We consider the problem of acoustic propagation and scattering in inhomogeneous waveguide governed by the Helmholtz equation. We focus on an ideal, cylindrically symmetric ocean waveguide, limited above by an acoustically soft boundary modelling the free surface, and below by a hard boundary modelling the impenetrable seabed with general bottom topography. The wave field is excited by a monochromatic point source, and thus, the present solution is equivalent to the construction of the Green’s function in the inhomogeneous domain. An improved coupled-mode method is developed, based on an enhanced local-mode series for the representation of the acoustic field, which includes an additional mode accounting for the effects of the bottom slope and curvature. The additional mode provides an implicit summation of the slowly convergent part of the series, rendering the remaining part to converge much faster, pemitting truncation of the modal expansions keeping only a few evanescent terms. Using the enhanced representation, in conjunction with an appropriate variational principle, a system of coupled-mode equations on the horizontal plane is derived for the determination of the complex modal-amplitude functions. Numerical results are presented including comparisons with analytical solutions illustrating the role and significance of the additional mode and the efficiency of the present coupled-mode tmodel, which can be naturally extended to treat propagation and scattering problems in three-dimensional, multi-layered ocean acoustic waveguides.

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