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 of pressure fluctuations generated by a compressible circular jet under free-stream conditions at subsonic Mach numbers. Measurements were carried out at the Centre Acoustique of the Laboratoire de Mécanique des Fluides et d’Acoustique of the École Centrale de Lyon using microphone arrays installed in both the near and far fields. Matching Pursuit represents complex pressure signals as a linear superposition of simple waveforms, called atoms, selected from a predefined set known as the Dictionary. The atoms are chosen iteratively to provide the best match with the signal in terms of maximum correlation. In this paper, the method adaptively decomposes near-field jet pressure fluctuations into a small set of Gabor atoms, providing simplified versions of the original random pressure 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 functions of the flow conditions and include the waiting time between successive atoms, their phase speed, and the parameters characterizing the shape of each atom, namely the Gaussian envelope and frequency content. The robustness of the proposed model is assessed by including an additional database obtained in a different experimental facility (Camussi et al., 2025). 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.