Influence of ground blocking on the acoustic phase variance in a turbulent atmosphere

Abstract

A number of previous studies have analyzed the impacts of anisotropy and inhomogeneity on sound propagation in a turbulent atmosphere. However, these studies did not address the potentially important factor of ground blocking, namely the inhibition of buoyancy-produced velocity fluctuations by the ground surface. The current presentation accounts for this effect following the reference D. K. Wilson, “A three-dimensional correlation/spectral model for turbulent velocities in a convective boundary layer,” Boundary-Layer Meteorol. 85, 35–52 (1997). The temperature and shear-produced velocity fluctuations are not significantly blocked by the ground and are modeled as in the study by V. E. Ostashev and D. K. Wilson [Acoustics in Moving Inhomogeneous Media, 2nd ed. (2015)]. The resulting turbulence model is used to calculate the variance of the phase fluctuations for vertical and slanted sound propagation in the atmosphere. The calculations are done without the Markov approximation which might not be applicable for the largest turbulence eddies in the atmospheric boundary layer such as those due to buoyancy-produced velocity fluctuations. Theoretical formulations for the phase variance are compared with the data in a recent experiment involving sound propagation from a ground-based source to microphones installed at different heights of a 135-m tower.