反常波海面参数计算方法及其色散关系

提出了一种计算反常波海面参数及色散关系的数值方法.将反常波海面看成变幅变频的波列，在各个具体时间、空间点用不同参数的延拓正弦波进行插值.在具体的时间、空间点处，根据海面及其一阶、二阶导数关系，求出相应的延拓正弦波各个参数.数值模拟出的振幅结果表明该方法有效，利用该方法计算的反常波海面参数进行海面重构的结果与原海面完全符合.比较非线性海面波数和角频率的关系式ω²/k与重力加速度g值，发现反常波海面的主要非线性色散区域不是位于反常波区域，而是位于 关键词： 反常波 非线性 色散

Numerical calculation of parameters of freak wave and its dispersion relation

A numerical method for extracting parameters of extreme sea wave and calculating its dispersion relation is presented. The nonlinear sea surface can be regarded as waves whose wave numbers and frequencies change with temporal and spatial points. At every point, the height of sea surface can be interpolated by the value of an extending sine wave whose parameters （such as wave numbers and frequencies） are constant. From the first order and the second order derivative of extreme wave, we can extract wave numbers, frequencies, and amplitudes of the extreme wave. The numerical amplitude results show that this method is valid. Comparing values of ω²/k with g, we can find that the nonlinear area does not lie in the area of extreme waves, but lies very closely to both sides of them. The corresponding wave heights in these areas are lower than that in the linear dispersion area. Compared with wavelet and Hilbert transform analysis method, our method has two advantages: Firstly, it saves much buffer capacity and CPU time. Secondly, it can supply disperse relationship of systems which other methods cannot supply. The disadvantage of this method is that, in the area of engineering application, it is only applicable to systems with coexisting temporal series data and spatial data.