The evolution of oceanic nonlinear internal waves over variable topography

This thesis is concerned with the evolution of oceanic nonlinear internal waves over variable one-dimensional and two-dimensional topography. The methodology is based on a variable-coefficient Korteweg-de Vries (vKdV) equation and its vari- ants, including the Ostrovsky equation which takes rotation into account and a Kadomtsev-Petviashvili (KP) equation which extends these one-dimensional models to two space dimensions. In addition, a fully nonlinear and non-hydrostatic three- dimensional primitive equation model, MIT general circulation model (MITgcm), is invoked to provide supplementary analyses. First, the long-time combined effect of rotation and variable topography on the evolution of internal undular bore is stud- ied; then an initial mode-2 internal solitary wave propagating onto the continental shelf-slope in a three-layer fluid is investigated. After that, the research is extended to two-dimensional space in which submarine canyon and plateau topography are implemented to examine a mode-1 internal solitary wave propagating over these topographic features. Finally, the topographic effect on internal wave-wave interac- tions is examined using an initial ‘V-shape’ wave representing two interacting waves in the framework of the KP equation