M.Sc Thesis

M.Sc StudentEyov Erez
SubjectProgressive Acoustic-Gravity Waves on Top of an Elastic
DepartmentDepartment of Civil and Environmental Engineering
Supervisors ASSOCIATE PROF. Assaf Klar
Full Thesis textFull thesis text - English Version


Water compressibility is an essential component required for a thorough study of ocean waves. Its inclusion in the governing equations may result in special types of propagating waves (named acoustic-gravity waves) that otherwise would not emerge from the analytical treatment. From engineering point of view these waves are extremely important as they may be used for tsunami warning, since they travel at greater speed than the tsunami wave. Previous study investigated the behavior of the acoustic-gravity waves in different ocean conditions, all of which with a perfectly rigid bottom.

The current thesis investigates the behavior of acoustic-gravity waves for more realistic conditions of an ocean over a deformable bottom. The ocean bottom is represented as an elastic half-space. In specific, purely progressive modes of gravity and acoustic-gravity are sought after. Beyond the engineering importance of considering more realistic conditions, the more extensive treatment may shed light on the mechanisms involved in conveying energy from the ocean to the land as part of the phenomenon of microseisms.

The thesis is composed of 9 chapters. Chapters 1 and 2 present the problem and review related research works to the topic. Chapter 3 presents the governing equations and the boundary conditions. Chapter 4 presents the derived dispersion equation for gravity and acoustic-gravity waves, and includes a comparison to previously published solution of rigid bottom ocean. Chapter 5 presents parametric study results using the Preliminary Reference Earth Model (PREM) parameters. Chapter 6 conducts a JWKB analysis with a constant energy flux to investigate how waves propagate towards the shore at slowly varying bathymetry. It is found that while for rigid bottom ocean, acoustic-gravity waves never reach the coast, for ocean with elastic bottom the first mode is capable of reaching the shoreline. It is also shown that this wave change into Rayleigh wave as it reaches the shore. It is well recognized that ocean waves may be responsible for microseisms, but the exact mechanism of how the energy is conveyed to the land is not well understood. The current finding may well be the missing link. Chapter 7 discusses the effect of water compressibility and bottom elasticity on the tsunami phase velocity. Chapter 8 discusses some of the limitations associated with the ideal conditions assumed in the current work, and approximates their effect using simplified engineering concepts. Chapter 9 summarizes the main conclusions of the thesis and outlines topics for possible future research.