Resolvent modelling of subsonic jet noise

When the jet noise is cast in the form of a linear input-output problem, the cross-spectraldensity (CSD) matrix of the sound field is forced by the CSD of non-linear interactions via the resolvent operator. The forcing CSD is difficult to compute or measure, but its projection onto the resolvent input space can be identified from the CSD of the sound field. In a recent study using data from numerical simulation [1], such an identification showed that a low-rank truncation of the forcing-projection matrix can be used to reconstruct the acoustic field of transonic and supersonic turbulent jets with Mach numbers 0.9 and 1.5 respectively. Encouraged by this result, we performed two-point acoustic measurements in isothermal turbulent jets over a broad range of subsonic Mach numbers [2]. In the present work, these CSD matrices are used to obtain an empirical model of the forcing-projection matrix, following the procedure reported in Pickering et al., 2021 [1]. We investigate the parametric dependence of the low-rank, forcing-projection matrix on Mach number, frequency, and azimuthal mode, and we propose a model that captures this dependence and, allowing computation of downstream radiation with 1.5dB precision for subsonic jets in the Mach-number range 0.7 to 0.9.