Abstract
Acoustic ray theory provides an effective means for predicting propagation in general environments. Ray theory fails in the vicinity of caustics and must there be augmented by uniform asymptotic treatment. However, even such corrections are inadequate at long ranges in a ducting channel, where the caustics due to multiple reflected and/or refracted rays accumulate at locations near the duct axis. To repair this deficiency of ray acoustics, the caustic forming ray spectra have previously been replaced by guided modes in a self-consistent ray-mode scheme. It is now shown that the troublesome ray spectra at long ranges can be replaced as well by a narrow-angle parabolic equation (PE) approximation to the full pressure field. Taken together, the hybrid ray-PE form can be regarded either as correcting via PE the failure of ray acoustics near the guiding axis or as removing the narrow-angle restriction from PE by filling the wide angle spectra with rays. The theory is developed first for a range-independent surface duct, and then for a range-dependent guiding-to-antiguiding transition. Unlike the adiabatic modes, the numerical PE algorithm can accommodate changes from guiding to antiguiding. The analogous problem of propagation along a circular concave boundary and along a boundary with concave–convex transition is treated briefly in the Appendix.
Published Version
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