Dual-PIV with Exact Dynamic Mode Decomposition: an experimental method to investigate the spatio-temporal dynamics with a high spatial resolution of high-speed turbulent shear flows.*

High-speed turbulent shear flows are prevalent in many industrial and air transport applications. Despite these flows' chaotic and fluctuating nature, it is still possible to identify large-scale coherent structures, which are often the consequence of shear layer instabilities, that help understand and control their dynamics. Quantitative experimental techniques are employed to study the actual physics of these flows and identify patterns. One commonly used technique is particle image velocimetry (PIV), which estimates the velocity vector field in the measured flow region. To ensure accurate measurements, high spatial resolution is required to enable important aspects of turbulent shear flows such as turbulence statistics, velocity gradients, and vorticity, as well as flow topologies to be assessed and studied. However, due to current limitations in camera sensor technology, time-unresolved measurements are only possible at a high spatial resolution. These methods do not provide information about the frequencies and corresponding growth or decay rates of flow oscillations, thus limiting insight into the temporal dynamics of high-speed turbulent shear flows. A dual-PIV system combined with exact dynamic mode decomposition (EDMD) is presented that enables the extraction of turbulent shear flow dynamics. This approach enables high-resolution spatial and temporal measurements, overcoming the limitations of traditional time-resolved low-spatial resolution or standard time-unresolved high-spatial resolution PIV systems. By applying this experimental approach and utilizing EDMD on the acquired high spatial resolution dual-PIV dataset, it is possible to extract frequencies of interest, as well as their corresponding spatial modes, providing insight into the dominant turbulent shear flow dynamics. Results of the application of the dual-PIV system combined with EDMD to high-speed turbulent jet flows will be presented as a pertinent application example.