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Modelling the noise emitted by turbulent jets is made difficult by their acoustic inefficiency: only a tiny fraction of the near-field turbulent kinetic energy is propagated to the far field as acoustic waves. As a result, jet-noise models must accurately capture this small, acoustically efficient component hidden among comparatively inefficient fluctuations. In this paper, we identify this acoustically efficient near-field source from large-eddy simulation data and use it to inform a predictive model. Our approach uses the resolvent framework, in which the source takes the form of nonlinear fluctuation terms that act as a forcing on the linearised Navier-Stokes equations. First, we identify the forcing that, when acted on by the resolvent operator, produces the leading spectral proper orthogonal decomposition modes in the acoustic field for a Mach 0.4 jet. Second, the radiating components of this forcing are isolated by retaining only portions with a supersonic phase speed. This component makes up less than 0.05% of the total forcing energy but generates most of the acoustic response, especially at peak (downstream) radiation angles. Finally, we propose an empirical model for the identified acoustically efficient forcing components. The model is tested at other Mach numbers and flight-stream conditions and predicts noise within 2 dB accuracy for a range of frequencies, downstream angles and flight conditions. [ABSTRACT FROM AUTHOR]

Self-similarity of wall-attached coherent structures in a turbulent channel at Reτ = 543 is explored by means of resolvent analysis. In this modelling framework, coherent structures are understood to arise as a response of the linearised mean-flow operator to generalised frequency-dependent Reynolds stresses, considered to act as an endogenous forcing. We assess the self-similarity of both the wall-attached flow structures and the associated forcing. The former are educed from direct numerical simulation data by finding the flow field correlated with the wall shear, whereas the latter is identified using a frequency space version of extended proper orthogonal decomposition (Borée, Exp. Fluids, vol. 35, issue 2, 2003, pp. 188-192). The forcing structures identified are compared to those obtained using the resolvent-based estimation introduced by Towne et al. (J. Fluid Mech., vol. 883, 2020, A17). The analysis reveals self-similarity of both wall-attached structures - in quantitative agreement with Townsend's hypothesis of self-similar attached eddies - and the underlying forcing, at least in certain components. [ABSTRACT FROM AUTHOR]

Linearisation of the Navier–Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier–Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and can be modified under nonlinear transformation of variables. For example, we show that using primitive and conservative variables leads to differences in the singular values and modes of the resolvent operator for turbulent jets, and that the differences become more severe as variable-density effects increase. This lack of uniqueness of mean-flow-based linear analysis provides new opportunities for optimising models by specific choice of variables while also highlighting the importance of carefully accounting for the nonlinear terms that act as a forcing on the resolvent operator. [ABSTRACT FROM AUTHOR]