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
a Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; b College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
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.
Received: 17 November 2005
Revised: 18 December 2005
Accepted manuscript online:
Fund: 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).
Cite this article:
Chen Xiao-Gang (陈小刚), Song Jin-Bao (宋金宝) Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid 2006 Chinese Physics 15 756
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