The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock’s expansion of water wave potential function reduces each problem to an integral equation of first kind on the horizontal component of velocity across the gap above or below the barrier. Multi-term Galerkin approximations involving polynomials as basis functions multiplied by appropriate weight functions are used to solve these equations numerically. Evaluated numerical results for the reflection coefficients are plotted graphically for both the barriers. The study reveals that the reflection coefficient depends significantly on the thickness of the barrier. The accuracy of the numerical results is checked by using energy identity and by obtaining results available in the literature as special cases.

中文翻译：

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深水中矩形截面厚障壁散射的斜水波

这里研究了在深水中无限向下延伸的厚的部分浸没的矩形屏障或厚的浸没的矩形屏障对表面波的倾斜散射问题，以半解析地获得反射和透射系数。使用哈夫洛克对水波势函数的展开式将每个问题简化为第一类积分方程，该方程关于跨越障碍物上方或下方间隙的速度水平分量。使用多项式作为基函数乘以适当的权重函数的多项式伽辽金近似来数值求解这些方程。反射系数的评估数值结果以图形方式绘制为两个屏障。研究表明，反射系数显着取决于屏障的厚度。