Optimal and Suboptimal Spatiotemporal Dynamics of Multi-Shear-Layers in Rectangular Jet

We analyze the perturbation dynamics of a complex supersonic multistream rectangular jet. The dynamics are examined through the 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 suboptimal 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 overoptimizes the optimal mechanism, and the suboptimal mode instead is more aligned with the leading SPOD mode. An intriguing shift phenomenon where the optimal and suboptimal 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.