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Accurate approximations for planetary and gravity waves in a polar basin
Citation
Bassom, AP and Willmott, AJ, Accurate approximations for planetary and gravity waves in a polar basin, Tellus, Series A: Dynamic Meteorology and Oceanography, 71, (1) Article 1618133. ISSN 0280-6495 (2019) [Refereed Article]
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Copyright Statement
Copyright 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly
DOI: doi:10.1080/16000870.2019.1618133
Abstract
The eigenfrequencies of freely propagating divergent barotropic planetary and gravity waves in a spherical polar cap are discussed. The key amplitude equation is derived with the full spherical geometry maintained and leads to a second-order differential equation with coefficients functions of the co-latitude. Previous study of this problem has derived approximations to the requisite frequencies by evaluating these coefficients at some chosen fixed value of the co-latitude thereby reducing the problem to that of a constant coefficient differential equation solved easily using routine methods. Here, we demonstrate that such a simplification can be avoided since the full equation can be solved by standard asymptotic methods based on the latitudinal limit of the polar basin as the natural small parameter. Three-term asymptotic series are developed which are in remarkably good accord with numerical solutions of the full equation.
Item Details
| Item Type: | Refereed Article |
|---|---|
| Keywords: | polar basin, wave frequencies |
| Research Division: | Mathematical Sciences |
| Research Group: | Applied mathematics |
| Research Field: | Theoretical and applied mechanics |
| Objective Division: | Expanding Knowledge |
| Objective Group: | Expanding knowledge |
| Objective Field: | Expanding knowledge in the mathematical sciences |
| UTAS Author: | Bassom, AP (Professor Andrew Bassom) |
| ID Code: | 135818 |
| Year Published: | 2019 |
| Web of Science® Times Cited: | 3 |
| Deposited By: | Mathematics and Physics |
| Deposited On: | 2019-11-15 |
| Last Modified: | 2021-06-01 |
| Downloads: | 20 View Download Statistics |
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