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Derivation of a wide-angle parabolic equation for sound waves in inhomogeneous moving media. (English) Zbl 0896.76085
Many types of atmospheric acoustic problems cannot be properly solved by the small-angle parabolic equation (PE), and the wide-angle parabolic equation is needed to examine these problems. However, the existing wide-angle PE’s do not describe the effects of regular and random inhomogeneities in the wind velocity and density on sound propagation and scattering in the turbulent atmosphere. Here, the author shows that the wide-angle PE currently in use is really based on an equation for sound in medium with small scattering angles. This paper derives a wide-angle PE for sound waves in moving media with regular and random inhomogeneities in the sound speed, density and medium velocity by using the formalism of pseudodifferential operators and Padé approximation. It is shown that in the limit of small-angle application in atmospheric acoustics, the derived wide-angle PE reduces to the small-angle PE.
When the density is constant and the medium velocity is negligible as in the underwater acoustics, the wide-angle PE agrees with that derived for underwater acoustics. The author presents solutions obtained by using the derived wide-angle PE, and gives some applications.

MSC:
76Q05 Hydro- and aero-acoustics
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