波高非线性概率分布高阶谱数值模型研究

Study on high order spectral numerical model of wave height nonlinear probability distribution

由于波浪的调制不稳定以及非线性波-波相互作用等因素的存在,波浪的分布会偏离线性假设下瑞利分布的结果。通过使用高阶谱模型对不同初始条件下波浪数值模拟。对统计得到的波高与线性理论下的瑞利分布和考虑非线性下改进的埃奇沃思-瑞利(MER)分布和依据Gram-Charlier展开的分布(GC分布)进行对比。结果表明,深水条件下波浪传播过程中偏度值变化较小,而峰度值出现增长。在较小有效波高值的波况下波高分布符合瑞利分布,但随着有效波高值的增加,波浪的非线性增强,波高分布与考虑非线性影响下的GC和MER分布结果相符。宽谱下的波高分布偏离瑞利分布的程度小于窄谱的情况,波高分布更接近瑞利分布的结果。

Due to the instability modulation(Benjamin-Feir instability)and nonlinear wave-wave interaction,the distribution of waves deviates from the Rayleigh distribution under the linear hypothesis.Numerical simulation of waves in different initial conditions by using High-Order Spectral model,compares the Rayleigh distributions in the linear theory and the modified Edgewood Rayleigh distribution(MER distribution)and the distribution based on the Gram-Charlier expansion(GC distribution)with wave height data.Results show that in the process of wave propagation skewness changed little and kurtosis increased gradually.Wave distribution is accord with Rayleigh distribution in smaller significant wave height.Wave distribution is accord with MER and GC distribution while significant wave height increased.The wave height distribution is more close to the Rayleigh distribution than the narrow spectrum under the condition of wide spectrum.