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深水随机波列中畸形波统计特征的研究

付睿丽 马玉祥 董国海

付睿丽,马玉祥,董国海. 深水随机波列中畸形波统计特征的研究[J]. 海洋学报,2021,43(10):1–9 doi: 10.12284/hyxb2021159
引用本文: 付睿丽,马玉祥,董国海. 深水随机波列中畸形波统计特征的研究[J]. 海洋学报,2021,43(10):1–9 doi: 10.12284/hyxb2021159
Fu Ruili,Ma Yuxiang,Dong Guohai. Researches on statistical properties of freak waves in uni-directional random waves in deep water[J]. Haiyang Xuebao,2021, 43(10):1–9 doi: 10.12284/hyxb2021159
Citation: Fu Ruili,Ma Yuxiang,Dong Guohai. Researches on statistical properties of freak waves in uni-directional random waves in deep water[J]. Haiyang Xuebao,2021, 43(10):1–9 doi: 10.12284/hyxb2021159

深水随机波列中畸形波统计特征的研究

doi: 10.12284/hyxb2021159
基金项目: 国家自然科学基金(51720105010,51679031,51979029);辽宁省兴辽人才计划(XLYC1807010);中央高校基本科研业务费(DUT2019TB02)
详细信息
    作者简介:

    付睿丽(1993—),女,甘肃省定西市人,主要从事波浪水动力研究。E-mail:frldlut@163.com

    通讯作者:

    马玉祥(1981—),男,河南省驻马店市人,教授,主要从事非线性水波动力学理论和数值算法等研究。E-mail:yuxma@126.com

  • 中图分类号: TV139.2

Researches on statistical properties of freak waves in uni-directional random waves in deep water

  • 摘要: 本文基于Longuet-Higgins随机波浪模型和JONSWAP谱,进行了大量深水随机波的模拟,获取了畸形波发生概率稳定的随机波列,并对随机波列中的畸形波进行了分析。结果表明,畸形波发生的概率小于基于Rayleigh分布预测结果,且随谱宽的减小而增大。在固定时间段内,畸形波发生的频次服从泊松分布,时间间隔服从指数分布,且随着谱宽的增大,畸形波的发生频次减小,相邻畸形波的发生时间间隔增加。通过小波变换方法分离随机波中的波群,研究了出现畸形波的波群特征,发现一个波群中最多会出现4个畸形波,但是在发生畸形波的波群中,单个畸形波的概率最大。随着谱宽减小,一个波群中包含多个畸形波的概率增加。另外,出现畸形波的波群时间长度服从广义极值分布,随着谱宽减小,畸形波波群的时间跨度增加。
  • 图  1  γ=1, 3, 5, 7时,T s内畸形波发生频率的概率密度分布

    Fig.  1  Probability distributions of frequency of freak waves for different peak enhancement factors (γ=1, 3, 5, 7).

    图  2  泊松分布参数λ与谱宽υ的关系

    Fig.  2  Relationships between Poisson distribution parameter λ and spetrum widths υ

    图  3  γ=1,3,5,7时,畸形波出现时间间隔分布

    Fig.  3  Probability distributions of time intervals of freak waves for different peak enhancement factors (γ=1, 3, 5, 7).

    图  4  指数分布参数μ与谱宽υ的关系

    Fig.  4  Relationships between exponential distribution parameter μ and spetrum wdths υ

    图  5  不同谱峰因子下,不同畸形波特征所占比例

    Fig.  5  Proportions of each characteristic of freak waves for different peak enhancement factors

    图  6  γ=1,3,5,7时,畸形波群无量纲时间长度概率分布

    Fig.  6  Probability distributions of non-dimensional time lengths of freak wave groups for different peak enhancement factors (γ=1, 3, 5, 7)

    图  7  GEV系数与谱宽υ的关系

    Fig.  7  Relationships between parameters of GEV distribution and spetrum widths υ

    表  1  不同谱宽的时间序列长度[31]

    Tab.  1  Time series lengths for different spectrum widths

    γ谱宽υ时间序列
    T0/s
    实际波数波数相对
    误差/%
    畸形波发生
    概率/%
    10.38111 988 6951 499 7240.018 40.007 5
    20.36712 565 1841 499 7390.017 40.009 3
    30.35512 959 0491 499 7600.016 00.010 7
    40.34313 257 5631 499 7190.018 70.012 1
    50.33313 496 0851 499 6960.020 20.013 3
    60.32413 693 1451 499 8210.011 90.014 3
    70.31513 859 8261 499 8800.008 00.015 2
    下载: 导出CSV

    表  2  不同谱宽下畸形波出现不同频次概率的预测值与数值结果对比

    Tab.  2  Comparisons of the numerical and predicted values of possibility for frequencies of freak waves

    γ谱宽υ出现1次畸形波的概率相对误差/%出现2次畸形波的概率相对误差/%
    理论值数值结果理论值数值结果
    20.3670.103 40.103 30.100.006 00.006 00.00
    40.3430.126 90.125 51.120.009 30.009 12.20
    60.3240.144 90.146 51.090.012 50.012 71.57
    下载: 导出CSV

    表  3  不同谱宽下相邻畸形波时间间隔预测值与数值结果对比

    Tab.  3  Comparisons of the numerical and predicted values of intervals of adjacent freak waves

    γ谱宽υTd /Tp=0.5×104相对误差/%Td /Tp=1.5×104相对误差/%
    预测值/10−4数值结果/10−4预测值/10−4数值结果/10−4
    20.3670.6610.6373.770.1970.2032.96
    40.3430.7050.6912.030.1620.1704.71
    60.3240.7310.7613.940.1240.1194.20
    下载: 导出CSV

    表  4  波群中包含畸形波的类型

    Tab.  4  Classifications of freak waves in wave groups

    包含畸形波的个数畸形波的特征和出现位置命名
    1同时具有最高波峰和最深波谷Ona
    只具有最高波峰或最深波谷Onb
    2相邻Twa
    间隔Twn
    3相邻Tha
    间隔Thn
    4相邻Foa
    间隔Fon
    下载: 导出CSV

    表  5  畸形波群无量纲时间长度众数预测值与数值结果对比

    Tab.  5  Comparisons of the numerical and predicted modes of the non-dimensional lengths of freak wave groups

    γ谱宽υ预测值数值结果相对误差/%
    20.3678.08.00
    40.3439.59.23.3
    60.32410.510.50
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-07-28
  • 修回日期:  2020-10-29
  • 网络出版日期:  2021-08-26

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