The nature of balance schemes and the concept of the slow manifold are discussed using Lorenz's (1980) model. It has been found that the Bear-Tribbia's (1977) scheme leads to a divergent series in locating the slow manifold of the model. The optimal asymptotic approximation and Pade approximant are use to "sum" the divergent series. / The optimal asymptotic approximation gives reasonable approximation to the full solutions of the model and provides the optimal balance relations which are quite accurate when the forcing is small. The accuracy seems to degrade rather quickly as the forcing increases. The "imbalance", which is the difference between the actual flow and the optimal balance state, is found to consist of nearly monochromatic inertial-gravity waves. It is shown that the optimal asymptotic approximation fails to give a reasonable estimate of the level of inertial-gravity wave activity from the Rossby modes. / For the case considered in this thesis, the Pade approximant does not seem to work well and hence offers no significant advantage over the optimal asymptotic approximation. The slow manifold, fuzzy slow manifold and effects of the scaling on the balance are also discussed in this thesis.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.60508 |
| Date | January 1991 |
| Creators | Guan, Shucai |
| Publisher | McGill University |
| 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 | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Meteorology.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001259444, proquestno: AAIMM72074, Theses scanned by UMI/ProQuest. |
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