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Dimension-Reduced Model for Deep-Water Waves

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Document pages: 21 pages

Abstract: Starting from the 2D Euler equations for anincompressible potential flow, a dimension-reduced model describing deep-watersurface waves is derived. Similar to theShallow-Water case, the z-dependenceof the dependent variables is found explicitly from the Laplace equation and aset of two one- dimensional equationsin x for the surface velocity and thesurface elevation remains. The model is nonlocal and can be formulated inconservative form, describing waves over an infinitely deep layer. Finally,numerical solutions are presented for several initial conditions. The side-bandinstability of Stokes waves and stable envelope solitons are obtained inagreement with other work. The conservation of the total energy is checked.

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