Coherence function of a sound field in an oceanic waveguide with horizontally isotropic statistics

The mean value and the coherence function of a sound field propagating in an oceanic waveguide with random inhomogeneities are important statistical characteristics of this field, which are needed for many practical applications. Closed equations for the coherence function were obtained in many works for both two dimensional and three dimensional geometries. For the 3D case, these equations are too involved even for a numerical treatment. In this paper, explicit expressions for the mean field and the coherence function due to a point omnidirectional monochromatic source in a 3D waveguide are derived for the case of random inhomogeneities, which are statistically isotropic in a horizontal plane. The solutions are much simpler than those obtained previously due to the cylindrical symmetry of the problem. The theory developed is used to study numerically the mean field and the coherence function in an oceanic waveguide perturbed by a random field of internal waves with the Garrett-Munk spectrum.