Laboratory and analytical modeling of internal waves in uniform and non-uniform stratifications

Abstract

Internal gravity waves are propagating disturbances in a stably stratified fluid. Ubiquitous in geophysical systems, they have significant impact on both fundamental processes and engineering applications. In the ocean, for example, internal waves are a significant means of tidal dissipation, eventually affecting abyssal mixing and the global energy budget. They are also of importance in engineering fields such as deep-water oil drilling, submarine technology and acoustic communications. In the atmosphere, internal waves affect momentum and energy transport processes. While the generation of internal waves in both the ocean and the atmosphere is beginning to be well understood, what is now of great interest is the life of internal waves after their generation. More specifically, how are they dissipated, and what fundamental phenomena occur along the way ? To investigate these issues, this thesis presents the results of internal wave studies using a combination of experimental and analytical modeling, with a focus on internal wave scattering in the ocean. In the first part of the thesis, the effectiveness of a novel wave generator, which comprises a series of vertically stacked plates that oscillate horizontally, in generating unidirectional plane waves/wave beams and distinct vertical modes is discussed and demonstrated in experiments. The experimental results show excellent agreement with corresponding numerical simulations, which model the wave generator as a vertical boundary on which desired velocity fields are enforced. Finally, it is shown that the Fourier transform of the spatial structure of the wave generator is a useful predictive tool for the emitted wave field. This novel technique of wave generation is then used in the experiments discussed in the remainder of the thesis. The second part of the thesis considers the viscous propagation of internal wave beams in nonuniform stratifications, and uses laboratory observations of wave beam ducting to explain the apparent vanishing of an internal wave beam at the Keana ridge, Hawaii. Furthermore, an analogy between internal wave transmission in nonuniform stratifications and light transmission in optical interferometry is established. Constructing an internal wave interferometer in the lab, selective transmission of wavelengths by nonuniform stratifications is demonstrated. In the final part of the thesis, an investigation of internal wave scattering by ocean-floor topography is carried out. An existing Green function method for internal tide generation is advanced to account for arbitrary two-dimensional topography in arbitrary nonuniform stratifications. The analytical model is then utilized to study the scattering of a mode-I internal tide by idealized topographic shapes in uniform and nonuniform stratifications. The thesis concludes with a case study of the scattering of mode-1 internal tide at the Line Islands Ridge at Hawaii, the location of an upcoming NSF field study, the EXperiment on Internal Tide Scattering (EXITS).