Abstract This paper presents a model for the evaluation of long waves amplification at coastal areas, based on a modal decomposition method. It is able of modelling the growth and the decay of the natural modes of the area under investigation, and their contribution to the total wave field. The model is an improvement of that developed by Bellotti et al. (2012b), that was able of calculating the frequencies and the shapes of the natural modes, but not their amplification under the action of forcing waves. Three test cases are used for the validation and to show the capabilities of the model. The first considers the long waves resonance into a long and narrow harbour/bay over a constant water depth. It is a case for which a high degree of wave trapping into the semi-enclosed coastal area is induced by the specific shape of the coastline. The second test deals with the propagation of a group of edge waves along a straight coast with a constant sloping bottom, generated in proximity of the shoreline by a special wave maker. The model in this case properly evaluates what are the edge waves modes that contribute to the total wave field. The third case involves the interaction of a solitary wave with a conical island, for which laboratory data are available. In this test a low degree of trapping exists, but it is interesting for the present aims as the propagation of the waves around the island is expected to occur under the form of wave modes partially trapped by the bathymetry i.e. edge waves, excited by the transient wave arriving from offshore. On the basis of the tests results it is shown what is the role of the more relevant natural modes in the formation of the total surface elevation.

中文翻译：

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沿海地区长波放大分析的模态分解方法

摘要 本文提出了一种基于模态分解方法的沿海地区长波放大评估模型。它能够模拟被调查区域的自然模式的增长和衰减，以及它们对总波场的贡献。该模型是对 Bellotti 等人开发的模型的改进。(2012b)，能够计算固有模式的频率和形状，但不能计算它们在强迫波作用下的放大。三个测试用例用于验证和展示模型的能力。第一个考虑长波在恒定水深上共振进入狭长的港口/海湾。这是一种由于海岸线的特定形状而导致高度陷波进入半封闭海岸区域的情况。第二个测试涉及一组边缘波沿着具有恒定倾斜底部的笔直海岸的传播，这些边缘波是由一个特殊的造波器在海岸线附近产生的。在这种情况下，模型正确地评估了对总波场有贡献的边缘波模式是什么。第三种情况涉及孤立波与锥形岛的相互作用，可获取实验室数据。在这个测试中存在低程度的俘获，但对于目前的目标来说是有趣的，因为波在岛屿周围的传播预计将以波模式的形式发生，即部分被水深测量所俘获的波模式，即边缘波，由瞬态激发来自海上的波浪。