Acoustic resolvent analysis of turbulent jets

Abstract

We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban \textit{et al.} An empirical model of noise sources in subsonic jets. \textit{Journal of Fluid Mechanics} (2023): A18).