Parabolized stability equation models of large-scale jet mixing noise

We report on the development of parabolized stability equation models to predict the evolution of low frequencies, large-scale wavepacket structures in turbulent jets and their radiated sound. We consider computations and data corresponding to high subsonic and supersonic jets from circular nozzles. Previous methods are extended to consider nonlinear interactions amongst the waves and use a Kirchhoff-surface type approach to project the near-field wavepacket amplitudes to the far-field. Linear PSE, whose initial conditions are chosen to provide an overall amplitude reference, show excellent agreement for the wavepacket amplitudes and phases with microphone array data just outside the jet shear layers, especially when the microphone data are processed to filter out contributions from uncorrelated fluctuations. Far-field sound predictions based on the linear PSE are also in reasonable agreement with far-field data. In order to investigate nonlinearity, we use an LES database to evaluate initial conditions for the PSE modes, and then compare their later evolution along the jet. Preliminary cases show some sensitivity to the initial amplitudes and their phases, and that nonlinear effects may be important in predicting the far-field sound based on the initial (near-nozzle) spectrum of disturbances