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Planetary waves in polar basins: Some exact solutions

Cockerill, M, Bassom, AP ORCID: 0000-0003-3275-7801 and Forbes, LK ORCID: 0000-0002-9135-3594 2021 , 'Planetary waves in polar basins: Some exact solutions' , Applied Mathematics Letters, vol. 117 , pp. 1-7 , doi: 10.1016/j.aml.2021.107121.

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Abstract

The equations of motion for fluid flow in a shallow circular ocean centred at the North Pole are considered. Small amplitude wave motions in the ocean are governed by a complicated two-point boundary-value problem that has been solved approximately using a combination of asymptotic and numerical methods. Here we point out that the problem admits two families of exact closed-form solutions: one set of solutions can be expressed in terms of associated Legendre functions while the other can be written in simple algebraic form.

Item Type: Article
Authors/Creators:Cockerill, M and Bassom, AP and Forbes, LK
Keywords: polar basin, Eigenfunctions, closed-form solutions, exact solutions
Journal or Publication Title: Applied Mathematics Letters
Publisher: Pergamon-Elsevier Science Ltd
ISSN: 0893-9659
DOI / ID Number: 10.1016/j.aml.2021.107121
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© 2021 Elsevier Ltd. All rights reserved.

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