A Combined Proper Orthogonal Decomposition–Wavelet Framework for Spatiotemporal Characterization of Reacting and Non-Reacting Flow Fields

With the rapid growth of spatiotemporal data generated by advanced experimental diagnostics, particularly high-speed laser-based imaging techniques, there is an increasing need for analytical frameworks capable of extracting physically meaningful information from complex nonstationary reacting flows. This study presents a unified Proper Orthogonal Decomposition (POD)–Continuous Wavelet Transform (CWT) framework capable of capturing the time- and frequency-domain dynamics of a spatiotemporally evolving reacting flow-field. An initial decomposition of spatial modes obtained from planar laser-induced fluorescence (PLIF) images of the hydroxyl radical (a flame marker) present in the wake region of a bluff body stabilized flame is conducted, and the time-varying coefficients of the dominant POD modes are further analyzed along with the fluctuating pressure field using the bivariate wavelet transform. These bivariate extensions enable the extraction of temporal measures of correlation between the chamber acoustics and flame shedding modes. The instantaneous phase relationship between the hydroxyl radical distribution and the wall pressure in the combustion chamber enables identification and time-dependent characterization of thermoacoustic instabilities within the turbulent reacting flow-field. To demonstrate the generality of the proposed framework, it is further applied to acoustically forced non-reacting cryogenic coaxial nitrogen jets, where it successfully identifies the dominant coherent flow structures and their time-dependent synchronization with the imposed acoustic perturbations. The proposed methodology establishes a general analysis framework applicable to a broad class of time-resolved experimental and computational flow-field datasets containing coherent, non-stationary dynamics.