Dimension-Reduced Model for Deep-Water Waves

• 作者: Michael Bestehorn Peder A. Tyvand Thomas Michelitsch
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: HYDRODYNAMICS OCEAN WAVES DEEP-WATER WAVES Numerical Solutions FRACTAL Derivatives
• 年，卷（期）: 2019,（1）
• 页码范围: 72-92
• 页数: 21页
• 分类号: O1

摘要

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 one- dimensional 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.