Optimal and suboptimal spatiotemporal dynamics of multi-shear-layers in rectangular jet

We analyze the perturbation dynamics of a complex supersonic multi-stream rectangular jet. The dynamics are examined through application of spectral proper orthogonal decomposition (SPOD) to elicit coherent structure and linear resolvent analysis to reveal forcing-response characteristics. SPOD of a large-eddy simulation identifies Kelvin--Helmholtz coherent structures at the dominating frequency in the splitter plate shear layer region, formed by mixing core Mach $1.6$ and bypass Mach $1.0$ streams. Resolvent analysis leverages the time-averaged flowfield on the center plane with discounting to capture flow response over a finite time window, addressing base flow instabilities. The optimal and first sub-optimal resolvent energy amplifications peak near the dominant frequency for a wide range of frequencies and spanwise wavenumbers. Comparing the resolvent and SPOD results, we find that the linear operator over-optimizes the optimal mechanism, and the sub-optimal mode instead is more aligned with the leading SPOD mode. An intriguing shift phenomenon where the optimal and sub-optimal gain distributions crossover is observed; these events are associated with receptive regions in the different shear layers. Subsequent input-output analyses with state-variable and spatial restrictions provide insights into componentwise amplification of the jet flow response, thus providing direction for tailored practical flow control.