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A nonlinear wave profile correction of the diffraction of a wave by a long breakwater: Fixed point approach

机译：用长防波堤对波的衍射进行非线性波剖面校正：定点法

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The authors of the present paper have suggested an iterative scheme to calculate the nonlinear wave profiles [Jang and Kwon, 2005. Application of nonlinear iteration scheme to the nonlinear water wave problem: Stokes wave. Ocean Engineering 32, 1862-1872]. The scheme was shown to be good for estimating nonlinear wave profiles. In the study, the iterative scheme is applied to the wave-diffraction problem by a long breakwater to calculate a diffracted wave by the breakwater. The iterative solution of diffraction was compared with the linear solution of Sommerfeld, 1896. [Mathematische Theoried der Diffraction. Mathematical Annals 47, 317-374]. For a small wave slope, the two solutions were in good agreement. However, the scheme enabled us to observe the nonlinear behaviors of a beating phenomenon and of wave profile such as Stokes' wave for a relatively large wave slope: as the wave slope becomes larger, we can examine the nonlinear wave characteristics of the actual shapes of waves, i.e., the crests are steeper and the troughs are flatter.
机译：本文的作者提出了一种迭代方案来计算非线性波轮廓[Jang and Kwon，2005。非线性迭代方案在非线性水波问题中的应用：斯托克斯波。海洋工程32，1862-1872]。结果表明，该方案可用于估计非线性波轮廓。在研究中，将迭代方案应用于长防波堤的波衍射问题，以计算防波堤的衍射波。将衍射的迭代解与1896年Sommerfeld的线性解进行了比较。[Mathematische Theoried der Diffraction。数学年鉴47，317-374]。对于较小的波浪斜率，两种解决方案非常吻合。但是，该方案使我们能够观察到跳动现象和波轮廓（例如斯托克斯波）的非线性行为（相对较大的波坡度）：随着波坡度变大，我们可以检查实际形状的非线性波特征。波浪，即波峰更陡峭，波谷更平坦。

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