Prediction of Turbulent Boundary-Layer Noise

Turbulent boundary layers, which are observed in almost all aerospace vehicles and in natural phenomena, radiate acoustic waves. A closed-form mathematical model is proposed to predict the intensity and coherence of acoustic radiation from turbulent boundary layers. For this purpose, the Navier–Stokes equations are rearranged and solved using a cross-spectral acoustic analogy. Arguments of the model are the spatial two-point cross correlations of the turbulent statistics and mean flow of the turbulent boundary layer. These arguments are modeled using relations whose coefficients are calibrated with numerical and measurement data drawn from a wide range of sources. Models for turbulent statistics are proposed for the zero-pressure-gradient turbulent boundary layer at a wide range of ambient Mach numbers. Predictions of acoustic intensity, spatial coherence, and model arguments are validated with numerical and measurement data. Predicted sound-pressure levels agree well with numerical results. The variation of the near-field, midfield, and far-field decay of acoustic intensity is investigated. The decay of spatial coherence is demonstrated to be a reflection of the turbulent statistics within the boundary layer. Finally, an analysis of the model equation shows that it is consistent with canonical theory.