Modulation of downstream-propagating waves in aeroacoustic resonance

The coherent component of turbulence in shock-containing flows undergoing aeroacous-tic resonance often displays a periodic spatial modulation. This modulation is generally thought to be driven either by the hydrodynamic/acoustic standing wave, or by the shock structures within the jet. In this work, we examine this spatial modulation and seek to determine its cause. Specifically, we consider whether the growth of the Kelvin-Helmholtz wavepackets associated with the resonance cycle is modulated by either of these mechanisms. A combined experimental and theoretical analysis is undertaken. Time-independent velocity snapshots of screeching jets are used to produce a reduced order model for the resonance via a Proper Orthogonal Decomposition. Streamwise Fourier filtering is then applied to isolate the negative and postive wavenumber componetns, which for this flow correspond to upstream and downstream-propagating waves. A global stability analysis on an experimentally derived base flow is conducted, producing remarkably similar results to those obtained via experiment. In both the global stability analysis and the experimental decomposition, three distinct structures are observed in the spatial wavenumber spectrum. One of these is associated with the downstream-propagating KH mode. One is associated with the upstream component of screech as previously identified. The third component has positive phase velocity, but a radial structure quite different to the other two waves. We provide evidence that this downstream-propagating wave is the result of an interaction between the KH wavepackets and the shocks embedded in the jet, much the same as the upstream-propagating acoustic wave, and has a structure very similar to duct-like modes previously identified in round jets. A weakly-non-parallel local analysis supplements the global analysis, and suggests that the growth of the KH wave is essentially un-modulated by the shocks, at least at the frequencies associated with screech.