Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents
Chen Xiao-Gang(陈小刚)a)b)† , Guo Zhi-Ping(郭志萍)a)c), and Song Jin-Bao(宋金宝)b)
a College of Science, Inner Mongolia University of Technology, Hohhot 010051, China; b Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; c Teaching Department of Basic Sciences, Shanxi Water Technical Professional College, Shanxi 044004, China
Abstract In the present paper, the random interfacial waves in $N$-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in $N$-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave--wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the $N$-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if $N = 2$.
Received: 14 October 2007
Revised: 30 October 2007
Accepted manuscript online:
Fund: Project supported by the Natural
Science Foundation of Inner Mongolia, China (Grant No 200711020116)
and Open Fund of the Key Laboratory of Ocean Circulation and Waves,
Chinese Academy of Sciences (Grant No KLOCAW0805) and the Key
Program of the Scientifi
Cite this article:
Chen Xiao-Gang(陈小刚), Guo Zhi-Ping(郭志萍), and Song Jin-Bao(宋金宝) Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents 2008 Chin. Phys. B 17 3387
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