Modeling of three-dimensional sound propagation through solitary internal waves

Abstract

An accurate and numerically efficient numerical model is very important for studying the effect of internal wave on underwawter sound propagation. A full-wave, three-dimensional (3D) coupled-mode model is able to deal with the internal wave problem with satisfactory accuracy, but such a model is in general numerically inefficient. A numerically efficient 3D model is presented for sound propagation in a range-dependent waveguide in the presence of solitary internal waves in this work. The present model is a forward-marching model that neglects backscattering. In this 3D model, an efficient two-dimensional (2D) coupled-mode model, C-SNAP, is adopted to compute 2D acoustic field solutions excited by a line source. The C-SNAP is a 2D forward-marching model, which uses an energy-conserving matching condition to preserve accuracy. An appealing aspect of C-SNAP is that its efficiency is competitive with that of the existing parabolic equation model. The integral transform technique is used to extend C-SNAP to a 3D model, where a complex integration contour is used for evaluating the wavenumber integral. A brief review of C-SNAP and formulation of the present 3D model are given. The forward-marching models are primarily suitable for treating the range-dependent problems with weak backscattering, such as with a slowly varying bathymetry. Since in general the backscattering from internal wave is weak, which is also validated numerically in this work, the present model is able to address the problem of sound propagation through internal wave with satisfactory accuracy. At the same time, it achieves an efficiency gain of at least an order of magnitude over that of full two-way, 3D model. In addition to the internal wave, the present model is also suitable for solving the general range-dependent problems where backscattering is weak, such as in the presence of a bottom ridge of a small height. Numerical simulations are also provided to validate the present model, where a two-way, 3D model serves as the benchmark. The numerical results show that the effect of the internal wave on the acoustic field is negligible for the region between the source and the internal wave. However, the effect is significant on the other side of the internal wave. A more interesting observation is the angular dependence of the interference pattern induced by the internal wave.