中国物理B ›› 2006, Vol. 15 ›› Issue (4): 756-766.doi: 10.1088/1009-1963/15/4/016

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Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

宋金宝1, 陈小刚2   

  1. (1)Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071,China; (2)Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071,China;College of Science, Inner Mongolia University of Technology,Hohhot 010051, China
  • 收稿日期:2005-11-17 修回日期:2005-12-18 出版日期:2006-04-20 发布日期:2006-04-20
  • 基金资助:
    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).

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

Chen Xiao-Gang (陈小刚)ab, Song Jin-Bao (宋金宝)a   

  1. a Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; b College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
  • Received:2005-11-17 Revised:2005-12-18 Online:2006-04-20 Published:2006-04-20
  • Supported by:
    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.

关键词: N-layer density-stratified fluid, interfacial internal waves, second-order random wave solutions

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.

Key words: N-layer density-stratified fluid, interfacial internal waves, second-order random wave solutions

中图分类号:  (Wave-structure interactions)

  • 47.35.Lf
47.10.A- (Mathematical formulations) 47.55.Hd (Stratified flows) 47.55.N- (Interfacial flows)