ß-Variational autoencoders and transformers for reduced-order modelling of fluid flows.

Variational autoencoder architectures have the potential to develop reduced-order models for chaotic fluid flows. We propose a method for learning compact and near-orthogonal reduced-order models using a combination of a ß-variational autoencoder and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The ß-variational autoencoder is trained to learn a compact latent representation of the flow velocity, and the transformer is trained to predict the temporal dynamics in latent-space. Using the ß-variational autoencoder to learn disentangled representations in latent-space, we obtain a more interpretable flow model with features that resemble those observed in the proper orthogonal decomposition, but with a more efficient representation. Using Poincaré maps, the results show that our method can capture the underlying dynamics of the flow outperforming other prediction models. The proposed method has potential applications in other fields such as weather forecasting, structural dynamics or biomedical engineering.

Revisiting History Effects in Adverse-Pressure-Gradient Turbulent Boundary Layers.

The goal of this study is to present a first step towards establishing criteria aimed at assessing whether a particular adverse-pressure-gradient (APG) turbulent boundary layer (TBL) can be considered well-behaved, i.e., whether it is independent of the inflow conditions and is exempt of numerical or experimental artifacts. To this end, we analyzed several high-quality datasets, including in-house numerical databases of APG TBLs developing over flat-plates and the suction side of a wing section, and five studies available in the literature. Due to the impact of the flow history on the particular state of the boundary layer, we developed three criteria of convergence to well-behaved conditions, to be used depending on the particular case under study. (i) In the first criterion, we develop empirical correlations defining the Re𝜃 -evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter ß = 1 and 2 (note that ß = δ∗/τw dPe /dx, where δ∗ is the displacement thickness, τw the wall-shear stress and dPe /dx the streamwise pressure gradient). (ii) In the second one, we propose a predictive method to obtain the skin-friction curve corresponding to an APG TBL subjected to any streamwise evolution of ß, based only on data from zero-pressure-gradient TBLs. (iii) The third method relies on the diagnostic-plot concept modified with the shape factor, which scales APG TBLs subjected to a wide range of pressure-gradient conditions. These three criteria allow to ensure the correct flow development of a particular TBL, and thus to separate history and pressure-gradient effects in the analysis.

Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization.

This manuscripts presents a study on adverse-pressure-gradient turbulent boundary layers under different Reynolds-number and pressure-gradient conditions. In this work we performed Particle Image Velocimetry (PIV) measurements supplemented with Large-Eddy Simulations in order to have a dataset covering a range of displacement-thickness-based Reynolds-number 2300