Effects of wind velocity fluctuations on the statistical moments of plane and spherical sound waves in the turbulent atmosphere with the Gaussian correlation function of wind velocity fluctuations.

Abstract

It is quite often assumed in the theories of waves in random media that medium inhomogeneities have a Gaussian correlation function. Equations for the main statistical moments of plane and spherical sound waves propagating in a medium with temperature fluctuations are well known in the literature. Among these statistical moments are the following: the mean sound field, the variances and correlation functions of log-amplitude and phase fluctuations, and the transverse coherence function. The present paper deals with a derivation of equations for these statistical moments for the case of plane and spherical wave propagation in the atmosphere with wind velocity fluctuations. It is shown that the derived equations can differ not only quantitatively but also qualitatively from analogous equations for the case of sound propagation in the atmosphere with temperature fluctuations even if the wind velocity and temperature fluctuations make the same contributions to the variance of the acoustical refractive-index fluctuations. The results obtained are generalized to the case of sound propagation in an arbitrary medium (for example, for sound propagation in the ocean with current fluctuations). [This material is based upon Work supported by the U.S. Army Research Office under Contract No. DAAH04-95-1-0593.]