期刊
APPLIED MATHEMATICS LETTERS
卷 117, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2021.107121
关键词
Polar basin; Eigenfunctions; Closed-form solutions
The equations of motion for fluid flow in a shallow circular ocean centred at the North Pole are considered, revealing 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.
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. (C) 2021 Elsevier Ltd. All rights reserved.
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