A complex-valued resonance model for axisymmetric screech tones in supersonic jets.

We consider the resonance mechanism underpinning generation of A1 and A2 screech tones in an under-expanded supersonic jet. Starting from the resonance model recently proposed by \cite{mancinelli2019screech}, where the upstream-travelling wave is a neutrally-stable, guided jet mode, we here present a more complete linear-stability-based model for screech prediction. We study temperature and shear-layer thickness effects and show that, in order to accurately describe the experimental data, the effect of the finite thickness of the shear layer has to be incorporated in the jet-dynamics model. We then present an improved resonance model for screech-frequency predictions in which both downstream- and upstream-travelling waves may have complex wavenumber and frequency. This resonance model requires knowledge of the reflection coefficients at the upstream and downstream locations of the resonance loop. We explore the effect of the reflection coefficients on the resonance model and propose an approach for their identification. The complex-mode model allows to identify frequency-flow regions of positive values of the frequency imaginary part for which the resonance loop is amplified in time and resonance is sustained and is finally found to provide the most complete description of the measured data.