Vertical and slanted sound propagation in the near-ground atmosphere: Coherence and distributions.

Atmospheric turbulence causes acoustic signals to fluctuate and diminishes their coherence. These phenomena are important in applications such as source localization and sonic boom propagation. This article provides formulations for the spatial, cross-frequency, and temporal coherences of narrowband acoustic signals propagating over vertical and slanted paths in the atmosphere. Formulations for single- and two-point distributions of acoustic signals are also overviewed. The theoretical formulations are compared with data from a comprehensive sound propagation experiment carried out in 2018 at the National Wind Technology Center (Boulder, CO). The theories for sound propagation in a turbulent atmosphere, when combined with turbulence models incorporating shear and buoyancy instabilities, correctly predict the measured spatial coherence, which is primarily affected by small-scale isotropic turbulence. For relatively small coherence times, this approach also correctly predicts the temporal coherence. However, the approach underpredicts the cross-frequency coherence and temporal coherence for relatively large coherence times, which are affected by large-scale anisotropic buoyancy-driven velocity fluctuations. For different regimes ranging from unsaturated to fully saturated scattering, the measured distributions agree well with the theoretical predictions.