Parameter dependence for acoustic propagation and tunneling in a curved nonlinear internal wave duct

The curved nonlinear internal waves (NIWs) commonly found in shallow-water ocean regions can have significant effects on acoustic propagation. Energy trapped in ducts between waves can be carried over distances of tens of kilometers or more. A three-dimensional feature model for curved NIWs with finite-width waves can produce horizontally tunneling “companion” modes with similar phase patterns to trapped modes, which carry greater energy into the far field than classical tunneling modes. Azimuthal (along-wavefront) wavenumbers and their corresponding mode shapes are presented, and wavenumber approximations obtained from a mode number conservation law compare favorably with benchmark values from the modal dispersion relation. Wavenumbers dependence on NIW radius of curvature is shown, and wavenumber approximations are accurate enough for use in sensitive computations such as modal transmission loss. Transmission loss computations for varying radius of curvature are performed, and the statistical distribution of solutions is examined. Favorable comparisons between this idealized model and a sech2 wave profile suggest that the enhanced tunneling effects of companion modes are realistic. Results for the computations and tests in this paper indicate that the approximation and analysis methods presented are appropriate for a variety of curved waveguide feature models, including those with multiple interfaces.