The thesis is mainly concerned with the initial-value problem for barotropic Rossby waves linearized around a parabolic zonal flow, U (y) = U$ sb0$ + U$ sp prime$ y + U$ sp{ prime prime}$ y$ sp2$/2. It is shown that the non-dimensional equation for the perturbation depends on only one essential parameter, a = $-$2 ($ beta -$ U$ sp{ prime prime}$)/U$ sp{ prime prime}$. The associated Rayleigh-Kuo equation has a continuous spectrum of singulars modes for all values of "a" and an infinite number of discrete Rossby waves for a $< -$.25. / In Fourier space the problem has a Lagrangian formulation which permits a simple qualitative discussion concerning the nature of the interaction between the perturbation and the zonal flow. We have found new conservation laws that give insight into the dynamics of the jet. These results show a significant difference between the dynamics of easterlies and westerlies. / Using results from the theory of Lie groups we have obtained a number of distinct separation of variables for a $ geq -$.25 in the long wave approximation. This allow the initial value problem to be completely solved and also provides a number of exact solutions which are localized in y. For certain values of "a" these have a simple analytical form that permits a comparison with previous results for a linear zonal wind. As in the uniform shear case we observe a temporary amplification for certain initial conditions, whose nature now depends on "a". / We have shown that for an arbitrary initial condition of small amplitude (of order $ varepsilon$), the linearity hypothesis is invalidated when a $ ll$ 1 after a time of the order of $ varepsilon sp{-1}$ in a critical layer of width of order $ epsilon sp{1/2}$ centered at the jet extremum. We have also obtained the governing equations for the nonlinear evolution stage, which have a striking similarity with those for a forced Rossby wave on a linear wind profile.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.75978 |
| Date | January 1989 |
| Creators | Brunet, Gilbert, 1958- |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | French |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Meteorology.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000945017, proquestno: AAINL57159, Theses scanned by UMI/ProQuest. |
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