Capillary-gravity waves and the Navier-Stokes equation (Q2766090)
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scientific article; zbMATH DE number 1695347
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Capillary-gravity waves and the Navier-Stokes equation |
scientific article; zbMATH DE number 1695347 |
Statements
2001
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velocity potential
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Laplace equation
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harmonic wave
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dispersion relation
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0.9394284
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0.9297332
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0.9260355
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0.9214012
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0.92027676
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0.92022395
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Capillary-gravity waves and the Navier-Stokes equation (English)
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The paper gives a brief and elementary introduction to water waves and their relation to Navier-Stokes equations. After the authors have shown that the velocity potential satisfies Laplace's equation, they derive equations for velocity and displacement of a water element under the action of a harmonic wave. Finally, from the requirement that the harmonic wave satisfies Navier-Stokes equations, the authors obtain the dispersion relation for gravity and capillarity-gravity waves.
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