Planetary waves in polar basins: Some exact solutions

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 met...

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Bibliographic Details
Published in:Applied Mathematics Letters
Main Authors: Cockerill, M, Bassom, AP, Forbes, LK
Format: Article in Journal/Newspaper
Language:unknown
Published: Pergamon-Elsevier Science Ltd 2021
Subjects:
polar basin
Eigenfunctions
closed-form solutions
exact solutions
North Pole
Online Access:https://eprints.utas.edu.au/37666/
Description
Summary: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.

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