Accurate approximations for planetary and gravity waves in a polar basin
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 c...
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Published in | Tellus. Series A, Dynamic meteorology and oceanography Vol. 71; no. 1; p. 1618133 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Stockholm
Taylor & Francis
01.01.2019
Ubiquity Press Stockholm University Press |
Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 1600-0870 1600-0870 |
DOI: | 10.1080/16000870.2019.1618133 |