线性水波越过有限周期排列拟理想人工沙坝的零反射分布

谢文洁; 谢健健; 刘焕文

doi:10.21656/1000-0887.450148

线性水波越过有限周期排列拟理想人工沙坝的零反射分布

doi: 10.21656/1000-0887.450148

1. 浙江海洋大学海洋工程装备学院, 浙江舟山 316022;
2. 鲁东大学水利土木学院, 山东烟台 264025

基金项目:

国家自然科学基金(51879237)；浙江省自然科学基金(LQN25E090005)

详细信息

作者简介:
谢文洁(1998—), 女, 硕士(E-mail: 1924691738@qq.com);谢健健(1983—), 女, 讲师, 博士(E-mail: jianjianxie126@126.com);刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

通讯作者:
刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

中图分类号: O357.41
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出版历程
- 收稿日期: 2024-05-20
- 修回日期: 2025-06-12
- 网络出版日期: 2025-10-17

The Zero Reflections Distribution of Linear Water Waves Crossing a Finite Periodic Array of Quasi-Idealized Artificial Bars

1. School of Marine Engineering Equipment, Zhejiang Ocean University, Zhoushan, Zhejiang 316022, P.R.China;
2. School of Hydraulic and Civil Engineering, Ludong University, Yantai, Shandong 264025, P.R.China

Funds:

The National Science Foundation of China(51879237)

摘要

摘要: 该文研究水波越过平整海床上N个p次拟理想人工沙坝组成的周期阵列时出现的零反射(亦即完全透射).所谓p次拟理想沙坝, 是指沙坝上方的水深函数为一个常数加上p次单项式, 其中p为正整数.研究表明, 若沙坝关于最深水深的相对高度远小于1, 则水波越过p=1的拟理想沙坝(即三角形)周期阵列时产生遗传性零反射的条件是沙坝宽度正好为入射波半波长的正偶数倍.随着p增加, 水波越过p次拟理想沙坝周期阵列时产生遗传性零反射的相位向低频移动.当p趋于无穷, p次拟理想沙坝退化为矩形沙坝, 此时产生遗传性零反射的条件是沙坝宽度正好为入射波半波长的正整数倍.此外, 任意相邻Bragg共振峰之间共生性零反射的个数为N-1，且这N-1个零反射恰好为第二类Chebyshev多项式U_N-1(cos(πx))的全部零点.若沙坝关于水深的相对高度不是很小, 则相邻Bragg共振峰之间共生性零反射的个数仍为N-1，且这些零反射的相位近似等于U_N-1(cos(πx))的N-1个零点再减去前后两个共振峰相位下移量的平均值, 而后者可通过修正Bragg原理估算.但对于遗传性零反射的相位, 目前仍无有效办法进行预测.无疑, 本研究丰富了对海床上周期排列的人工沙坝激发的Bragg共振反射现象的理解, 并在海岸保护和波浪能提取等方面具有潜在应用价值.
- 拟理想人工沙坝 /
- Bragg共振反射 /
- 遗传性零反射 /
- 共生性零反射 /
- 第二类Chebyshev多项式 /
- 修正Bragg原理
Abstract: The zero reflection of phenomenon occurring with linear water waves when they pass over a finite periodic array of quasiidealized bars of degree p on a flat seabed is studied. The socalled quasiidealized bar of degree p refers to the water depth function above the bar is a constant plus a monomial of degree p, where p is a positive integer. The results show that, when water waves crossing a periodic array of quasiidealized bars of degree 1 (i.e., triangular bars) with the relative bar height with respect to the water depth being much less than 1, the condition for the generation of genetic zero reflection is that the bar width is exactly a positive even multiple the half wavelength of the incident wave. As p increases, the phase of the genetic zero reflection shifts towards lower frequencies. When p approaches infinity, the quasiidealized bars of degree p tend to be a rectangular bar, and the condition for genetic zero reflection is that the bar width decreases to a positive integer multiple of the half wavelength of the incident wave. In addition, the total number of symbiotic zero reflections between any adjacent Bragg resonance peaks is N-1, and the excitation condition for these zero reflections is that the ratio of the bar spacing to the half wavelength of the incident wave is exactly N-1 zero points of the Chebyshev polynomial of the second kind U_{N-1(cos(πx)). If the relative bar height with respect to the water depth is not very small, the total number of symbiotic zero reflections between adjacent Bragg resonance peaks is still N-1, and the phases of these zero reflections are approximately equal to the N-1 zero points of U_N-1(cos(πx)) minus the mean of the phase shift of the two adjacent resonance peaks, where the latter can be estimated by the modified Bragg’s law. However, at present there is no effective method to predict the phase of the genetic zero reflection. Undoubtedly, this study enriches the understanding of the Bragg resonance reflection induced by periodically arranged artificial sandbars on the seabed, and has potential application values in coastal protection and wave energy extraction.}
- quasi-idealized artificial bar /
- Bragg resonance reflection /
- genetic zero reflection /
- symbiotic zero reflection /
- Chebyshev polynomial of the second kind /
- modified Bragg’s law

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参考文献(50)

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线性水波越过有限周期排列拟理想人工沙坝的零反射分布

doi: 10.21656/1000-0887.450148

作者简介:
谢文洁(1998—), 女, 硕士(E-mail: 1924691738@qq.com);谢健健(1983—), 女, 讲师, 博士(E-mail: jianjianxie126@126.com);刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

通讯作者:
刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

计量

The Zero Reflections Distribution of Linear Water Waves Crossing a Finite Periodic Array of Quasi-Idealized Artificial Bars

计量

目录

留言板

线性水波越过有限周期排列拟理想人工沙坝的零反射分布

doi: 10.21656/1000-0887.450148

作者简介: 谢文洁(1998—), 女, 硕士(E-mail: 1924691738@qq.com);谢健健(1983—), 女, 讲师, 博士(E-mail: jianjianxie126@126.com);刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

通讯作者: 刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

计量

出版历程

The Zero Reflections Distribution of Linear Water Waves Crossing a Finite Periodic Array of Quasi-Idealized Artificial Bars

计量

出版历程

目录

作者简介:
谢文洁(1998—), 女, 硕士(E-mail: 1924691738@qq.com);谢健健(1983—), 女, 讲师, 博士(E-mail: jianjianxie126@126.com);刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).

通讯作者:
刘焕文(1963—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: 6337@ldu.edu.cn).