Acoustic propagation in three-dimensional curved nonlinear internal waves

Abstract

Nonlinear internal waves (NIWs) in shallow water have significant acoustic impacts and cause three-dimensional ducting effects, for example, energy trapping in a duct between curved wavefronts that propagates over distances of tens of kilometers or more. A normal mode approach applied to a three-dimensional idealized parametric model using cylindrical coordinates determines the dependence of such effects on parameters of the features. Specifically, an extension of mode number conservation leads to convenient analytical formulas for along-duct (angular) acoustic wavenumbers. A simplified model with infinite-width waves bounding a finite duct is used to establish a classification system for normal modes depending on geometric characteristics, resulting in five distinct formulas to obtain wavenumber approximations. Finite-width wavefronts are then introduced, producing tunneling "companion modes" with similar phase patterns to trapped modes. Characteristics of companion modes are presented, including their relationship to trapped and leaky modes, their contributions to acoustic pressure, and their decaying behavior for large distances. Wavenumber prediction formulas are extended to the finite-width wavefront model, and approximations from the mode number conservation law compare favorably with benchmark values from the modal dispersion relation. Examples for wavenumber dependence on wavefront curvature, duct width, and wave width demonstrate approximation accuracy over a broad range of physical values, even where transitions in mode types occur with parameter changes. Curves showing dependence of wavenumbers on radius of curvature and wave width are used to predict parameter ranges for which companion modes occur. Approximated wavenumbers can be used in sensitive field computations such as transmission loss (TL), and several examples are shown with sources placed in the duct and outer wave regions of the model. Horizontal-mode TL contours found from approximate and numerically exact wavenumbers agree well in structure and location of intensity features, and cross-sectional plots show only small differences between pattern phases and amplitudes of the two calculations. The efficiency and accuracy of acoustic wavenumber and field approximations, in combination with the mode-type classifications, suggest their application to determining parameter sensitivity and also to other feature models, including those with multiple interfaces. In addition to normal mode methods, 2-D and 3-D Parabolic Equation (PE) codes are used to investigate modeling assumptions and results used throughout this thesis. The effects of using infinite-width waves in computations are tested for curved wavefronts of varying eccentricities, and comparisons are made between square NIWs and solutions of the KdV equation. Finally, the 3-D PE code is used to compute TL fields at a shelf break using real-world ocean bathymetry data collected off the coast of Taiwan. Cases with and without internal waves are considered, and the presence of NIWs has significant effects on acoustic propagation.