The importance of the shock-cell structure in the A1 and A2 jet screeching modes*

This work focuses on exploring jet screech closure mechanisms of the axisymmetric modes in shock-containing jets. The analysis is based on different types of waves supported by the jet medium (Mancinelli et al. 2019), and the interaction between the Kelvin-Helmholtz mode and the shock-cell structure (Tam $\&$ Tanna 1982, Shen $\&$ Tam 2002). Analysis of the convective terms in the Navier-Stokes equations expanded around a streamwise-oscillatory mean flow shows that new forcing terms arise in particular wavenumbers by the interaction between instability waves and shocks, creating new energy transfer paths for the generation of upstream-travelling waves that can close resonance. Predictions using locally parallel spatial stability analysis and the wavenumber spectrum of the shock-cell structure, educed from experiments, suggest that the A1 mode resonance is closed by the peak wavenumber of the shock-cell spectrum interacting with the Kelvin-Helmholtz mode, and the A2 mode is closed by a secondary peak, which arises from the spatial variation of the shock-cell wavenumber. Results are in good agreement with experiments in the region of dominance of each mode, and an analysis of the dominance of each mode is performed.