Spatial-temporal coherence of acoustic signals propagating in a refractive, turbulent atmosphere

Propagation of acoustic signals above an impedance ground in a refractive, turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity is considered. Starting from a parabolic equation, and using the Markov approximation and a locally frozen turbulence hypothesis, closed-form equations for the spatial-temporal statistical moments of arbitrary order of the sound-pressure field are derived. The general theory provides a basis for analysis of many statistical characteristics of broadband and narrowband acoustic signals for different geometries of propagation: line-of-sight propagation, multipath propagation in a refractive atmosphere above an impedance ground, and sound scattering into a refractive shadow zone. As an example of application of this theory, the spatial-temporal coherence of narrowband acoustic signals for line-of-sight propagation is calculated and analyzed. The coherence time of acoustic signals is studied numerically for meteorological conditions ranging from cloudy to sunny conditions, and with light, moderate, and strong wind. The results obtained are compared with available experimental data.