Using an asymptotic method, this article deals with flexural-gravity wave scattering with undulating bottom topography, including the effect of uniform currents. The interest in this problem lies in developing second-order solutions using the Fourier transform, which minimises the error gap between first and second-order solutions. The present method allows the physical processes involved in the sea-bed topography, uniform current, plate-covered surface, and wave interaction to be studied. Specifically, we observe Bragg resonance between the flexural-gravity waves and the bottom ripples, which are associated with the reflection of incident wave energy. We examine the effects of wave current and emphasise how crucial the asymptotic expansion method is to the emergence of the current response. We demonstrate that bottom topography dominates the effects of Bragg resonance for depth Froude numbers valued at 0.8 or less. Further, most reflected wave components have their frequencies shifted by the current, and wave action conservation causes reflected wave energy to be enhanced for following currents. Using the Joint North Sea Wave Observation Project spectrum and the discrete Fourier transform, the theory derived in the frequency domain is shown in the time domain to analyse wave propagation through the whole system.

中文翻译：

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均匀电流存在下弯曲重力波与起伏底部地形的相互作用：渐近方法


本文使用渐近方法处理具有起伏底部地形的弯曲重力波散射，包括均匀电流的影响。该问题的兴趣在于使用傅立叶变换开发二阶解，从而最小化一阶解和二阶解之间的误差差距。本方法允许研究涉及海底地形、均匀水流、板块覆盖表面和波浪相互作用的物理过程。具体来说，我们观察到弯曲重力波和底部波纹之间的布拉格共振，这与入射波能量的反射有关。我们研究了波流的影响，并强调渐近展开方法对于电流响应的出现有多么重要。我们证明，对于深度弗劳德数值为 0.8 或更小的情况，底部地形主导了布拉格共振的影响。此外，大多数反射波分量的频率会因电流而移动，并且波作用守恒会导致反射波能量针对后续电流而增强。利用北海联合波浪观测项目频谱和离散傅里叶变换，在时域中显示在频域中导出的理论，以分析整个系统中的波浪传播。