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An adiabatic mode Helmholtz equation for 3D underwater sound propagation is developed. The Gaussian beam tracing in this case is constructed. The test calculations are carried out for the crosswedge benchmark and proved an excellent agreement with the source images method., Comment: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:1406.6124

A pure analytic one-way coupled mode propagation model for resonant interacting modes is obtained by the multiscale expansion method. It is proved that the acoustic energy flux is conserved in this model up to the first degree of the corresponding small parameter. The test calculations with the COUPLE program give an excellent agreement., Comment: 11 pages, 2 figures

Ray mode parabolic equations which are suitable for shallow water acoustics propagation problems are derived by the multiple-scale method., Comment: 7 pp., 0 fig

A mode parabolic equation method for resonantly interacted modes was developed. The flow of acoustic energy is conserved for the derived equations with an accuracy adequate to the used approximation. The testing calculations were done for ASA wedge benchmark and proved excellent agreement with COUPLE program., Comment: 17 pages 7 figures

The problem of scattering of linear internal waves from small compact sea bottom inhomogeneities is considered from the point of view of mode-to-mode scattering. A simple formula for modal conversion coefficients, quantifying the amount of energy that is scattered into the n-th mode from the incident field m-th mode, is derived. In this formula the representation of inhomogeneities by their expansions into the Fourier and Fourier-Bessel series with respect to angular and radial coordinates respectively are used. Results of calculations, performed in a simple model case, are presented. The obtained formula can be used for a formulation of the inverse problem, as it was done in the acoustic case., Comment: 8 pages, 1 figure

A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation., Comment: Submitted to Coastal Engineering. 16 pages, 5 figures. One figure was excluded from article because of size problems