Modeling near-nozzle events in a subsonic jet via SPOD and Wiener–Hopf solutions

Recent large-eddy simulations of a Mach 0.9, Re = 10⁶ jet with a nozzle has shown strong higher-frequency (St >∽ 2) tonal peaks to radiate at the upstream and sideline angles (Vempati et al. 2020). This has been confirmed via extracting SPOD modes of the jet where such tones are found to be present at the lowest azimuthal mode of these specific frequencies. Moreover, these radiated waves seemed to be scattered by the nozzle as the coherent structures of the nozzle boundary layer interacted with the lip. Here, we construct a Wiener--Hopf scattering model of this interaction where the jet is now represented as a uniform flow separated by a cylindrical vortex sheet from a concentric coflow which interacts with a sharp-edged semi-infinite cylindrical surface, the latter representing the nozzle. Following the works of Tam & Hu (1989) and Samanta (2016) such jets support various instability modes: Kelvin-Helmholtz modes, the upstream and downstream traveling soft-duct modes, the upstream-traveling neutral subsonic mode (more recently, referred to as the guided jet mode GJM) and the hard-walled duct modes of the nozzle. The Wiener-Hopf method yields complete analytical solutions as any of these modes are allowed to be scattered at the nozzle, which is then compared with the corresponding SPOD picture. The solutions are used to compute reflectivity coefficients of these modes at the nozzle lip with an aim to identify potential candidates for completing the feedback loop associated with the resonance phenomena observed in the potential core of similar subsonic jets.