations (SHAP values) are formulated as the only possible interpretation that offers a unique solution for understanding the model. In this manuscript, the additive-feature-attribution methods are presented, showing four common implementations in the literature: kernel SHAP, tree SHAP, gradient SHAP, and deep SHAP. Then, the main applications of the additive-feature-attribution methods are introduced, dividing them into three main groups: turbulence modeling, fluid-mechanics fundamentals, and applied problems in fluid dynamics and heat transfer. This review shows that explainability techniques, and in particular additive-feature-attribution methods, are crucial for implementing interpretable and physics-compliant deep-learning models in the fluid-mechanics field.

This work investigates the influence of classically coherent structures on wall-shear stress and energy dissipation in turbulent channel flow, utilizing direct numerical simulations (DNS) data and explainable deep learning (XDL). Sweeps, defined as regions of low streamwise velocity moving toward the wall, are found to be the most influential structures for both energy dissipation and drag. Moreover, the volume of these key structures falls within a narrow range, making it easier to identify the most significant ones. Consequently, this work paves the way for the development of novel, highly efficient turbulence-control strategies for the reduction of drag.

UAV noise remains a major concern for the widespread implementation of these aircraft in a wide array of potential applications, especially in the urban environment. Moreover, not only overall noise levels must be considered when analyzing the impact of UAV noise; noise quality based on the spectral content of the acoustic signal must be considered due to the psychoacoustic impact on the listeners. Also, as UAVs become widespread, the ability to perform field replacement of propellers using additive manufacturing (AM) is of increased interest to many operators. However, as different AM techniques become popular, their impact on performance and noise must be assessed. In this investigation, we experimentally test the same propeller geometry manufactured using the most popular AM techniques, evaluating how different characteristics such as surface roughness, anisotropy, and flexibility affect the propeller. Finally, we performed a numerical campaign to isolate these effects and better understand their effect on propeller noise and performance.

Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.

The behavior of turbulent flows remains a significant unsolved problem in physics. Recently, a large quantity of effort has been directed toward understanding the non-linear interactions of the different flow structures in order to address this challenge. In this paper, different implementations of one exact method for identifying these structures are analyzed. This includes two sequential algorithms and a parallelizable one, developed to handle large-scale data efficiently. The new parallel algorithm offers significant advantages in handling the computational demands of large simulations, providing a more scalable solution for future research.