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    Reflections of internal gravity waves off bumpy surfaces

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    Reflections of internal gravity ...
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    Author
    Denning, Dylan
    Advisor
    Martin, P. A.
    Collis, Jon M.
    Date issued
    2015
    Keywords
    reflections
    internal gravity waves
    bumpy
    Gravity waves
    Wave equation
    Asymptotic expansions
    Differential equations, Partial
    Fourier transformations
    Perturbation (Mathematics)
    
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    URI
    https://hdl.handle.net/11124/17141
    Abstract
    Waves in a density stratified fluid, termed internal gravity waves, reflected by a sloping plane make an angle with the horizontal equal to the angle between the incident wave and the horizontal. We add a perturbation to the plane small in size when compared to the amplitude of the wave motion. An asymptotic expansion is used and problems are derived up to two orders O(1) and O(ε). The leading order problem is the same as the reflection problem by a flat plane. The problem on O(ε) is a radiation problem that we solve using Fourier transforms.
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