基于修正缓坡方程的珊瑚环礁断面地形波浪反射与透射特性数值模拟

李献丽; 倪云林; 陈松贵; 陈敬仁; 谢健健

doi:10.3969/j.issn.1001-909X.2026.02.007

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海洋学研究 ›› 2026, Vol. 44 ›› Issue (2) : 65-73. DOI: 10.3969/j.issn.1001-909X.2026.02.007

研究论文

基于修正缓坡方程的珊瑚环礁断面地形波浪反射与透射特性数值模拟

李献丽 ¹ ,
倪云林 ²^,³^,^* ,
陈松贵 ⁴ ,
陈敬仁 ² ,
谢健健 ²

作者信息 +

Numerical simulation of wave reflection and transmission characteristics over a cross-section of coral atoll topography based on the modified mild-slope equation

LI Xianli ¹ ,
NI Yunlin ²^,³^,^* ,
CHEN Songgui ⁴ ,
CHEN Jingren ² ,
XIE Jianjian ²

Author information +

文章历史 +

摘要

波浪由深海向近岸传播过程中，受近岸水深的变化以及复杂地形的影响会发生反射、透射等现象，尤其当海床地形呈现周期性变化时还会出现著名的波浪布拉格共振现象。本文基于修正缓坡方程，建立了相应的有限差分求解模型，研究了珊瑚环礁断面地形对波浪反射与透射的影响。首先，针对波浪入射水平海床上周期性梯形地形的反射问题进行了算例验证，计算结果与既有解析解吻合良好，验证了模型的可靠性。在此基础上，系统分析了不同潟湖相对深度（潟湖水深相对研究区水深，h₁/h₀）和采掘坑相对深度（采掘坑深度相对研究区水深，h_p/h₀）对波浪反射与透射系数的影响规律。结果表明：随着h₁/h₀的增加，波浪发生共振时对应的反射系数显著提高，透射系数逐渐减小，共振带的带宽扩展，且反射与透射波的共振频率均出现下移现象。而随着h_p/h₀的增加，波浪共振对应的反射系数略有降低，透射系数则呈现一定的增大趋势；并且随着h_p/h₀从3/7增至5/7，反射与透射波的共振频率还出现了上移现象。

Abstract

During the propagation of waves from deep sea to nearshore， reflection and transmission occur due to changes in water depth and complex topography. In particular， when the seabed topography exhibits periodic variations， the well-known wave Bragg resonance phenomenon emerges. Based on the modified mild-slope equation， this paper established a corresponding finite-difference numerical model to investigate the effects of cross-sectional topography of a coral reef profile on wave reflection and transmission. First， the model was validated by simulating wave reflection over a periodically undulating trapezoidal topography on a horizontal seabed. The numerical results showed good agreement with existing analytical solutions， confirming the reliability of the model. Subsequently， the systematic analysis was conducted to examine the effects of the relative lagoon depth （lagoon depth relative to the water depth in the study area， h₁/h₀） and the relative excavation pit depth （excavation pit depth relative to the water depth in the study area， h_p/h₀） on the coefficients of wave reflection and transmission. The results indicate that as h₁/h₀ increases， the reflection coefficient corresponding to wave resonance increases significantly， while the transmission coefficient gradually decreases. Moreover， the bandwidth of the resonance band widens， and the resonance frequencies of both reflected and transmitted waves shift downward. In contrast， with an increase in h_p/h₀， the reflection coefficient at resonance decreases slightly， while the transmission coefficient shows a certain increasing trend. Additionally， as h_p/h₀ increases from 3/7 to 5/7， the resonance frequencies of both reflected and transmitted waves shift upward.

导出引用

李献丽, 倪云林, 陈松贵, 等. 基于修正缓坡方程的珊瑚环礁断面地形波浪反射与透射特性数值模拟[J]. 海洋学研究. 2026, 44(2): 65-73 https://doi.org/10.3969/j.issn.1001-909X.2026.02.007

LI Xianli, NI Yunlin, CHEN Songgui, et al. Numerical simulation of wave reflection and transmission characteristics over a cross-section of coral atoll topography based on the modified mild-slope equation[J]. Journal of Marine Sciences. 2026, 44(2): 65-73 https://doi.org/10.3969/j.issn.1001-909X.2026.02.007

中图分类号： P731.22

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