基于改进分形海浪谱的海浪模拟

Sea wave simulation based on improved fractal sea wave spectrum

针对实验海谱只能表现海面的稳态特性而无法表现海面非稳态特性的问题,利用分形海谱作为Longuet-Higgins海面模型的靶谱以体现海面的动态特性。根据经典分形海谱在空间波数小于基波波数时不能满足正幂率的问题,利用海浪能量传递过程中的动态特性对归一化带限Weierstrass分形海谱的相关函数进行了改进,在相关函数中加入了与海面波长相关的指数因子以体现波长对相关长度的影响。对相关函数进行Fourier变换得到海谱,把改进后的分形海谱和有关文献的数据进行了对比,并进一步分析了分形维数、尺度因子、常量因子等参量对海面轮廓的影响。研究表明:改进分形海谱和P-M谱、文圣常谱和南海的实测数据都拟合得很好,海面轮廓会随分形参数及常量因子的变化而动态地改变,另外分形模型的性质在改进模型中依然适用,由此验证了该模型的有效性。

Fractal spectrum was used as target spectrum to show the sea surfacers dynamic characteristics when the experimental sea-wave spectrum could only reflect the sea surfacers steady-state characteristics but not the unsteady characteristics. The functions related to the normalization band-limited Weierstrass-Mandelbrot （WM） fractal sea-wave spectrum were improved by using the dynamic characteristics of sea wave energy transmission, considering that the fractal spectrum could not satisfy the needs of positive power when the number of waves was smaller than that of fundamental waves. The related functions was added to the exponential function correlating with wave length to show the impact of wave length on correlation length. Sea spectrum was derived from the Fourier transform by which the related function was improved. Then, the improved fractal sea-wave spectrum was compared with the data given in the literature to make a further study of fractal dimension, the frequency and amplitude factor and constant factor affecting sea surface. The simulation results show that omnidirectional sea-wave spectrum agrees well with the common spectrum of Pierson-Moskowitz （P-M） and Wen Sheng Chang and the real data of the South China Sea; the improved fractal sea surface varies with fractal parameters and constant factor; the characters of fractal model are still suitable for the improved fractal model. All these show that these improved model is useful and efficient.