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Obtaining accurate and dense three-dimensional estimates of turbulent wall-bounded flows is notoriously challenging, and this limitation negatively impacts geophysical and engineering applications, such as weather forecasting, climate predictions, air quality monitoring, and flow control. This study introduces a physics-informed variational autoencoder model that reconstructs realizable three-dimensional turbulent velocity fields from two-dimensional planar measurements thereof. Physics knowledge is introduced as soft and hard constraints in the loss term and network architecture, respectively, to enhance model robustness and leverage inductive biases alongside observational ones. The performance of the proposed framework is examined in a turbulent open-channel flow application at friction Reynolds number Reτ=250. The model excels in precisely reconstructing the dynamic flow patterns at any given time and location, including turbulent coherent structures, while also providing accurate time- and spatially-averaged flow statistics. The model outperforms state-of-the-art classical approaches for flow reconstruction such as the linear stochastic estimation method. Physical constraints provide a modest but discernible improvement in the prediction of small-scale flow structures and maintain better consistency with the fundamental equations governing the system when compared to a purely data-driven approach. 

In recent years, the global transition towards green energy, driven by environmental concerns and increasing electricity demands, has remarkably reshaped the energy landscape. The transformative potential of marine wind energy is particularly critical in securing a sustainable energy future. To achieve this objective, it is essential to have an accurate understanding of wind dynamics and their interactions with ocean waves for the proper design and operation of offshore wind turbines (OWTs). The accuracy of met-ocean models depends critically on their ability to correctly capture sea-surface drag over the multiscale ocean surface—a quantity typically not directly resolved in numerical models and challenging to acquire using either field or laboratory measurements. Although skin friction drag contributes considerably to the total wind stress, especially at moderate wind speeds, it is notoriously challenging to predict using physics-based approaches. The current work introduces a novel approach based on a convolutional neural network (CNN) model to predict the spatial distributions of skin friction drag over wind-generated surface waves using wave profiles, local wave slopes, local wave phases, and the scaled wind speed. The CNN model is trained using a set of high-resolution laboratory measurements of air-side velocity fields and their respective surface viscous stresses obtained over a range of wind-wave conditions. The results demonstrate the capability of our model to accurately estimate both the instantaneous and area-aggregate viscous stresses for unseen wind-wave regimes. The proposed CNN-based wall-layer model offers a viable pathway for estimating the local and averaged skin friction drag in met-ocean simulations. 

In order to improve the predictive abilities of weather and climate models, it is essential to understand the behaviour of wind stress at the ocean surface. Wind stress is contingent on small-scale interfacial dynamics typically not directly resolved in numerical models. Although skin friction contributes considerably to the total stress up to moderate wind speeds, it is notoriously challenging to measure and predict using physics-based approaches. This work proposes a supervised machine learning (ML) model that estimates the spatial distribution of the skin-friction drag over wind waves using solely wave elevation and wave age, which are relatively easy to acquire. The input–output pairs are high-resolution wave profiles and their corresponding surface viscous stresses collected from laboratory experiments. The ML model is built upon a convolutional neural network architecture that incorporates the Mish nonlinearity as its activation function. Results show that the model can accurately predict the overall distribution of viscous stresses; it captures the peak of viscous stress at/near the crest and its dramatic drop to almost null just past the crest in cases of intermittent airflow separation. The predicted area-aggregate skin friction is also in excellent agreement with the corresponding measurements. The proposed method offers a practical pathway for estimating both local and area-aggregate skin friction and can be easily integrated into existing numerical models for the study of air–sea interactions. 

Abstract In large‐eddy simulations, subgrid‐scale (SGS) processes are parameterized as a function of filtered grid‐scale variables. First‐order, algebraic SGS models are based on the eddy‐viscosity assumption, which does not always hold for turbulence. Here we apply supervised deep neural networks (DNNs) to learn SGS stresses from a set of neighboring coarse‐grained velocity from direct numerical simulations of the convective boundary layer at friction Reynolds numbersRe_τup to 1243 without invoking the eddy‐viscosity assumption. The DNN model was found to produce higher correlation between SGS stresses compared to the Smagorinsky model and the Smagorinsky‐Bardina mixed model in the surface and mixed layers and can be applied to different grid resolutions and various stability conditions ranging from near neutral to very unstable. The DNN model can capture key statistics of turbulence ina posteriori(online) tests when applied to large‐eddy simulations of the atmospheric boundary layer.