Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.

A nonlinear interaction model is used to study sources of sound in jets. The model uses quadratic interactions of instability modes, which are obtained by solving the linear parabolized stability equations. Source terms involving nonlinear interactions are evaluated and a linear wave equation is solved with direct injection of the source terms. Thus the complete method solves only linear partial differential equations, coupled by nonlinear source terms. It allows the contribution of each modal interaction to be studied separately, giving a breakdown of the radiation pattern of each interaction. The method is demonstrated using a fixed base flow matched to the experiment of Stromberg et al. (J. Fluid Mech. 72(2), 1980). The squared streamwise velocity quadrupole is the largest source term for axisymmetric mode interactions, while for helical-helical mode interactions both the squared radial and squared azimuthal velocities are the main contributing sources, despite a strong cancelation effect between them. Results are also presented for an alternative implementation, in which the base flow is allowed to vary according to the Reynolds stresses of the developing instability modes. This model demonstrates sound production during mode growth and subsequent saturation.

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