The coherence function of a sound field propagating in a turbulent atmosphere

Abstract

The coherence function of a sound field propagating through an atmosphere with temperature and wind velocity fluctuations is important for many practical applications involving microphone arrays. In the literature, the transverse coherence function has been studied in detail, when acoustic sensors are located in a plane perpendicular to the sound propagation path. In this paper, for the case of line‐of‐sight sound propagation, a closed‐form expression for the coherence function of a plane wave is derived for arbitrary location of acoustic sensors. Using this expression, for some limiting cases simple formulas for the coherence function are obtained which are valid for arbitrary spectra of turbulence. Furthermore, the coherence function is calculated and analyzed in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. In particular, the longitudinal coherence radius, when acoustic sensors are located along the sound propagation path, is calculated. It is also shown that contours of the coherence radius are elongated perpendicular to this path for relatively small propagation distances, and along it for large distances.