A coupled mode model is presented for the propagation of acoustic-gravity waves
in layered ocean waveguides. The analysis extends previous work for acoustic waves in
inhomogeneous environment. The coupled mode system is derived by means of a variational
principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction
systems defined in the vertical section. These are obtained through the solution of vertical
eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of
additional modes accounting for the effects of spatialy varying boundaries and interfaces. This
enhancement provides an implicit summation for the slowly convergent part of the localmode
series, rendering the series rapidly convergent, increasing substantialy the efficiency of
the method. Particular aspects of the method include high order Lagrange Finite Element
Methods for the solution of local vertical eigenvalue problems in the case of multilayered
waveguides, and Gauss-type quadrature for the computation of the coupled-mode system
coefficients. The above aspects make the present method quite efficient for long range
propagation in extended waveguides, such as the ones found in geophysical applications, e.g.
ocean basins, as only few modes are needed for the accurate representation of the wave field
