Planetary waves in polar basins: Some exact solutions. (July 2021)

• Record Type: Journal Article
• Authors: Cockerill, Madeleine; Bassom, Andrew P.; Forbes, Lawrence K.
• Is Part Of: Applied mathematics letters. Volume 117(2021)
• Publication Date: 2021-07
• Subjects: Polar basin -- Eigenfunctions -- Closed-form solutions; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107121
• Languages: English
• ISSNs: 0893-9659

Abstract

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.