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Dimension-Reduced Model for Deep-Water Waves

Abstract : Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two onedimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.
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https://hal-cnrs.archives-ouvertes.fr/hal-03028144
Contributor : Thomas Michelitsch <>
Submitted on : Friday, November 27, 2020 - 2:25:43 PM
Last modification on : Tuesday, December 8, 2020 - 3:35:21 AM

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Michael Bestehorn, Peder Tyvand, Thomas Michelitsch. Dimension-Reduced Model for Deep-Water Waves. Journal of Applied Mathematics and Physics (JAMP), Scientific Research Publishing, 2019, 07 (01), pp.72-92. ⟨10.4236/jamp.2019.71007⟩. ⟨hal-03028144⟩

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