Periodic undulating topographies (such as sandwaves and sandbars) are very common in coastal and estuarine areas. Normally incident water surface waves propagating from open sea to coastal areas may interact strongly with such topographies. The wave reflection by the periodic undulating topography can be significantly amplified when the surface wavelength is approximately twice the wavelength of the bottom undulations, which is often called as Bragg resonant reflection. Although the investigations on the hydrodynamic characteristics related to Bragg reflection of a region of undulating topography have been widely implemented, the effects of Bragg reflection on harbors have not yet been studied. Bragg resonant reflection can effectively reduce the incident waves. Meanwhile, however, it can also significantly hinder the wave radiation from the harbor entrance to the open sea. Whether Bragg reflection can be utilized as a potential measure to alleviate harbor oscillations is unknown.

In the present study, Bragg reflection and their interactions with the harbor are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. For the purpose, an elongated harbor with constant depth is considered, and a series of sinusoidal bars with various amplitudes and numbers are deployed outside the harbor. The incident waves considered in this paper include regular long waves and bichromatic short wave groups. It is revealed for the first time that for both kinds of incident waves, Bragg resonant reflection can significantly alleviate harbor resonance. The influences of the number and the amplitude of sinusoidal bars on the mitigation effect of harbor resonance and on the optimal wavelength of sinusoidal bars that can achieve the best mitigation effect are comprehensively investigated, and it is found that the former two factors have remarkable influences on the latter two parameters. The present research provides a new option for the mitigation of harbor oscillations via changing the bottom profile, which is feasible as long as the navigating depth is guaranteed.

周期性起伏的地形（如沙浪和沙洲）在沿海和河口地区非常普遍。通常从公海传播到沿海地区的入射水面波可能会与此类地形发生强烈的相互作用。当表面波长约为底部起伏波长的两倍时，周期性起伏地形的波反射会被显着放大，这通常称为布拉格共振反射。尽管已经广泛开展了与波状地形区域的布拉格反射相关的水动力特性的研究，但尚未研究布拉格反射对港口的影响。布拉格共振反射可以有效地减少入射波。然而与此同时，它还可以显着阻碍从港口入口到公海的波浪辐射。布拉格反射是否可以用作减轻港口振荡的潜在措施尚不清楚。

在本研究中，使用完全非线性 Boussinesq 模型 FUNWAVE 2.0 模拟布拉格反射及其与港口的相互作用。为此，考虑了一个具有恒定深度的细长港口，并在港口外部署了一系列具有不同幅度和数量的正弦杆。本文考虑的入射波包括规则长波和双色短波群。首次揭示，对于两种入射波，布拉格共振反射都能显着减轻港口共振。综合考察了正弦波条的数量和幅值对港口共振缓解效果的影响，以及对能达到最佳缓解效果的正弦波条最佳波长的影响，发现前两个因素对后两个参数影响显着。目前的研究为通过改变底部剖面来减轻港口振荡提供了一种新的选择，只要保证航行深度，这是可行的。