Please wait a minute...
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

Cite this article: 

Chen Xiao-Gang, Guo Zhi-Ping, Song Jin-Bao Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents 2008 Chin. Phys. B 17 3387

[1] Wavefront modulation of water surface wave by a metasurface
Sun Hai-Tao, Cheng Ying, Wang Jing-Shi, Liu Xiao-Jun. Chin. Phys. B, 2015, 24(10): 104302.
[2] Instantaneous frequency and wave mode identification in a magnetosheath using few spatial points
Nathaniel E U, Beloff N, George N J. Chin. Phys. B, 2013, 22(8): 084701.
[3] Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms
Zhong Lan-Hua, Wu Fu-Gen, Zhong Hui-Lin. Chin. Phys. B, 2010, 19(2): 020301.
[4] Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid
Chen Xiao-Gang, Guo Zhi-Ping, Song Jin-Bao, He Xiao-Dong, Guo Jun-Ming, Bao Shu-Hong, Cui Wei. Chin. Phys. B, 2009, 18(5): 1906-1916.
[5] Three-dimensional interfacial wave theory of dendritic growth: (I). multiple variables expansion solutions
Chen Yong-Qiang, Tang Xiong-Xin, Xu Jian-Jun. Chin. Phys. B, 2009, 18(2): 671-685.
[6] Three-dimensional interfacial wave theory of dendritic growth: (II). non-axi-symmetric global wave modes and selection criterion of pattern formation
Chen Yong-Qiang, Tang Xiong-Xin, Xu Jian-Jun. Chin. Phys. B, 2009, 18(2): 686-698.
[7] A kind of extended Korteweg--de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system
Yang Lian-Gui, Song Jin-Bao, Yang Hong-Li, Liu Yong-Jun. Chin. Phys. B, 2007, 16(12): 3589-3594.
[8] The classification of travelling wave solutions and superposition of multi-solutions to Camassa-- Holm equation with dispersion
Liu Cheng-Shi. Chin. Phys. B, 2007, 16(7): 1832-1837.
[9] A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid
Song Jin-Bao. Chin. Phys. B, 2006, 15(12): 2796-2803.
[10] Different localized states of travelling-wave convection in a rectangular container
Li Guo-Dong, Huang Yong-Nian. Chin. Phys. B, 2006, 15(12): 2984-2988.
[11] Interaction of a submerged horseshoe vortex with a free surface
Wu Yun-Gang, Tao Ming-De. Chin. Phys. B, 2006, 15(6): 1137-1142.
[12] Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel
Jian Yong-Jun, E Xue-Quan. Chin. Phys. B, 2004, 13(8): 1191-1200.
[13] Surface waves in a vertically excited circular cylindrical container
Jian Yong-Jun, E Xue-Quan, Zhang Jie, Meng Jun-Min. Chin. Phys. B, 2004, 13(10): 1623-1630.
[14] Instability of the vertically forced surface wave in a circular cylindrical container
Jian Yong-Jun, E Xue-Quan. Chin. Phys. B, 2004, 13(10): 1631-1638.
[15] General explicit solutions of a classical Boussinesq system
Zhang Shan-Qing, Li Zhi-Bin, Xu Gui-Qiong. Chin. Phys. B, 2002, 11(10): 993-995.
No Suggested Reading articles found!