通信学报 ›› 2013, Vol. 34 ›› Issue (2): 177-185.doi: 10.3969/j.issn.1000-436x.2013.02.021

• 学术通信 • 上一篇    下一篇

二维改进分形海面模型及海谱分析

陈瑜,胡云安,林涛   

  1. 海军航空工程学院 控制工程系,山东 烟台 264001
  • 出版日期:2013-02-25 发布日期:2017-07-17

Two-dimensional improved fractal model of the sea surface and sea spectrum evaluation

Yu CHEN,Yun-an HU,Tao LIN   

  1. Department of Control Engineering,Naval Aeronautical and Astronautical University,Yantai 264001,China
  • Online:2013-02-25 Published:2017-07-17

摘要:

摘 要:针对分形海面模型的功率谱在空间波数小于基波波数时不能满足正幂率的问题,提出了一种统计模型和归一化带限Weierstrass分形模型相结合的二维海面模型,确定了方向海谱的闭式解,得到了表面功率谱和方向分布函数,并且和有关文献的数据进行了对比,对分形维数、频率幅度尺度因子、风速和风向等参量对海面轮廓的影响做了进一步分析。从仿真结果可知:表面功率谱和PM谱、JONSWAP 谱、文圣常谱和南海的实测数据都拟合的很好,方向分布规律和 Mitsuyasu 方向函数相似,海面形状具有大尺度涌浪和小尺度张力波的特性,并且统计模型和分形模型的性质在改进模型中依然适用,验证了模型的有效性。

关键词: 分形模型, 海谱, Longuet-Higgin模型, PM谱

Abstract:

Aiming at the problem that the ominidirectional sea-wave spectrum of fractal sea-wave model could not satisfy the positive power law when spatial wave numbers was smaller than the fundamental wave number,2-D sea-wave model was proposed by combining statistical sea model and normalization band-limited Weierstrass-Mandelbrot (WM) fractal sea model.With the proposed method,the closed form expression of the directional sea-wave spectrum was calculated and the ominidirectional sea-wave spectrum and the angular distribution function derived,the comparison with the results in the literature was made,and influences of fractal dimension,frequency and amplitude factor,wind speed and wind direction on sea-surface were further analyzed.Simulation results show that omnidirectional sea-wave spectrum is in good agreement with the common spectrum of Pierson-Moskowitz (PM) and JONSWAP and Wen Sheng Chang and the real data of the South China Sea,angular distribution function is very similar to the Mitsuyasu’s distribution function,sea surface have both characters of large-scale turbulent waves and micro-scale capillary wave,statistical model and fractal model’s characters are still suitable for improved fractal model,and the correctness of the improved model was validated.

Key words: fractal model, sea-wave spectrum, Longuet-Higgin model, PM spectrum

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