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Accurate approximations for planetary and gravity waves in a polar basin


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 (, 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


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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