135818 - Accurate approximations for planetary and gravity waves in a polar basin - print version.pdf (216.8 kB)
Accurate approximations for planetary and gravity waves in a polar basin
journal contribution
posted on 2023-05-20, 08:21 authored by Andrew BassomAndrew Bassom, Willmott, AJThe 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.
History
Publication title
Tellus, Series A: Dynamic Meteorology and OceanographyVolume
71Article number
1618133Number
1618133Pagination
1-7ISSN
0280-6495Department/School
School of Natural SciencesPublisher
Blackwell MunksgaardPlace of publication
35 Norre Sogade, Po Box 2148, Copenhagen, Denmark, Dk-1016Rights 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 properlyRepository Status
- Open