Lookup NU author(s): Professor Andrew Willmott
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
The eigenfrequencies of freely propagating divergent barotropic planetary and gravity waves in a sphericalpolar cap are discussed. The key amplitude equation is derived with the full spherical geometry maintainedand leads to a second-order differential equation with coefficients functions of the co-latitude. Previous studyof this problem has derived approximations to the requisite frequencies by evaluating these coefficients atsome chosen fixed value of the co-latitude thereby reducing the problem to that of a constant coefficientdifferential equation solved easily using routine methods. Here, we demonstrate that such a simplification canbe avoided since the full equation can be solved by standard asymptotic methods based on the latitudinallimit of the polar basin as the natural small parameter. Three-term asymptotic series are developed which arein remarkably good accord with numerical solutions of the full equation.
Author(s): Bassom AP, Willmott AJ
Publication type: Article
Publication status: Published
Journal: Tellus A: Dynamic Meteorology & Oceanography
Online publication date: 27/05/2019
Acceptance date: 07/05/2019
Date deposited: 20/05/2019
ISSN (print): 0280-6495
ISSN (electronic): 1600-0870
Publisher: Taylor and Francis
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