The Library
Sharp fronts and almost-sharp fronts of a singular surface quasi-geostrophic equation
Tools
Tools
Tools
Khor, Calvin (2019) Sharp fronts and almost-sharp fronts of a singular surface quasi-geostrophic equation. PhD thesis, University of Warwick.
|
PDF
WRAP_Theses_Khor_2019.pdf - Submitted Version - Requires a PDF viewer. Download (1840Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3493289~S15
Abstract
In this thesis, we generalise results on sharp fronts and almost-sharp fronts by Fe↵erman, Luli, and Rodrigo [67], [68], [28], [26], [27], [19] to a singular variant of the Surface Quasi-Geostrophic Equation (SQG), where the velocity u = ∇⊥|∇|-1θ is replaced with the more singular velocity ∇⊥|∇|-1+αθ, for α ∈ (0, 1).
First, we derive the contour dynamics equation for a sharp front from the definition of a weak solution to our singular variant of SQG.
Then, we prove the existence of analytic sharp fronts to the sharp front equation using the abstract Cauchy–Kowalevskaya Theorem. This result is analogous to the result of Fefferman and Rodrigo in [27], which was a key result for proving the existence of analytic almost-sharp fronts whose existence time does not depend on the thickness of the transition region are transported by the velocity u = ∇⊥|∇|-1+αθ. This work generalises the result of [19] to our more singular equation.
Finally, we define a spine curve for the almost-sharp front analogously to the spine curve of SQG in the model where one space variable is periodised, defined in the work of Fefferman and Rodrigo. The spine evolves according to the sharp front equation modulo an O(δ2-a) error. As this does not vanish as α → 1, this formally suggests that the equation is in some sense not degenerate in this limit.
| Item Type: | Thesis (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | G Geography. Anthropology. Recreation > GC Oceanography Q Science > QA Mathematics |
||||
| Library of Congress Subject Headings (LCSH): | Geostrophic currents -- Mathematical models, Fronts (Meteorology) -- Mathematical models | ||||
| Official Date: | June 2019 | ||||
| Dates: |
|
||||
| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Rodrigo, José L. | ||||
| Sponsors: | European Research Council | ||||
| Format of File: | |||||
| Extent: | viii, 112 leaves : illustrations | ||||
| Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
