Chin. Phys. B, 2008, Vol. 17(9): 3387-3393    DOI: 10.1088/1674-1056/17/9/040
 CLASSICAL AREAS OF PHENOMENOLOGY Prev   Next

# Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

Chen Xiao-Ganga, Guo Zhi-Pingb, Song Jin-Baoc
a College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; b College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;Teaching Department of Basic Sciences, Shanxi Water Technical Professional College, Shanxi 044004, China; c 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:  second-order solutions      N-layer density-stratified fluid      uniform currents      random interfacial waves
Received:  14 October 2007      Revised:  30 October 2007      Published:  08 September 2008
 PACS: 47.35.-i (Hydrodynamic waves) 47.10.A- (Mathematical formulations) 47.55.Hd (Stratified flows)
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