基于KdV方程的浅水畸形波演化特征-《集美大学学报（自然科学版）》

文章信息/Info

Title:: Study on Evolution Characteristics of Freak Wave Within the Framework of KdV Equation

Author(s):: GAO Senlin; HU Zhe; ZHANG Xiaoying; MA Yazhou; MAO Fufeng; (School of Marine Engineering，Jimei University，Xiamen 361021，China)

Keywords:: freak wave; KdV equation; pseudo-spectral method; CMOR wavelet analysis; cnoidal wave

摘要:: 为了研究高斯脉冲型畸形波解的演化特征，运用虚拟波谱法数值求解KdV（Korteweg-de Vries）方程。以JONSWAP谱为目标谱，分别以线性余弦波、椭圆余弦波为基础组成波，采用叠加思想模拟随机波列，数值求解了高斯脉冲型畸形波在随机波浪场中的演化特征。采用CMOR小波分析畸形波演化过程中的波数、能量分布状况。模拟结果反映了畸形波生成时的能量集中以及高频能量转移特征。计算随机波浪场中不同参数条件下高斯脉冲型畸形波的持续时间和传播距离，曲线拟合结果表明，畸形波的持续时间与传播距离和高斯脉冲的波幅与脉冲参量之间近似呈二次函数关系。

Abstract:: In this paper，the Korteweg-de Vries (KdV) equation is solved by pseudo-spectral method，which provides a reference for the study of evolution characteristics of the Gaussian pulse type freak wave solution.Taking the JONSWAP spectrum as the target spectrum，based on linear cosine wave and cnoidal wave respectively，the random wave is simulated by superposition ideas，numerically solved the evolution characteristics of Gaussian pulse type freak wave in random wave field.To analyze the wave number and energy distribution of the freak wave during the evolution，the cmor wavelet transform are used.When the freak wave is generated，the simulation results reflect the characteristics of energy concentration and high-frequency energy transfer.The curve fitting results show that the duration and propagation distance of the freak wave have a quadratic function relationship with the amplitude and width of the Gaussian pulse under different wave conditions.