| Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid |
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| 作者姓名： | 陈小刚 宋金宝 |
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| 作者单位： | Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071,China;College of Science, Inner Mongolia University of Technology,Hohhot 010051, China;Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071,China |
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| 基金项目： | Project supported by the National Science Fund for Distinguished Young Scholars (Grant No 40425015), the Cooperative Project of Chinese Academy Sciences and the China National Offshore oil Corporation (``Behaviours of internal waves and their roles on the marine structures') and
the National Natural Science Foundation of China (Grant No10461005). |
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| 摘 要： | This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.
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| 关 键 词： | N层密度分层流体 随机波 流体学 解法 内波 |
| 收稿时间： | 2005-11-17 |
| 修稿时间： | 2005-11-172005-12-18 |
Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid |
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| Chen Xiao-Gang and Song Jin-Bao.Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid[J].Chinese Physics B,2006,15(4):756-766. |
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| Authors: | Chen Xiao-Gang and Song Jin-Bao |
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| Institution: | Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071,China; Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071,China;College of Science, Inner Mongolia University of Technology,Hohhot 010051, China |
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| Abstract: | This paper studies the random internal wave equations describing the
density interface
displacements and the velocity potentials of N-layer stratified fluid
contained between two rigid walls at the top and bottom. The
density interface displacements and the velocity potentials were solved to
the second-order by an expansion approach used by Longuet-Higgins (1963) and
Dean (1979) in the study of random surface waves and by Song (2004) in the
study of second-order random wave solutions for internal waves in a
two-layer fluid. The obtained results indicate that the first-order
solutions are a linear superposition of many wave components with different
amplitudes, wave numbers and frequencies, and that the amplitudes of
first-order wave components with the same wave numbers and frequencies
between the adjacent density interfaces are modulated by each other. They
also show that the second-order solutions consist of two parts: the first
one is the first-order solutions, and the second one is the solutions of the
second-order asymptotic equations, which describe the second-order nonlinear
modification and the second-order wave--wave interactions not only among the
wave components on same density interfaces but also among the wave
components between the adjacent density interfaces. Both the first-order and
second-order solutions depend on the density and depth of each layer. It is
also deduced that the results of the present work include those derived by
Song (2004) for second-order random wave solutions for internal waves in a
two-layer fluid as a particular case. |
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| Keywords: | N-layer density-stratified fluid interfacial internal waves second-order random wave solutions |
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