Internal Wave Generation and Near-Resonant Interactions: Theory and Applications
| dc.comment.hidden | I have fixed the four required revisions from my previous submission. | en |
| dc.contributor.author | Rees, Timothy | |
| dc.date.accessioned | 2011-04-29T17:36:36Z | |
| dc.date.available | 2011-04-29T17:36:36Z | |
| dc.date.issued | 2011-04-29T17:36:36Z | |
| dc.date.submitted | 2011 | |
| dc.description.abstract | Near-resonant triad interactions and wave generation theory are investigated for continuously stratified fluids. Interaction equations are derived for spatially-varying wave trains under the inviscid Boussinesq approximation. Rotational effects are included, and properties of the underlying eigenvalue problem are explored. To facilitate a numerical study of the near-resonant interactions, numerical methods are developed and an analysis of wave generation on a periodic domain is performed. Numerical experiments using laboratory and ocean-scale parameters are conducted, and the simulations confirm the validity of the wave forcing theory. Interaction experiments demonstrate a strong tendency for waves to exhibit nonlinear behaviour. While resonant interactions are observed in the laboratory scale simulations, nonlinear steepening effects and the formation of solitary-like waves dominate the ocean-scale experiments. The results suggest that the weakly-nonlinear interaction theory is only appropriate in a limited parameter regime. The problem of analyzing forced wave equations on an infinite domain is also considered. Motivated by the results obtained on a periodic domain, asymptotic analysis is applied to three important wave equations. The method of steepest descents is used to determine the large-time behaviour for the linearized Korteweg-de Vries, Benjamin-Bona-Mahony, and internal gravity wave equations. The asymptotic results are compared with numerical experiments and found to agree to high precision. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/5888 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.subject | internal waves | en |
| dc.subject | resonant interactions | en |
| dc.subject | wave forcing theory | en |
| dc.subject.program | Applied Mathematics | en |
| dc.title | Internal Wave Generation and Near-Resonant Interactions: Theory and Applications | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Applied Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |