On the jump in the frequency of acoustic oscillations in supersonic flows over rectangular cavity

In this study, we analyze the jump in the frequency of acoustic oscillations that is observed in supersonic flows over a rectangular cavity. Frequency jumps have previously been observed in experiments when the length-to-depth ratio of a cavity is gradually varied. However, the reason for their occurrence has not been well understood. In order to explain the occurrence of the frequency jump, we improved the classical acoustic oscillation model by taking the acoustic reflections at the cavity walls into account. The results obtained using our analytical model are found to agree with experimental results with respect to both the frequency jump and the variation in frequency with the length-to-depth ratio. On the basis of the analytical model, a simple model is also proposed; in the simple model, it is assumed that the acoustic waves in the cavity are one-dimensional waves. This simple model can provide clearly the fundamental reason for the occurrence of the jump in the frequency of acoustic oscillations in the cavity.