  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 linearized 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.
