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Basic Studies on the Qauntumzation of Nonlinear Coastal Waves

非线性海岸波量子化的基础研究

基本信息

批准号：
60550363
负责人：
TSUCHIYA Yoshito
金额：
$ 1.28万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1985
资助国家：
日本
起止时间：
1985 至 1986
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60550363/
关键词：
Wave Soliton energy distribution statistical theory Kdv方程式

项目摘要

It has recently been recongnized that waves in shallow water are composed of a dynamic coherent structure in which solitons are elementary excitation. To formulate the waves with soliton modes, qauntumzation of Stokes waves and solitons which are deduced from the KdV equation is made and energy distribution function is obtained. Based on the formulation, a statistical theory of random solitons is proposed. The main results are summarized as:1) For the qauntumzation of Stokes waves, solutions to the Schroedinger equation which was derived from the Hamiltonian of Stokes waves were obtained to have wave energy distribution functions. Similar distribution functions of solitons were obtained from the KdV equation.2) From the view point of dynamic coherent structures of the waves in shallow water, a statistical theory of random solitons was proposed. Its applications to waves in various conditions were made using wave data obtained at Ogata Wave Observatory.3) Applicability of the solitons in wave profiles is very good for the nonlinear waves having greater Ursell numbers than 10, as well as waves including breaking waves.4) Three types of soliton eigenvalue distribution functions were obtained for various wave conditions and they are conservative in propagation of the waves in shallow water as soliton modes. The theoretical energy distribution function was compared with the observed ones with good agreement.

最近人们认识到，浅水中的波是由一个以孤子为基本激励的动态相干结构组成的。为了描述具有孤子模的波，对KdV方程导出的Stokes波和孤子进行了量子化，得到了能量分布函数。在此基础上，提出了随机孤子的统计理论。主要结果如下：1)对于Stokes波的量子化，得到了由Stokes波的哈密顿量导出的薛定谔方程的解具有波的能量分布函数。从KdV方程出发，得到了相似的孤子分布函数。2)从浅水中波的动态相干结构出发，提出了随机孤子的统计理论。利用Ogata波浪观测站获得的波浪数据，将其应用于不同条件下的波浪。3)孤子在波浪剖面中的适用性很好，适用于Ursell数大于10的非线性波，以及包括破碎波在内的波。4)得到了三种不同情况下的孤子本征值分布函数，它们作为孤子模在浅水中传播时是保守的。将理论能量分布函数与实测值进行了比较，两者吻合较好。