Analysis of the spectral relationships of cavity tones in subsonic resonant cavity flows

The understanding of the self-sustained flow-acoustic coupling mechanism in flows over shallow rectangular cavities is of great interest owing to its various practical applications. The ability to understand and predict the resonant frequencies in such flows has recently been advanced through contributions from signal processing theory and by viewing the Rossiter tones as the product of an amplitude modulation process between a fundamental aeroacoustic loop frequency (f_a) and a modulating lower frequency. The results obtained using this approach applied to detailed and high-quality spectral data of shallow cavity flow over the Mach number range of 0.20-0.65 are presented and discussed. The new approach, while not a predictive technique, is used to clearly identify all the tones (Rossiter modes, their harmonics, and harmonics of f_a) observed in the pressure spectra and to show relationships between the tones. The asymptotic growth with Mach number of f_a and the small-step changes of the modulating lower frequency over the Mach number range studied provide insight into the variation of the Rossiter mode parameters. The results also indicate that the empirical parameters in the Rossiter equation vary with Mach number for fixed cavity geometry.