应用数学和力学2025，Vol.46Issue(9)：1176-1195,20.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
Zero Reflections of Linear Water Waves Crossing a Finite Periodic Array of Quasi-Idealized Artificial Bars
摘要
Abstract
The zero reflection of linear water waves when they pass over a finite periodic array of quasi-ideal-ized 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 re-sults 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 reso-nance 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,UN-1(cos(πx)).If the relative bar height with respect to the water depth is not very small,the total num-ber 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 UN-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.Undoubted-ly,this study enriches the understanding of the Bragg resonance reflection induced by periodically arranged arti-ficial sandbars on the seabed,and has potential application values in coastal protection and wave energy extrac-tion.关键词
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Key words
quasi-idealized artificial bar/Bragg resonance reflection/genetic zero reflection/symbiotic zero reflection/Chebyshev polynomial of the second kind/modified Bragg's law分类
数理科学引用本文复制引用
谢文洁,谢健健,刘焕文..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[J].应用数学和力学,2025,46(9):1176-1195,20.基金项目
国家自然科学基金(51879237) （51879237）
浙江省自然科学基金(LQN25E090005) 本文作者衷心感谢鲁东大学水利土木学院滕斌教授帮助提供了图5中边界元数值结果的通用计算程序.第二作者感谢浙江海洋大学科研启动基金(JX6311040423)对本文的资助. （LQN25E090005）
