A model function for jet noise events at aft angles and what it says about the statistical relationships of the events

Previous works have shown that subsonic jet noise radiating to aft angles can be described as a succession of independent large fluctuations (i.e. events). Building on these previous works, a model function is found that can accurately reproduce the observed spectra for jets whose aft angle noise is well described the Large-scale Similarity Spectrum (LSS). The selection of the model function is informed by the LSS and autocorrelation analysis of experimental data. It is determined that the model function should be a bipolar pulse with zero mean in order to reproduce the LSS over low to midrange frequencies (i.e. frequencies much higher than the spectral peak frequency are not considered). It is also found that, without sacrificing much fidelity in terms of the resulting spectrum, the model function can be antisymmetric leading to a compact analytical expression with a minimal number of parameters. Along with the statistical parameters and distributions extracted from the data, it is shown that this model function for the events can reproduce the measured spectral characteristics quite well. The model function is then used to explore the link between the event distributions and parameters and the resulting spectrum.