Tones and upstream-traveling waves in ideally expanded round impinging jets

We study the generation of tones by ideally expanded round jets impinging on a flat plate. Data from large-eddy simulations performed for different nozzle-to-plate distances are explored, and we consider closure of the aeroacoustic feedback loop responsible for the tones by guided jet modes. Allowable frequency ranges for resonance, underpinned by the existence of modes with upstream-directed group velocities, are computed using two different models: a cylindrical vortex-sheet model, and a locally parallel stability model which considers a finite-thickness velocity profile. It is shown that inclusion of a finite-thickness velocity profile consistent with the mean flow in the vicinity of the plate improves the agreement between observed tones and model predictions. The frequencies of the largest tones found in the data are found to fall within, or very close to, the frequency limits of the finite-thickness model, correcting discrepancies observed with the vortex-sheet model. The same trend is observed in comparisons with experimental and numerical data gathered from the literature. Pressure eigenfunctions of the stability model are in good agreement with upstream-traveling disturbances educed from the data at the tone frequencies. This provides further evidence for the involvement of guided jet modes in the resonance mechanism.