Applicability of the paraboic equation to problems of wave propagation in a turbulent atmosphere. I. Spatial coherence
V.A. Banakh, I.V. Zaloznaya, A.V. Falits
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: parabolic equation, wave equation, spatial coherence, turbulent atmosphere, path integral
Abstract
Based on the representation of the solution of the stochastic wave equation for a point source as a path integral, a formula for the spatial coherence function of a spherical wave propagating in the atmosphere is derived, taking into account the entire set of virtual paths in the path integral. For the Kolmogorov turbulence spectrum model, the spatial coherence of a spherical wave is calculated for various path-length-to-wavelength ratios. The results are compared with calculations in the parabolic approximation. Conditions are determined under which the coherence function calculations based on the wave and parabolic equations coincide. A geometrical-optical approximation is rigorously justified in calculating the spatial coherence function based on a path integral. It is established that a virtual trajectory in the form of a straight line connecting the source and receiver, the only one considered in the geometrical-optical approximation, completely determines the coherent properties of a wave in a turbulent atmosphere. The results of this work can be used to solve problems of radio wave propagation in random media.
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