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 |
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Elsevier BV
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/48135 |
| Summary: | 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. |
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