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Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents
Authors:Chen Xiao-Gang  Guo Zhi-Ping and Song Jin-Bao
Institution:College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;Teaching Department of Basic Sciences, Shanxi Water Technical Professional College, Shanxi 044004, China; Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, 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 $N = 2$.
Keywords:N-layer density-stratified fluid  uniform currents  random interfacial waves  second-order solutions
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