Physics-informed data-driven reconstruction of turbulent wall-bounded flows from planar measurements

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.