Observable-augmented manifold learning for multi-source turbulent flow data

This study seeks a low-rank representation of turbulent flow data obtained from multiple sources. To uncover such a representation, we consider finding a finite-dimensional manifold that captures underlying turbulent flow structures and characteristics. While nonlinear machine-learning techniques can be considered to seek a low-order manifold from flow field data, there exists an infinite number of transformations between data-driven low-order representations, causing difficulty in understanding turbulent flows on a manifold. Finding a manifold that captures turbulence characteristics becomes further challenging when considering multi-source data together due to the presence of inherent noise or uncertainties and the difference in the spatiotemporal length scale resolved in flow snapshots, which depends on approaches in collecting data. With an example of numerical and experimental data sets of transitional turbulent boundary layers, this study considers an observable-augmented nonlinear autoencoder-based compression, enabling data-driven feature extraction with prior knowledge of turbulence. We show that it is possible to find a low-rank subspace that not only captures structural features of flows across the Reynolds number but also distinguishes the data source. Along with machine-learning-based super-resolution, we further argue that the present manifold can be used to validate the outcome of modern data-driven techniques when training and evaluating across data sets collected through different techniques. The current approach could serve as a foundation for a range of analyses including reduced-complexity modelling and state estimation with multi-source turbulent flow data.