| 摘要: |
| 通过构造带有随机初条件的微分方程 ,论述了在线性海浪范围内动力学与统计学的协调性 ,然后把水波动力学中的研究成果引进随机波面统计中获得了非线性波面的概率分布形式 ,并由浅水因子和浅水波陡作为分布函数中的控制参量 ,从而发展了随机海浪的统计理论。 |
| 关键词: 波浪 动力学 统计学 |
| DOI：10.11693/hyhz200004001001 |
| 分类号: |
| 基金项目:国家自然科学基金资助项目，49876007号;中国科学院九五重点项目，KZ952-S1-420号;国家863资助项目，818-06-01号 |
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| THE APPLICATIONS OF DYNAMICS IN PROBABILITY STATISTICS OF RANDOM WAVE SURFACE |
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HOU Yi-jun, LI Ming-kui, XIE Qiang, YIN Bao-shu, SU Jing-zhi, YANG Lian-gui
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Institute of Oceanology, The Chinese Academy of Sciences, Qingdao266071
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| Abstract: |
| Applying some results of dynamics such as stokes wave to the study of random waves, we obtained a new model of probability statistics of waves:
f(ζ)=f(ζ0)|dζ0/dζ|=1/[square root (2π)]|1-δζ|e-δζe-0.5ζ2e-2δζ
The excellence of the model is more notable in the study of nonlinear phenomena. According to the results of the article, the wave steepness is an important parameter not only in dynamics but also in statistics. And the magnitude of the wave steepness is able to show the degree that the distribution of wave surface deviates from the Gaussian distribution and to describe the change of the distribution function as a control parameter. The normal form of the traditional Gaussian distribution keeps the same form in any kind of depth, but the distribution function can describe the degree of the convergence or decentralization. This is another significance of the distribution besides the degree of deflection. We got a function form which is valid in physics by the study of the distribution of wave surface that is influenced by water depth:
f(ζ)=1/[square root (2π)]|{1–μηζcoth[μ(1+ηζ)]}/sinh[μ(1+ηζ)]|e-0.5*(ζ2/2sinh2[μ(1+ηζ)]
We can learn that the wave steepness of shallow water describes the degree of deviation and the parameter of shallow water shows the degree of the convergence or decentralization. These could improve the traditional statistical theory of waves. |
| Key words: Wave, Dynamics, Statistics |
