Furthering resolvent-based jet noise models

Resolvent analysis continues to provide promising results for modeling the hydrodynamic near-field and acoustic far-field in turbulent jets, particularly when compared to modes deduced through spectral proper orthogonal decomposition (SPOD) of high-fidelity large eddy simulations (LES). Although previous studies have shown that the acoustic field for supersonic jets is of low-rank and primarily described by the Kelvin-Helmholtz instability, the agreement between the acoustically optimal resolvent mode (Kelvin-Helmholtz) and optimal SPOD mode is still lacking. The discrepancy is due to the spatial coloring of turbulent mechanisms in supersonic jets and presents a challenge for reconstructing the acoustic field, as well as the full field flow statistics. To account for coloring, additional (i.e., suboptimal) resolvent modes, associated with the Orr mechanism, must be included and their correlation to other modes determined. Here, we estimate the coloring between resolvent modes by projecting onto an ensemble of LES realizations and reconstructing the realizations in the resolvent basis. The associated projection coefficients provide an ensemble of observations which inherently possess the statistical information necessary to reconstruct the flow and to which we propose a reduced-order stochastic model. We find that the inclusion of a few resolvent suboptimal modes (i.e., Orr-type) allows for modeling of the acoustic field to within 2 dB and increases the region of acoustic agreement when compared to a single mechanism model