Linear and Nonlinear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN
Linear and Nonlinear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN
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DOI：
10.1115/1.4000503
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发表时间：
2010-05
影响因子：
1.6
通讯作者：
J. W. Kim;R. Ertekin;K. Bai
中科院分区：
文献类型：
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作者：
J. W. Kim;R. Ertekin;K. Bai
最近，从重力波的汉密尔顿原理出发，导出了两种基于流函数理论的波动模型。一个是无旋Green-Naghdi方程（IGN），另一个是互补缓坡方程（CMSE）。推导了IGN方程来描述非线性重力波在有限但任意水深的时域和水中的折射和绕射。CMSE已经被导出以考虑（线性）频域中的相同问题。本文首先从汉密尔顿原理的角度讨论了这两种模型。然后将这两个模型应用于周期波动上斯托克斯波的共振散射或布拉格散射问题。数值结果与现有的数值预测和实验数据进行了比较。结果表明，Level 3 IGN方程可以很好地描述任意水深下的布拉格散射。
Recently, two wave models based on the stream-function theory have been derived from Hamilton’s principle for gravity waves. One is the irrotational Green–Naghdi (IGN) equation and the other is the complementary mild-slope equation (CMSE). The IGN equation has been derived to describe refraction and diffraction of nonlinear gravity waves in the time domain and in water of finite but arbitrary bathymetry. The CMSE has been derived to consider the same problem in the (linear) frequency domain. In this paper, we first discuss the two models from the viewpoint of Hamilton’s principle. Then the two models are applied to a resonant scattering of Stokes waves over periodic undulations, or the Bragg scattering problem. The numerical results are compared with existing numerical predictions and experimental data. It is found here that Level 3 IGN equation can describe Bragg scattering well for arbitrary bathymetry.