Characterization and Reconstruction of Coherent Structures in Wake Flows using Modal Analysis

Large-scale coherent structures play a vital role in many turbulent flows of interest: atmospheric flows, astrophysical phenomena, oceanic circulation, and engineering applications over a variety of fields. In aerodynamics/fluid mechanics, wake flows are some of the most prevalent and practical flows of interest. Despite major advances in computational capabilities, the cost of direct numerical simulation will remain exorbitant for the foreseeable future. Reduced-order reconstructions of flows provide a `real-time' CFD analog, approximating representation of large-scale structures and maintaining reasonable physical fidelity. These representations specifically capture the dominant instabilities and resulting large-scale phenomena, which often satisfy engineering purposes. This also aids in data compression, alleviating a growing problem of memory allocation and storage. Various system-level analysis tools are enabled, making the fluid dynamic effects readily accessible to subsystems for automated monitoring. Developments in these techniques stand to provide physically accurate flow phenomena for the field of visualization, too. By isolating the large-scale structures, components of the full reconstruction can be superimposed on base flows, providing cost-effective physical fidelity where small-scale features can be introduced independently toward desired aesthetics. Modal decomposition techniques like proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are ideally suited for developing a reduced-order representation of various flow field quantities. Both are well-established in the analysis of complex flows. However, a consensus is lacking regarding how such techniques should contribute toward representations of variable fidelity as prescribed by an end-user. The primary objectives of this dissertation are to (i) characterize large-scale coherent structures in wake flows; and (ii) investigate different aspects of reduced-order reconstruction of wake flow fields utilizing POD and DMD. To accomplish this the canonical flow past a square cylinder has been computed in three key regimes: (i) steady laminar (Re=200; steady in-flow); (ii) pulsatory laminar (Re=200; pulsatory in-flow); and (iii) steady turbulent (Re=22,000; steady in-flow). The flow past a square cylinder contains several flow phenomena of importance to engineering applications, namely: massive separation, vortex-shedding, secondary instabilities, and coherent structures. Adequately capturing and isolating the effects of these phenomena contributes to a fuller understanding of the critical mechanisms inherent in wake flow physics