Peregrine呼吸子解畸形波在水底障碍物作用下演化数值研究

Numerical study on the evolution of freak waves based on Peregrine breathers with bottom obstacles

畸形波是一种持续时间短,波高极大,能量高度集中的波浪,能给海洋工程结构物带来严重的危害。该文选取三阶薛定谔方程(NLS)的Peregrine呼吸子解,作为畸形波非线性模型,研究其在穿过水底障碍物时的演化规律。建立求解N-S方程的二维数值波浪水槽,分析不同计算参数对生成畸形波的影响,并与理论解对比,验证数值波浪水槽的有效性。在水底布置不同尺寸的方形障碍,模拟不同畸形波穿越水底障碍时的演化过程,采用小波变换(CWT)分析畸形波时频能量特征,模拟结果表明畸形波在遭遇水底障碍物时,其非线性、能量分布等参数的变化皆会受其影响。

Freak waves are waves with short life, great crests and highly focusing energy, which can bring serious harm toocean engineering structures. In this paper, Peregrine breather of the third-order nonlinear Schr?dinger equation is chosen as thenonlinear model of freak waves, to study the evolution of freak waves while going through obstacles under water. A 2 Dnumerical wave tank solving N-S equations is established to simulate the evolution of freak waves with flat bottoms, and theinfluence of various calculation parameters is analyzed. The numerical solutions are compared with the theoretical solutions toverify the validity of the numerical wave tank. Square obstacles of different sizes are arranged at the bottom to simulate the evolution of freak waves. Furthermore, analysis of the time-frequency energy spectrum of freak waves is performed with wavelet transformation, and the impact of bottom obstacles on the evolution of freak waves is investigated. The simulation results show that nonlinearity and energy distribution of freak waves will be affected by bottom obstacles.