Mode-Switching and Nonlinear Effects in Compressible Flow Over a Cavity

Multiple distinct peaks of comparable strength in unsteady pressure autospectra often characterize compressible ?ow-induced cavity oscillations. It is unclear whether these different large-amplitude tones (i.e., Rossiter modes) coexist or are the result of a mode-switching phenomenon. The cause of additional peaks in the spectrum, particularly at low frequency, is also unknown. This article describes the analyses of unsteady pressure data in a cavity using time-frequency methods, namely the short-time Fourier transform (STFT) and the continuous Morlet wavelet transform, and higher-order spectral techniques. The STFT and wavelet analyses clearly show that the dominant mode switches between the primary Rossiter modes. This is veri?ed by instantaneous schlieren images acquired simultaneously with the unsteady pressures. Furthermore, the Rossiter modes experience some degree of low-frequency amplitude modulation. An estimate of the modulation frequency, obtained from the wavelet analysis, matches the low-frequency peak seen in the autospectrum. Higher-order spectral methods were employed to investigate potential quadratic nonlinear interactions between the Rossiter modes and to determine if they are responsible for the low-frequency mode present in the autospectrum. In turn, this low-frequency mode could interact with the Rossiter modes to modulate their amplitude. Signi?cant nonlinearities, in the form of sum and difference frequencies of the Rossiter modes, are present in the L/d = 2 cavity at M = 0.4, while nonlinear effects are much smaller in the L d = 4 at M = 0.6. The bispectral analysis indicates that quadratic interactions between Rossiter modes in the near-?eld pressure are not responsible for the observed low-frequency peak in the pressure autospectrum. Furthermore, the low-frequency mode does not exhibit a strong nonlinear coupling with the Rossiter modes.