Jet noise from instability mode interactions

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.