Abstract
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.
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