The trapping and scattering of topographic waves by estuaries and headlands
The trapping and scattering of topographic waves by estuaries and headlands
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河口和岬角对地形波的捕获和散射
DOI：
10.1017/s0022112091001192
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发表时间：
1991
影响因子：
3.7
通讯作者：
E. Johnson
中科院分区：
文献类型：
--
作者：
T. Stocker;E. Johnson
本文扩展了最近关于海湾亚惯性捕获模式的理论工作，以考虑沿海大陆架上河口附近的能量捕获。理论预测的定性形式与最近在苏格兰大陆架上的观测结果很好地吻合，这些观测结果表明，劳伦海峡附近捕获的能量频率高于大陆架上传播波的频率。在陆架-河口或陆架-海岬系统中，通过考虑具有附加矩形河口或被矩形海岬打断的直无限通道中的正压波，模拟了陆架波的捕获和散射。将深度随离海岸的距离呈指数增长，并在跨陆架模式下展开，将问题简化为一个真正的线性代数方程组。在河口附近发现了频率高于传播波截止频率的捕获模态。向河口传播的波浪是强烈散射的，对于特定的频率，入射能量可以完全传输或完全反射。入射波可以与河口共振，使能量穿透河口。给出了捕获解和谐振解的频率边界，并允许简单的模态解释。如果入射波的频率足够高，波就不能通过海岬。然而，这些频率的能量可以穿过该区域，在远端以衰减波的形式出现。对于特定的频率，所有的能量都通过海岬而没有被反射。对于较长入射波的海岬，单模散射的透射系数遵循空间一维波动力学。
This paper extends recent theoretical work on sub-inertial trapped modes in bays to consider trapping of energy in the neighbourhood of estuary mouths on coastal shelves. The qualitative form of the theoretical predictions accords well with recent observations on the Scotian Shelf that show energy trapped near the Laurentian Channel at a frequency higher than that of the propagating waves on the shelf. The trapping and scattering of shelf waves is modelled for a shelf–estuary or shelf–headland system by considering barotropic waves in a straight, infinite channel with an attached rectangular estuary or interrupted by a rectangular headland. Taking the depth to increase exponentially with distance from the coast and expanding in cross-shelf modes reduces the problem to a system of real linear algebraic equations. Trapped modes with frequencies above the cutoff frequency of propagating waves are found near the mouth of the estuary. Waves propagating towards the estuary are strongly scattered and, for particular frequencies, incident energy can be either perfectly transmitted or totally reflected. An incident wave can be in resonance with the estuary causing energy to penetrate the estuary. Bounds on the frequencies of trapped and resonant solutions are given and allow an easy modal interpretation. If the frequency of an incident wave is sufficiently high, waves cannot propagate past a headland. Energy at these frequencies can however tunnel through the region and appear as an attenuated wave on the far side. For particular frequencies all energy passes the headland and none is reflected. For headlands long compared with the incident wave, transmission coefficients for single-mode scattering follow from spatially one-dimensional wave mechanics.