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首页> 外文期刊>International Journal of Offshore and Polar Engineering >On Step Approximation of Water-Wave Scattering over Steep or Undulated Slope
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On Step Approximation of Water-Wave Scattering over Steep or Undulated Slope

机译：陡峭或波状斜坡上水波散射的逐步逼近

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摘要

In this paper, Miles's variational formulation (Miles, 1967) is extended to study problems of water-wave scattering by steep slopes. In the procedure for obtaining the solution, the arbitrary bottom profiles are represented by flat shelves separated by abrupt steps. By applying the stationary condition of the variational formulation, a system of linear equations is obtained with unknown coefficients that represent the horizontal velocities. Our variational formulation is extended by considering the evanescent eigenfunctions in the representations of these horizontal velocities. The extended variational formulation is applied to solving water-wave scattering by using Roseau's curved bottom profiles of both mild and steep slopes (Roseau, 1976). The solutions obtained by the extended variational formulation are convergent with Roseau's analytical solution up to four decimal places for the mild and steep cases, while the solutions obtained by the traditional variational formulation (Miles, 1967) and the transfer-matrix method of Devillard et al. (1988) are not accurate enough for the steep case. Furthermore, by using the integral equation method, the improvement of the proposed method is enforced by two types of bottom profiles considered by Porter and Porter (2000). Finally, numerical experiments are performed to compare the present method with the extended mild-slope equation of Porter and Staziker (1995).
机译：在本文中，将Miles的变分公式（Miles，1967）扩展到研究陡坡上水波散射的问题。在获得解决方案的过程中，任意底部轮廓均由用陡峭步骤隔开的平坦架子表示。通过应用变分公式的平稳条件，可获得具有未知系数的线性方程组，这些系数表示水平速度。通过考虑这些水平速度表示中的the逝本征函数，可以扩展我们的变分公式。扩展的变分公式通过使用Roseau的缓坡和陡坡的弯曲底部轮廓来解决水波散射问题（Roseau，1976）。通过扩展变分公式获得的解与Roseau的解析解在温和陡峭情况下收敛到小数点后四位，而通过传统变分公式（Miles，1967年）和Devillard等人的传递矩阵法获得的解。 （1988）对于陡峭的情况还不够准确。此外，通过使用积分方程方法，Porter和Porter（2000）考虑了两种类型的底部剖面，从而对所提出的方法进行了改进。最后，进行数值实验以将本方法与Porter和Staziker（1995）的扩展的缓坡方程进行比较。

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