The noise from large-scale coherent turbulent structures within jets remains the dominant source. For the purpose of developing future control systems for the large-scale noise source, we investigate the statistics between upstream and downstream radiating waves. We investigate two off-design supersonic jet flows with instability theory and associated noise radiation, large-eddy simulation (LES), and experiments. We compare the auto-correlation, cross-correlation, coherence, and other statistics predicted by aeroacoustic instability theory. As instability waves are closely connected with the formation of large-scale turbulent structures, they yield insight into large-scale noise statistics. We investigate two nozzles at two supersonic off-design conditions. The first is a biconic nozzle operating at an unheated condition, and the second is a NASA nozzle operating at a heated condition. We find that for these jets, the noise from instability waves is coherent between 0.40 to 0.70 at large-scale radiation frequencies between the downstream and upstream radiation directions.
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