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首页> 外文期刊>Applied Mathematical Modelling >Scattering of surface gravity waves over a pair of trenches
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Scattering of surface gravity waves over a pair of trenches

机译：表面重力波在一对沟槽上的散射

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摘要

A numerical model based on boundary element method is developed to study the scattering of surface gravity waves over a pair of trenches of varied configurations under the assumption of small amplitude water wave theory. Both the cases of symmetric and asymmetric trenches are considered in the present study. The accuracy of the numerical results is validated by comparing the reflection and transmission coefficients with energy identity, and the known results associated with single trench available in the literature. The study reveals that wave reflection decreases in an oscillatory manner with an increase in trench width. Moreover, Bragg resonance in wave reflection is observed for wave number corresponding to waves in shallow and intermediate depths in the case of a pair of trenches. Further, Bragg reflection increases with an increase in the number of trenches. In the case of multiple trenches, subharmonic peaks in Bragg reflection are depicted and the number of subharmonic peaks between two harmonic peaks is found to be two less than the number of trenches. However, for triangular trenches, the occurrence of the subharmonic peak is invariant of the number of trenches and the same vanishes for larger trench depth. Irrespective of trench configurations, wave reflection follows certain uniform oscillatory pattern with an increase in the gap between the trenches in case of deep water.
机译：在小振幅水波理论的假设下，建立了基于边界元法的数值模型，研究了表面重力波在一对不同构形的沟槽上的散射。在本研究中考虑对称沟槽和非对称沟槽的情况。数值结果的准确性通过将反射系数和透射系数与能量标识以及文献中可获得的与单个沟槽相关的已知结果进行比较来验证。研究表明，随着沟槽宽度的增加，波反射以振荡的方式减小。此外，在一对沟槽的情况下，观察到与浅和中深度的波相对应的波数的波反射中的布拉格共振。此外，布拉格反射随着沟槽数量的增加而增加。在多个沟槽的情况下，描绘了布拉格反射中的次谐波峰，并且发现两个谐波峰之间的次谐波峰的数量比沟槽的数量少两个。但是，对于三角形沟槽，次谐波峰的出现不会改变沟槽的数量，并且对于更大的沟槽深度而言，相同的消失会消失。不论沟槽配置如何，在深水情况下，波反射都遵循某些均匀的振荡模式，且沟槽之间的间隙会增加。

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