论文标题
底部的隧道和井的通道中的表面波在底部：不反射水下断层扫描
Surface waves in a channel with thin tunnels and wells at the bottom: non-reflecting underwater tomography
论文作者
论文摘要
我们考虑在底部通过几条细弯曲的隧道和井在底部扰动的直平通道中的地表水波的传播。我们提出了一种以任意规定的波浪数来构建这种类型的非反射水下地形的方法。为了进行，我们根据边界层现象的存在，计算衍射溶液的渐近扩展。我们建立误差估计值以使用具有分离的渐近线的加权空间的进步技术来验证扩展。在此过程中，我们显示了没有被捕获的表面波以使扰动足够小。该分析为散射矩阵提供了渐近公式，我们使用它们来确定不反射的水下地形。给出了理论和数值示例。
We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an arbitrary prescribed wave number. To proceed, we compute asymptotic expansions of the diffraction solutions with respect to the small parameter of the geometry taking into account the existence of boundary layer phenomena. We establish error estimates to validate the expansions using advances techniques of weighted spaces with detached asymptotics. In the process, we show the absence of trapped surface waves for perturbations small enough. This analysis furnishes asymptotic formulas for the scattering matrix and we use them to determine underwater topographies which are non-reflecting. Theoretical and numerical examples are given.
