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波浪在局部可渗透水平海床上传播的解析解

倪云林 滕斌

倪云林,滕斌. 波浪在局部可渗透水平海床上传播的解析解[J]. 海洋学报,2021,43(10):1–7 doi: 10.12284/hyxb2021131
引用本文: 倪云林,滕斌. 波浪在局部可渗透水平海床上传播的解析解[J]. 海洋学报,2021,43(10):1–7 doi: 10.12284/hyxb2021131
Ni Yunlin,Teng Bin. Analytical solution for waves propagating over a local permeable seabed[J]. Haiyang Xuebao,2021, 43(10):1–7 doi: 10.12284/hyxb2021131
Citation: Ni Yunlin,Teng Bin. Analytical solution for waves propagating over a local permeable seabed[J]. Haiyang Xuebao,2021, 43(10):1–7 doi: 10.12284/hyxb2021131

波浪在局部可渗透水平海床上传播的解析解

doi: 10.12284/hyxb2021131
基金项目: 浙江省自然科学基金青年基金(LQ18E090006)
详细信息
    作者简介:

    倪云林(1986-),男,浙江省舟山市人,博士,主要从事缓坡方程研究。E-mail:oceannyl@zjou.edu.cn

    通讯作者:

    滕斌(1958-),男,山东省日照市人,教授,主要从事波浪对海上建筑物作用研究。bteng@dlut.edu.cn

  • 中图分类号: P731.22

Analytical solution for waves propagating over a local permeable seabed

  • 摘要: 本文建立了波浪在局部可渗透水平海床上传播的解析解,并研究了波浪在局部可渗透海床上的透、反射问题。研究中将计算域划分为4个区域,中间区域为流域,海底可渗透,其下区域为多孔介质海床,左右两个区域也为流域,但海底不可渗透。应用线性波浪理论,建立了各流域包含非传播模态的速度势表达式,给出了海床内部的压强表达式,并利用交界面上匹配条件,求解了表达式中的待定系数。基于该解析模型,探讨了海床渗透系数、相对水深、渗透海床长度对波浪传播变形的影响。结果表明,波高沿程衰减,强度随渗透系数、渗透海床长度的增加以及相对水深的减小而变大;局部可渗透海床会引起波浪的反射和透射,随着海床长度的增加,反射系数振荡变化,并最终趋于常数,透射系数指数衰减,并最终趋于0。
  • 图  1  波浪在局部可渗透海床上传播示意图

    Fig.  1  Definition sketch of wave propagation over a local porous seabed

    图  2  动水压强截断项M取值分析

    Fig.  2  Analysis of the value of the pore pressure truncation item M

    图  3  不同渗透系数情况下相对波高分布情况

    Fig.  3  Wave height distribution for different permeability coefficients

    图  4  反射系数和透射系数随渗透系数变化情况(h/l=0.375,L=6l

    Fig.  4  The Change of reflection coefficient and transmission coefficient with permeability coefficients (h/l=0.375, L=6l)

    图  5  不同相对水深情况下相对振幅分布情况

    Fig.  5  Wave height distribution for different water depth

    图  6  反射系数和透射系数随相对水深变化情况(ks=0.5 m/s,L=6l

    Fig.  6  The change of reflection coefficient and transmission coefficient with water depth (ks=0.5 m/s, L=6l)

    图  7  反射系数随渗透海床相对长度变化情况

    Fig.  7  The change of reflection coefficient with the length permeable seabed

    图  8  透射系数随渗透海床相对长度变化情况

    Fig.  8  The change of transmission coefficient with the length permeable seabed

    表  1  不同渗透系数情况下复波数计算结果

    Tab.  1  Complex wavenumber calculated for different permeability coefficients

    水深h
    /m
    h/l波浪圆频率
    ω/Hz
    渗透系数ks
    /(m·s−1)
    实部kr
    /m−1
    虚部ki
    /m−1
    150.3751.229 60.000.157 080.000 00
    150.3751.229 60.050.157 080.000 03
    150.3751.229 60.080.157 080.000 05
    150.3751.229 60.200.157 070.000 13
    150.3751.229 60.500.157 060.000 32
    下载: 导出CSV

    表  2  不同相对水深情况下复波数计算结果

    Tab.  2  Complex wavenumber calculated for different water depth

    水深h
    /m
    h/l波浪圆频率
    ω/Hz
    渗透系数ks
    /(m·s−1)
    实部kr
    /m−1
    虚部ki
    /m−1
    200.5001.238 40.50.157 080.000 07
    150.3751.229 60.50.157 060.000 32
    120.3001.212 40.50.157 050.000 75
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-05-19
  • 修回日期:  2021-01-21
  • 网络出版日期:  2021-07-05

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