Experimental observations and theoretical studies show that nonlinear internal waves occur widely in shallow water and cause acoustic propagation effects including ducting and mode coupling. Horizontal ducting results when acoustic modes travel between internal wave fronts that form waveguide boundaries. For small grazing angles between a mode trajectory and a front, an interference pattern may arise that is a horizontal Lloyd mirror pattern. An analytic description for this feature is provided along with comparisons between results from the formulated model predicting a horizontal Lloyd mirror pattern and an adiabatic mode parabolic equation. Different waveguide models are considered, including boxcar and jump sound speed profiles where change in sound speed is assumed 12 m/s. Modifications to the model are made to include multiple and moving fronts. The focus of this analysis is on different front locations relative to the source as well as on the number of fronts and their curvatures and speeds. Curvature influences mode incidence angles and thereby changes the interference patterns. For sources oriented so that the front appears concave, the areas with interference patterns shrink as curvature increases, while convexly oriented fronts cause patterns to expand.

The acoustic ducting effect by curved nonlinear gravity waves in shallow water is studied through idealized models in this paper. The internal wave ducts are three-dimensional, bounded vertically by the sea surface and bottom, and horizontally by aligned wavefronts. Both normal mode and parabolic equation methods are taken to analyze the ducted sound field. Two types of horizontal acoustic modes can be found in the curved internal wave duct. One is a whispering-gallery type formed by the sound energy trapped along the outer and concave boundary of the duct, and the other is a fully bouncing type due to continual reflections from boundaries in the duct. The ducting condition depends on both internal-wave and acoustic-source parameters, and a parametric study is conducted to derive a general pattern. The parabolic equation method provides full-field modeling of the sound field, so it includes other acoustic effects caused by internal waves, such as mode coupling/ scattering and horizontal Lloyd's mirror interference. Two examples are provided to present internal wave ducts with constant curvature and meandering wavefronts.

Nonlinear internal waves have 3-D random variability arising from smaller scale physical oceanographic processes. Internal wave fronts form acoustic waveguides, and we examine propagation in directions nearly parallel to the fronts. Intensity fluctuations arising from the variability are treated by 3-D radiative transport methods, which provide insight into the parametric dependence on waveguide randomness. We focus on situations where the frozen field approximation applies, the acoustic modes represent the vertical energy distribution in the waveguide, and the modes propagate adiabatically. Under these conditions, horizontal modal variations are specified by 2-D radiative transport equations. With additional assumptions, the transport equations simplify to diffusion-type equations. An alternative energy scattering interpretation describes the duct in terms of a 2-D Galton’s box, assuming discrete scattering events occur as modes propagate down the duct. The resulting equations also reduce to diffusion-type equations in the continuous limit. We use appropriate spatial variability scales from the SW06 experiment to investigate properties of acoustic intensity. [Work supported by the ONR.]

When two trains of nonlinear internal waves roughly align, their lead waves form effective boundaries of an acoustic duct in which energy is trapped. This type of propagation may be considered a scattering process resulting from the broken internal wave fronts between the lead waves. A traditional approach uses adiabatic normal modes and sound speed perturbations to calculate energy propagation along horizontal rays. An alternate is a radiative transport method in which acoustic vertical modes carry energy and a two-dimensional (2D) transport equation describes horizontal propagation. This model has parameters that are related to waveguide properties and are found from physical internal wave features. One parameter incorporates the significant curvature observed in many internal wave fronts. The two solution approaches are compared and contrasted. Data from the Shallow Water ‘06 Experiment are used to specify internal wave parameters and to compare with model calculations. [Work supported by the ONR.]

Observations and numerical simulations have shown that nonlinear internal waves in continental shelf and shelfbreak regions can form 3-D acoustic ducts. The strength of ducting depends on the size of internal waves, the width of the gap between waves and the curvature of the wave front, and also on the acoustic frequency and the vertical mode number. It has been seen in numerical simulations and simplified ray theory that for a given internal wave structure and a given frequency, higher vertical modes are easier being trapped in a curved internal wave duct. Also, the number of the lowest mode trapped between curved waves increases as the frequency goes up. In this talk, a 3-D normal mode theory is employed to analyze these observed characteristics. The analysis is carried out in a cylindrical coordinates, and two types of horizontal modes are found: whispering-gallery modes and full bouncing modes. Both types of modes can be described by Bessel functions, and the asymptotic formulas can be used in some limiting cases. [Work supported by the ONR.]