Coherence of Screech Generation at the 2nd Harmonic for a Rectangular Jet

Abstract

High-fidelity large-eddy simulation (LES) data is used to analyze the dominant coherent structures associated with screech for a supersonic rectangular jet with an aspect ratio of 4. The focus of this work is on the second harmonic frequency of screech and establishing a theoretical explanation of its generation in relation to the fundamental screech tone. Spectral proper orthogonal decomposition (SPOD) is used to analyze flow structures associated with hydrodynamic and acoustic fluctuations at the fundamental and harmonic frequencies. Spatial wavenumbers of the leading SPOD modes identify potential triadic interactions inside the jet which give rise to to external acoustics. These results, combined with amplitude and symmetry considerations, suggest that external acoustics at the second harmonic are generated by non-linear interaction between the downstream-traveling Kelvin-Helmholtz (KH) wave at the harmonic frequency and the shock-cell structure. A clear distinction between the guided jet mode and the mode associated with far-field acoustics is also observed at the harmonic frequency, which is in contrast to the fundamental frequency. Phase-averaging of the density gradient magnitude reveals anti-symmetric oscillations in the shock-cell structure at the fundamental frequency that are consistent with symmetry induced by the KH wave. At the harmonic frequency, symmetric shock-cell oscillations can also be linked to interaction with the KH wave, which gives rise to symmetric far-field acoustic patterns.