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 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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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.