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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
Copyright Information:	© 2021 Elsevier Ltd. All rights reserved.
Related URLs:	Google Scholar: Bassom, AP Google Scholar: Forbes, LK UTAS Profile: Forbes, LK
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