A method for predicting acoustic signal fluctuations using a distribution of Gaussian correlation functions

Abstract

The autocorrelation function of the refractive index inhomogeneities in a turbulent medium was modeled as a continuous distribution of Gaussian functions. The advantage of this approach lies in the simplicity of the solutions of the wave scattering integral for a weakly inhomogeneous medium with a Gaussian spatial correlation function. The density function of the distribution for the case of a turbulent medium was constructed. Convolution of the solution of the wave scattering integral for a unit Gaussian function with the density function yields the solution for the turbulent medium. The results are identical with those obtained by Tatarskii [Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961 and Dover, New York, 1967); and The Effects of the Turbulent Atmosphere on Wave Propagation, translated by the Israel Program of Scientific Translations Ltd., available as TT-68-50464 from the U.S. Dept. of Commerce] by the more complicated approach of using the wavenumber spectrum and the structure function.