Investigating Planar Shear Layer Mixing Dynamics via Mori-Zwanzig Formalism

In this work, we apply the data-driven Mori-Zwanzig Mode Decomposition (MZMD), a technique generalizing Dynamic Mode Decomposition (DMD), used for extracting large-scale spatio-temporal coherent structures to analyze the dominant physical mechanisms in free shear layer flows. MZMD represents an accurate and efficient generalization of DMD and we demonstrate that MZ mem- ory improves the ability to capture nonlinearities in flow and provide insights into the underlying mechanisms that lead to the generation of turbulence. We demonstrate that MZMD models enhance prediction of small- and large-scale flow features and allow refinement of these predictions via targeted manipulation of unstable modes. This leads to markedly improved agreement with ground truth across instantaneous fields and higher-order turbulence statistics, includ- ing production and dissipation rates, compared to standard DMD. This opens the door to identify modal couplings that drive the distribution of production and dissipation processes in the flow, enabling a clearer understanding of how coherent-structure dynamics influence turbulent energy pathways.