On functional equations leading to exact solutions for standing internal waves
The Dirichlet problem for the wave equation is a classical example of a problem which is ill-posed. Nevertheless, it has been used to model internal waves oscillating harmonically in time, in various situations, standing internal waves amongst them. We consider internal waves in two-dimensional doma...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
Elsevier BV
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/48135 |
| _version_ | 1848758027155406848 |
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| author | Beckebanze, F. Keady, Grant |
| author_facet | Beckebanze, F. Keady, Grant |
| author_sort | Beckebanze, F. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The Dirichlet problem for the wave equation is a classical example of a problem which is ill-posed. Nevertheless, it has been used to model internal waves oscillating harmonically in time, in various situations, standing internal waves amongst them. We consider internal waves in two-dimensional domains bounded above by the plane z=0 and below by z=−d(x) for depth functions d. This paper draws attention to the Abel and Schröder functional equations which arise in this problem and use them as a convenient way of organising analytical solutions. Exact internal wave solutions are constructed for a selected number of simple depth functions d. |
| first_indexed | 2025-11-14T09:37:27Z |
| format | Journal Article |
| id | curtin-20.500.11937-48135 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:37:27Z |
| publishDate | 2016 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-481352017-10-09T01:08:20Z On functional equations leading to exact solutions for standing internal waves Beckebanze, F. Keady, Grant The Dirichlet problem for the wave equation is a classical example of a problem which is ill-posed. Nevertheless, it has been used to model internal waves oscillating harmonically in time, in various situations, standing internal waves amongst them. We consider internal waves in two-dimensional domains bounded above by the plane z=0 and below by z=−d(x) for depth functions d. This paper draws attention to the Abel and Schröder functional equations which arise in this problem and use them as a convenient way of organising analytical solutions. Exact internal wave solutions are constructed for a selected number of simple depth functions d. 2016 Journal Article http://hdl.handle.net/20.500.11937/48135 10.1016/j.wavemoti.2015.09.009 Elsevier BV fulltext |
| spellingShingle | Beckebanze, F. Keady, Grant On functional equations leading to exact solutions for standing internal waves |
| title | On functional equations leading to exact solutions for standing internal waves |
| title_full | On functional equations leading to exact solutions for standing internal waves |
| title_fullStr | On functional equations leading to exact solutions for standing internal waves |
| title_full_unstemmed | On functional equations leading to exact solutions for standing internal waves |
| title_short | On functional equations leading to exact solutions for standing internal waves |
| title_sort | on functional equations leading to exact solutions for standing internal waves |
| url | http://hdl.handle.net/20.500.11937/48135 |