Internal gravity waves grow in amplitude as they propagate upwards in a non-Boussinesq fluid and weakly nonlinear effects develop due to interactions with an induced horizontal mean flow. In this work, a new derivation for this wave-induced mean flow is presented and nonlinear Schrodinger equations are derived describing the weakly nonlinear evolution of these waves in an anelastic gas and non-Boussinesq liquid. The results of these equations are compared with fully nonlinear numerical simulations. It is found that interactions with the wave-induced mean flow are the dominant mechanism for wave evolution. This causes modulational stability for hydrostatic waves, resulting in propagation above the overturning level predicted by linear theory for a non-Boussinesq liquid. Due to high-order dispersion terms in the Schrodinger equation for an anelastic gas, hydrostatic waves become unstable and break at lower levels. Non-hydrostatic waves are modulationally unstable, overturning at lower levels than predicted by linear theory.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/878 |
| Date | 06 1900 |
| Creators | Dosser, Hayley V |
| Contributors | Sutherland, Bruce R. (Physics / Earth and Atmospheric Sciences), Swaters, Gordon E. (Mathematical and Statistical Sciences), Sydora, Richard D. (Physics), Mann, Ian (Physics) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 12144157 bytes, application/pdf |
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