Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier-Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle.