Sound propagation in a turbulent atmosphere near the ground: a parabolic equation approach.

The interference of the direct wave from the point source to the receiver and the wave reflected from the impedance ground in a turbulent atmosphere is studied. A parabolic equation approach for calculating the sound pressure p at the receiver is formulated. Then, the parabolic equation is solved by the Rytov method yielding expressions for the complex phases of direct and ground-reflected waves. Using these expressions, a formula for the mean squared sound pressure [absolute value(p)2] is derived for the case of anisotropic spectra of temperature and wind velocity fluctuations. This formula contains the "coherence factor," which characterizes the coherence between direct and ground-reflected waves. It is shown that the coherence factor is equal to the normalized coherence function of a spherical sound wave for line-of-sight propagation. For the case of isotropic turbulence, this result allows one to obtain analytical formulas for [absolute value(p)2] for the Kolmogorov, Gaussian, and von Karman spectra of temperature and wind velocity fluctuations. Using these formulas, the effects of temperature and wind velocity fluctuations, and the effects of different spectra of these fluctuations on the mean squared sound pressure, are numerically studied. Also the effect of turbulent anisotropy on the interference of direct and ground reflected waves is numerically studied. Finally, it is shown that the mean squared sound pressure [absolute value(p)2] calculated for the von Karman spectrum of temperature fluctuations agrees well with experimental data obtained in a laboratory experiment.