水下岛屿和引力类似物引起的波聚焦
Wave focusing by submerged islands and gravitational analogues
摘要：
我们研究了水波在不同深度的流体中的光滑障碍物上传播，其动机是观察到海洋中的淹没岛屿作为有效的透镜，增加了海啸波在焦点附近的振幅和破坏力。我们发现，岛屿的高度（水深相比）导致强烈的聚焦在其附近，并产生焦散的尖瓣或蝴蝶型。我们强调的相似性和差异与聚焦（高频）引力波的中子星。在线性制度，比较精确，通过有效的时空描述的岛屿流体系统。这种描述然后投入实际用途：我们通过沿着有效度规的射线求解Raychaudhuri方程（一种输运方程）来识别焦散。接下来，详细研究了岛流体散射过程（即~偏转角、相移、散射振幅），包括程函近似及其以高斯光束近似形式的推广。我们表明，该技术捕捉模拟的关键特征。最后，我们扩展程函近似的色散制度，证明了基本功能是强大的色散设置。这为未来在受控实验室设置中进行探索铺平了道路。
英文摘要：
We study water waves propagating over a smooth obstacle in a fluid of varying depth, motivated by the observation that submerged islands in the ocean act as effective lenses that increase the amplitude and destructive power of tsunami waves near focal points. We show that islands of substantial height (compared to the water depth) lead to strong focusing in their immediate vicinity, and generate caustics of either cusp or butterfly type. We highlight similarities and differences with focusing of (high-frequency) gravitational waves by a neutron star. In the linear regime, the comparison is made precise through an effective-spacetime description of the island-fluid system. This description is then put to practical use: we identify caustics by solving the Raychaudhuri equation (a transport equation) along rays of the effective metric. Next, the island-fluid scattering processes are examined in detail (i.e.~deflection angle, phase shifts, scattering amplitudes) using numerical simulations and analytical techniques, including the eikonal approximation and its generalisation in the form of the Gaussian beam approximation. We show that the techniques capture the key features of the simulations. Finally, we extend the eikonal approximation to the dispersive regime, demonstrating that the essential features are robust in dispersive settings. This paves the way for future exploration in a controlled laboratory set-up.
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