The present study delineates the effects of pressure gradient history and local disequilibration on the small and large-scale energy in turbulent boundary layers (TBLs) imposed with a broad range of adverse-pressure-gradients (APG). This is made possible by analyzing four published high-fidelity APG TBL databases, which span weak to strong APGs and cover dynamic conditions ranging from near-equilibrium to strong disequilibrium. These databases enable the development of a methodology to understand the effects of PG history and local disequilibration, the latter defined here as the local streamwise rate of change of the pressure force contribution in the force balance. The influence of PG history on TBL statistics is quantified by the accumulated PG parameter (β¯), proposed previously by Vinuesa et al. (2017) to study integral quantities, which is compared here between cases at matched local PG strength (β), Reynolds number (Re) and dβ/dRe at nominally similar orders of magnitude. Here, β denotes a general umbrella term used for pressure gradient parameters that is estimated using different scaling parameters in this study. While the effects of local disequilibration (dβ/dRe) are investigated by considering TBL cases at matched β, Re, and fairly matched β¯. This enables analysis of accumulated PG history and local disequilibration effects separately, where applicable, to highlight qualitative differences in statistical trends. It is found that β¯ cannot unambiguously capture history effects when dβ/dRe levels are significantly high, as it does not account for the delayed response of the mean flow and turbulence, nor the attenuation of the pressure gradient effect with distance. In two comparisons of APG TBLs under strong non-equilibrium, the values of β¯ and dβ/dRe expressed using Zagarola–Smits scaling were found to be consistent with the trends in mean velocity defect and Reynolds stresses noted previously for weak APG TBLs. While an increase in β¯ is associated with energization of both the small and large scales in the outer regions of APG TBLs, it affects only the large scales in the near-wall region. This confirms the ability of near-wall small scales to rapidly adjust to changes in PG strength. By attempting to provide a structured parametric methodology to isolate effects of PG history and local disequilibration, this study reports the influence of these effects on turbulent flow statistics across the widest APG strengths documented in the literature.

A phenomenological description is presented to explain the intermediate and low-frequency/large-scale contributions to the wall-shear-stress (τw) and wall-pressure (pw) spectra of canonical turbulent boundary layers, both of which are well known to increase with Reynolds number, albeit in a distinct manner. The explanation is based on the concept of active and inactive motions (Townsend, J. Fluid Mech., vol. 11, issue 1, 1961, pp. 97-120) associated with the attached-eddy hypothesis. Unique data sets of simultaneously acquired τw, pw and velocity-fluctuation time series in the log region are considered, across a friction-Reynolds-number (Reτ) range of O(103) ≲ Reτ ≲ O(106). A recently proposed energy-decomposition methodology (Deshpande et al., J. Fluid Mech., vol. 914, 2021, A5) is implemented to reveal the active and inactive contributions to the τw- and pw-spectra. Empirical evidence is provided in support of Bradshaw's (J. Fluid Mech., vol. 30, issue 2, 1967, pp. 241-258) hypothesis that the inactive motions are responsible for the non-local wall-ward transport of the large-scale inertia-dominated energy, which is produced in the log region by active motions. This explains the large-scale signatures in the τw-spectrum, which grow with Reτ despite the statistically weak signature of large-scale turbulence production, in the near-wall region. For wall pressure, active and inactive motions respectively contribute to the intermediate and large scales of the pw-spectrum. Both these contributions are found to increase with increasing Reτ owing to the broadening and energization of the wall-scaled (attached) eddy hierarchy. This potentially explains the rapid Reτ-growth of the pw-spectra relative to τw, given the dependence of the latter only on the inactive contributions.

This study presents novel drag reduction active-flow-control (AFC) strategies for a three-dimensional cylinder immersed in a flow at a Reynolds number based on freestream velocity and cylinder diameter of ReD=3900. The cylinder in this subcritical flow regime has been extensively studied in the literature and is considered a classic case of turbulent flow arising from a bluff body. The strategies presented are explored through the use of deep reinforcement learning. The cylinder is equipped with 10 independent zero-net-mass-flux jet pairs, distributed on the top and bottom surfaces, which define the AFC setup. The method is based on the coupling between a computational-fluid-dynamics solver and a multi-agent reinforcement-learning (MARL) framework using the proximal-policy-optimization algorithm. This work introduces a multi-stage training approach to expand the exploration space and enhance drag reduction stabilization. By accelerating training through the exploitation of local invariants with MARL, a drag reduction of approximately 9% is achieved. The cooperative closed-loop strategy developed by the agents is sophisticated, as it utilizes a wide bandwidth of mass-flow-rate frequencies, which classical control methods are unable to match. Notably, the mass cost efficiency is demonstrated to be two orders of magnitude lower than that of classical control methods reported in the literature. These developments represent a significant advancement in active flow control in turbulent regimes, critical for industrial applications.

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.

To meet the 2030 Agenda for Sustainable Development, all Sustainable Development Goals (SDGs) must receive adequate and balanced funding. This study applies artificial intelligence to analyze research proposals accepted between 2015 and 2023 in the European Union and the United States, focusing on datasets from the European Research Council and the National Science Foundation, respectively. Despite the growing application of Artificial Intelligence (AI) in various domains, there remains a lack of comprehensive analysis that applies AI to examine funding allocation across SDGs and gender disparities in scientific research. This study addresses this unmet need by using AI to uncover imbalances in funding distribution, offering insights into current funding instruments. We reveal critical coverage disparities across SDGs, with both funding instruments prioritizing SDG 9 (Industry, Innovation, and Infrastructure), highlighting a potential overemphasis on this goal. Additionally, we document pronounced gender imbalances among principal investigators across nearly all SDGs, except for SDG 5 (Gender Equality), in which female researchers are comparatively better represented. Our results indicate an urgent need for more inclusive and balanced approaches to achieve sustainable development, starting with allocation of research funding. By providing a nuanced understanding of funding dynamics and advocating strategic reallocations, this study offers actionable policy design and planning insights to foster a more equitable and comprehensive support system for sustainability-focused research endeavours.

The wake topology behind a wall-mounted square cylinder immersed in a turbulent boundary layer is investigated using high-resolution large-eddy simulations (LES). The boundary-layer thickness at the obstacle location is fixed, with a Reynolds number based on cylinder height ℎ and free-stream velocity 𝑢∞ of 10,000 while the aspect ratio (AR), defined as obstacle height divided by its width, ranges from 1 to 4. The mesh resolution is comparable to DNS standards used for similar wall-mounted obstacles, though with relatively lower Reynolds numbers. The effects of AR on wake structures, turbulence production, and transport are analyzed via Reynolds stresses, anisotropy-invariant maps (AIM), and the turbulent kinetic energy (TKE)budget. In particular, the transition from ‘‘dipole’’ to a ‘‘quadrupole’’ wake is extensively examined as AR increases. With increasing AR, the wake shrinks in both the streamwise and spanwise directions, attributed to the occurrence of the base vortices (AR = 3 and 4). This change in the flow structure also affects the size of the positive-production region that extends from the roof and the flank of the obstacle to the wake core. The AIMs confirm three-dimensional wake features, showing TKE redistribution in all directions (Simonsen and Krogstad, 2005). Stronger turbulence production in AR = 3 and 4 cases highlights the role of tip and base vortices behind the cylinder. The overall aim is to refine the dipole-to-quadrupole transition as a function of AR and accounting for the incoming TBL properties. The novelty relies on proposing the momentum-thickness-based Reynolds number Re𝜃 as a discriminant for assessing TBL effects on turbulent wake structures.

The environmental impact of air travel, largely driven by fossil-fuel consumption, remains a critical subject of debate. Addressing this challenge requires immediately adopting sustainable practices to mitigate its environmental footprint. While hydrogen and hybrid-electric propulsion technologies show promise for the future, current efforts focus on Sustainable Aviation Fuels (SAF) as a viable near-term solution to reduce aviation emissions while ensuring compatibility with existing aviation infrastructure. This paper examines the environmental impact of air travel, focusing on the emissions associated with conventional fuel and SAF. Using two methodologies, namely the subsonic fuel flow method (SF2) and an improved version of it, the emissions corrected subsonic fuel flow method (EC-SF2), non-CO2 emissions trends are analyzed along a flight trajectory from Stockholm to Bordeaux. The comparison between the two methods underscores the importance of accurate emission modeling, particularly for SAF correction on emission index. The SF2 method reveals that SAF fuels with higher calorific value than conventional fuel increased total HC and CO emissions while decreasing NOx emissions. Conversely, the EC-SF2 method resulted in a more homogeneous emissions reduction trend. Our proposed methodology, which corrects both fuel flow and emission index based on SAF-specific data, could, therefore, offer a more reliable estimation of emissions behavior for SAF. These findings highlight the sensitivity of emissions modeling on environmental assessment.

The control efficacy of deep reinforcement learning (DRL) compared with classical periodic forcing is numerically assessed for a turbulent separation bubble (TSB). We show that a control strategy learned on a coarse grid works on a fine grid as long as the coarse grid captures main flow features. This allows to significantly reduce the computational cost of DRL training in a turbulent-flow environment. On the fine grid, the periodic control is able to reduce the TSB area by 6.8%, while the DRL-based control achieves 9.0% reduction. Furthermore, the DRL agent provides a smoother control strategy while conserving momentum instantaneously. The physical analysis of the DRL control strategy reveals the production of large-scale counter-rotating vortices by adjacent actuator pairs. It is shown that the DRL agent acts on a wide range of frequencies to sustain these vortices in time. Last, we also introduce our computational fluid dynamics and DRL open-source framework suited for the next generation of exascale computing machines.

The aim of this study is to discover new active-flow-control (AFC) techniques for separation mitigation in a two-dimensional NACA 0012 airfoil at a Reynolds number of 3000. To find these AFC strategies, a framework consisting of a deep-reinforcement-learning (DRL) agent has been used to determine the action strategies to apply to the flow. The actions involve blowing and suction through jets at the airfoil surface. The flow is simulated with the numerical code Alya, which is a low-dissipation finite-element code, on a high-performance computing system. Various control strategies obtained through DRL led to 43.9% drag reduction, while others yielded an increase in aerodynamic efficiency of 58.6%. In comparison, periodic-control strategies demonstrated lower energy efficiency while failing to achieve the same level of aerodynamic improvements as the DRL-based approach. These gains have been attained through the implementation of a dynamic, closed-loop, time-dependent, active control mechanism over the airfoil.