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Accurate approximations for planetary and gravity waves in a polar basin


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Bassom, AP ORCID: 0000-0003-3275-7801 and Willmott, AJ 2019 , 'Accurate approximations for planetary and gravity waves in a polar basin' , Tellus, Series A: Dynamic Meteorology and Oceanography, vol. 71, no. 1 , pp. 1-7 , doi: 10.1080/16000870.2019.1618133.

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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 Type: Article
Authors/Creators:Bassom, AP and Willmott, AJ
Keywords: polar basin, wave frequencies
Journal or Publication Title: Tellus, Series A: Dynamic Meteorology and Oceanography
Publisher: Blackwell Munksgaard
ISSN: 0280-6495
DOI / ID Number: 10.1080/16000870.2019.1618133
Copyright Information:

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

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