Second-order solutions for random interfacial waves in N-layer density-stratified fluid with
steady uniform currents |
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Authors: | Chen Xiao-Gang Guo Zhi-Ping and Song Jin-Bao |
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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 |
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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 $N = 2$. |
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Keywords: | N-layer density-stratified
fluid uniform currents random interfacial waves second-order
solutions |
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