A weak scattering model for tone haystacking

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Description/Abstract

The scattering of sound by turbulence in a jet shear layer is considered. Spectral broadening or `haystacking' is the process whereby the turbulent, time-varying inhomogeneities in the flow scatter tonal sound fields, which decreases
the level of the incident tone, but increases the broadband level around the frequency of the tone. The scattering process is modelled analytically, using high-frequency asymptotic methods and a weak-scattering assumption. Analytical models for the far-field spectral density of the scattered field are derived for two cases: (1) any polar angle including inside the cone of silence; (2) polar angles outside the cone of silence. At polar angles outside the cone of silence, the predictions from the two models are very similar, but using the second model it is considerably simpler to evaluate the far-fileld spectral density. Simulation results are compared to experimental data, albeit only at a polar angle of 90±. The model correctly predicts the behaviour of the scattered field as a function of jet velocity and tone frequency. Also simulations at other polar angles and a parametric study are presented. These simulations indicate how the `haystacking' is predicted to vary as a function of the polar angle, and also as a function of the characteristic length, time and convection velocity scales of the turbulence contained in the jet shear layer.