Matching pursuit decomposition and stochastic modelling of pressure fluctuations in the near field of compressible subsonic jets

The Matching Pursuit decomposition is applied to an extensive experimental database containing pressure fluctuations generated by a compressible circular jet in free-stream conditions at subsonic Mach numbers. Measurements were carried out at the Centre Acoustique of the Ecole Centrale de Lyon using microphone arrays installed in both the near and far fields. The Matching Pursuit method provides the decomposition of the near-field pressure time series into linear expansions of waveforms selected from a prescribed set of functions, referred to as the Dictionary. The adopted Dictionary is composed of Gabor functions, called atoms, and a few hundred atoms are adaptively selected to construct simplified versions of the original random signals. It is shown that the approximate representation of the near-field pressure retains key features associated with noise generation mechanisms, including spectral content and correlation with the far field. A predictive model for the main statistical properties of the simplified signals is then developed. These statistics are analysed as a function of flow conditions and include the waiting time between successive atoms, their phase speed, and the parameters characterizing the atom’s shape, namely the Gaussian envelope and the frequency content. The robustness of the proposed model is assessed by including an additional database obtained in a different experimental facility [1]. It is shown that the stochastic model can generate synthetic pressure time series at arbitrary axial positions in the jet near field and for different subsonic Mach numbers. The overall agreement highlights the generality of the findings and supports the application of the proposed approach to jet-noise modelling.