The initial value problem on a plane beach (Q2743620)
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scientific article; zbMATH DE number 1652302
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The initial value problem on a plane beach |
scientific article; zbMATH DE number 1652302 |
Statements
15 September 2003
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linearized hydrostatic theory
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small times
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two-dimensional initial value problem
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inviscid incompressible fluid
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plane beach
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non-hydrostatic theory
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asymptotic representations
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large times
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fluctuating surface pressure
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Ursell edge-wave mode
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0.80958873
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0.8054346
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0.8045414
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0.8036244
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0.79401505
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0.78676015
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0.78649133
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The initial value problem on a plane beach (English)
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The two-dimensional initial value problem is examined for an inviscid incompressible fluid on a plane beach using a linearized but non-hydrostatic theory. Solutions are obtained in integral form and the computed and studied using asymptotic representations for small and large times. An extension of the theory is made to allow the examination of forced motions due to a fluctuating surface pressure, or movements of the solid bed. One of the main observations is that, in general, such disturbances will lead to unbounded wave heights for large time in the case when the longshore wavelength equals the wavelength of Ursell edge-wave mode.
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