Executive Summary : | Turbulent flows are a paradigm for spatiotemporally complex nonlinear systems such as the weather, cardiac dynamics, and chemical reactions, just to name a few. Under most practical conditions, such systems exhibit spatiotemporally chaotic evolution which is very challenging to model, predict, and control. Yet, careful analysis of real-world, laboratory, and numerical data points to the presence of intermittent coherent dynamics hidden within strongly chaotic evolution. In the case of transitionally (moderately) turbulent two-dimensional flows, recent numerical and experimental studies have demonstrated that coherent structures can be employed for flow modelling and prediction. Similar approaches, however, proved ineffective in the case of three-dimensional (3D) wall-bounded transitional flows (e.g., in pipes). One clear hurdle is that 3D direct numerical simulation (DNS) of such flows is prohibitively time-consuming for generating statistically significant number of intermittent events. The limitations of DNS are even more apparent when dealing with complex fluids through curved geometries, where equations governing the flow are not readily available. The proposed research addresses these limitations by employing data-driven techniques to extract coherent structures from experimental data and build coherent structure-based models. We propose to employ state-of-the-art techniques, namely persistent homology (PH) and dynamic mode decomposition (DMD) to detect coherent structures. Persistent homology can quantify which flow features persist (are most robust) when a scalar/vector field is binary-thresholded and the threshold is varied across all possible values. Since persistence is an inherent feature of coherent structures, PH serves as an effective tool to detect them. Dynamic mode decomposition, akin to proper orthogonal decomposition, identifies large-scale, spatiotemporally correlated/coherent flow features. Employing these mathematical tools, we plan to develop coherent structure-based reduced order models (ROMs) of transitional steady/pulsatile flows in straight/curved pipes, two canonical laboratory systems that represent a wide range of wall-bounded flows in both industrial and natural (biological) settings. The proposed research lays foundation for data-driven modelling of laboratory flows, which should eventually enable a better theoretical understanding of complex flows, such as blood flow in the ascending aorta. |