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Accurate approximations for planetary and gravity waves in a polar basin

Lookup NU author(s): Professor Andrew Willmott

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Abstract

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.

Publication metadata

Author(s): Bassom AP, Willmott AJ

Publication type: Article

Publication status: Published

Journal: Tellus A: Dynamic Meteorology & Oceanography

Year: 2019

Volume: 71

Issue: 1

Pages: 1-7

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

URL: https://doi.org/10.1080/16000870.2019.1618133

DOI: 10.1080/16000870.2019.1618133

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