On the data-driven reduced order modelling in fluid dynamics

Fluid dynamics is characterized by several physical phenomena, leading to complex spatial and temporal structures characterized by different spatial and temporal scales. This thesis is a comprehensive exploration of data-driven approaches for modal analysis, stability analysis and reduced-order modeling in fluid dynamics, aiming to enhance the understanding of complex flow phenomena. As regarding the modal analysis, this work delves into the extraction of coherent flow structures using conventional techniques like Spectral Proper Orthogonal Decomposition (SPOD) and introduces innovative approaches like Robust SPOD to deal with noisy or corrupt data and Gappy POD for handling two-phase PIV measurements. These methods are applied to various flow configurations, including the vertical liquid jet, the turbulent jet, the open cavity flow and the two-phase mixing layer. A data-driven approach to estimate the global spectrum of gravitational liquid jet is presented. The underlying linear operator has been extracted with the Dynamic Mode Decomposition (DMD), considering random perturbations of the base flow. This analysis has shed light on sinuous and varicose modes, their interaction, and the influence of the main governing parameters. Conventional and novel Reduced-order models (ROM) are presented, including Extended Cluster-based Network Modeling (eCNM) and functional based CNM. These methods offer efficient ways to capture flow dynamics, forecast fluid behaviours and handle undersampled data. This thesis advances data-driven approaches in fluid dynamics, providing valuable tools for the comprehension of complex flow phenomena.