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...
Published in: | Applied Mathematics Letters |
---|---|
Main Authors: | , , |
Format: | Article in Journal/Newspaper |
Language: | unknown |
Published: |
Pergamon-Elsevier Science Ltd
2021
|
Subjects: | |
Online Access: | https://eprints.utas.edu.au/40593/ |
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. |
---|