On functional equations leading to exact solutions for standing internal waves
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Open access
Authors
Beckebanze, F.
Keady, Grant
Date
2016Type
Journal Article
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Beckebanze, F. and Keady, G. 2016. On functional equations leading to exact solutions for standing internal waves. Wave Motion. 60: pp. 181-195.
Source Title
Wave Motion
ISSN
School
Department of Mathematics and Statistics
Collection
Abstract
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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