A fully three-dimensional coupled mode approach is used in this paper to describe the physics of low frequency acoustic signals propagating through a train of internal waves at an arbitrary azimuth. A three layer model of the shallow water waveguide is employed for studying the properties of normal modes and their coupled interaction due to the presence of nonlinear internal waves. Using a robust wave number integration technique for Fourier transform computation and a direct global matrix approach, an accurate three-dimensional coupled mode full field solution is obtained for the tonal signal propagation through straight and parallel internal waves. This approach provides accurate results for arbitrary azimuth and includes the effects of backscattering. This enables one to provide an azimuthal analysis of acoustic propagation and separate the effects of mode coupled transparent resonance, horizontal reflection and refraction, the horizontal Lloyd's mirror, horizontal ducting and anti-ducting, and horizontal tunneling and secondary ducting.

This thesis describes the physics of fully three-dimensional low frequency acoustic interaction with internal waves, bottom sediment waves and surface swell waves that are often observed in shallow waters and on continental slopes. A simple idealized model of the ocean waveguide is used to analytically study the properties of acoustic normal modes and their perturbations due to waves of each type. The combined approach of a semi-quantitative study based on the geometrical acoustics approximation and on fully three-dimensional coupled mode numerical modeling is used to examine the azimuthal dependence of sound wave horizontal reflection from, transmission through and ducting between straight parallel waves of each type. The impact of the natural crossings of nonlinear internal waves on horizontally ducted sound energy is studied theoretically and modeled numerically using a three-dimensional parabolic equation acoustic propagation code. A realistic sea surface elevation is synthesized from the directional spectrum of long swells and used for three-dimensional numerical modeling of acoustic propagation. As a result, considerable normal mode amplitude scintillations were observed and shown to be strongly dependent on horizontal azimuth, range and mode number. Full field numerical modeling of low frequency sound propagation through large sand waves located on a sloped bottom was performed using the high resolution bathymetry of the mouth of San Francisco Bay. Very strong acoustic ducting is shown to steer acoustic energy beams along the sand wave's curved crests.

It is known that the waveguide depth variability causes horizontal refraction and coupling of acoustic normal modes. Presence of large bottom sediment waves and sea swell are examples of strongly anisotropic waveguides that result in range dependence of the acoustic scintillation index. In the directions parallel to the wave crests, three-dimensional effects of mutual horizontal focusing, defocusing and diffusion between such waves are the main mechanisms of intensity fluctuations. For acoustic propagation in the perpendicular to the wave crests directions, intensity fluctuations are mainly driven by random mode coupling and scattering. Analytical studies and numerical examples of the acoustic scintillation index, as well as its azimuthal and range dependence in the shallow water with both types of waves, will be provided. Directions for future studies will be discussed.

Crossing internal wave trains are commonly observed in continental shelf shallow water. In this paper, we study the effects of crossing internal wave structures on three-dimensional acoustic ducts with both theoretical and numerical approaches. We show that, depending on the crossing angle, acoustic energy, which is trapped laterally between internal waves of one train, can be either scattered, cross-ducted or reflected by the internal waves in the crossing train. We describe the governing physics of these effects and illustrate them for selected internal wave scenarios using full-field numerical simulations.

Observations show that shallow water bottom relief often has a band-limited directional spectrum produced by various oceanographic and geological processes. This directional bottom feature is shown to have a noticeable effect on three-dimensional low-frequency acoustic propagation. An analytical study with an idealized model of straight sea bottom ripples has shown that acoustic energy can be partially ducted between neighboring ripples, and this ducting will affect acoustic propagation in shallow water. In our work, we also study ducting and refracting due to idealized curved sea bottom ripples. Previous research has shown that non-linear internal waves can also create acoustical ducts. Comparative analysis of these two different ducts is performed using our idealized model. The combined effects of internal waves and bathymetry are studied for various relative directions of internal wave front and bottom ripples. A numerical simulation of three-dimensional sound propagation across realistic bathymetry and internal wave fluctuations is performed. In conclusion, both water column fluctuations and bathymetry variability need to be taken into account when studying three-dimensional acoustic propagation in shallow water.