Kinematics and Dynamics of Amplitude Modulation Phenomenon of Screech Tones

It is well known that imperfectly expanded supersonic jets emit screech tones. The amplitudes of the tones remain nearly constant over time. However, in a recent experiment involving large aspect ratio rectangular jets, Malla and his coworkers reported the observation of screech tones with amplitudes that vary periodically in time. The phenomenon does not seem to have been reported in the literature before. They referred to the phenomenon as amplitude modulation. The present investigation studies the kinematics and dynamics of the phenomenon. Kinematically, it is found that amplitude modulation is akin to beats of two tones in vibration theory. However, the observed phenomenon is not simple harmonic. Strong higher harmonics are involved. Dynamically, amplitude modulation is driven by a pair of screech tones with a slight difference in frequencies. The nozzle used in Malla’s experiment has a nonsymmetric design. This results in slightly nonuniform jet flow. Such a jet supports a pair of Kelvin–Helmholtz instabilities with a slight difference in frequency. They form the energy sources of the screech tones. In this investigation, a two-layer vortex-sheet jet model is used to account for the slightly nonuniform jet flow. The screech tone frequencies predicted by the model are found to be in good agreement with experiment.