Second-order Stokes wave solutions for gravity capillary water waves in three-layer dendity-stratified fluid

Cui Wei; Yan Zai-Zai; Mu Ren

doi:10.7498/aps.63.140301

Abstract

In this paper, gravity-capillary water waves in a three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the gravity-capillary water waves are presented based on the small amplitude wave theory. As expected, both the first-order and second-order solutions derived depend on not only the depth and density of the three-layer fluid but also the surface tension.

Keywords:

Authors and contacts

1.
College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;
2.
Management College, Inner Mongolia University of Technology, Hohhot 010051, China
Funds: Project supported by the National Natural Science Foundation of Inner Mongolia, China (Grant No. 2013MS1012), Jointed Funding Project of 2013 Higher Education Specialized Research Fund for the Doctoral Program, China (Grant No. 20131514110005).

References

[1]	Umeyama M 1998 Memoirs Tokyo Met. Univ. 48 5765
[2]	Umeyama M 2000 Memoirs Tokyo Met. Univ. 50 120
[3]	Song J B 2004 Geophys. Res. Lett. 31 6
[4]	Cheng Y L 2003 Acta Mech. Sin. 35 213 (in Chinese) [程友良 2003 力学学报 35 213]
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[10]	Pang J, Chen X G, Song J B 2007 Acta Phys. Sin. 56 4733 (in Chinese) [庞晶, 陈小刚, 宋金宝 2007 物理学报 56 4733]
[11]	Gui Q X 2013 Chin. Phys. B 22 050203
[12]	Tinao I, Porter J, Laverón S A, Fernández J 2014 Phys. Fluids 26 024111

Cited By

[1]	Umeyama M 1998 Memoirs Tokyo Met. Univ. 48 5765
[2]	Umeyama M 2000 Memoirs Tokyo Met. Univ. 50 120
[3]	Song J B 2004 Geophys. Res. Lett. 31 6
[4]	Cheng Y L 2003 Acta Mech. Sin. 35 213 (in Chinese) [程友良 2003 力学学报 35 213]
[5]	YouY X, Miao G P, Cheng J S, Zhu R C 2005 Acta Mech. Sin. 37 529 (in Chinese) [尤云祥, 缪国平, 程建生, 朱仁传 2005 力学学报 37 529]
[6]	Wei G, YouY X, Miao G P, Qin X M 2007 Acta Mech. Sin. 39 45 (in Chinese) [魏岗, 尤云祥, 缪国平, 秦学明 2007 力学学报 39 45]
[7]	Zhang S Y, Yang H J 1999 Shanghai Fish. Univ. 8 226 (in Chinese) [章守宇, 杨红 1999 上海水产大学学报 8 226]
[8]	Chen X G, Song J B, Sun Q 2005 Acta Phys. Sin. 54 5699 (in Chinese) [陈小刚, 宋金宝, 孙群 2005 物理学报 54 5699]
[9]	Chen X G, Song J B 2006 Chin. Phys. 15 7566
[10]	Pang J, Chen X G, Song J B 2007 Acta Phys. Sin. 56 4733 (in Chinese) [庞晶, 陈小刚, 宋金宝 2007 物理学报 56 4733]
[11]	Gui Q X 2013 Chin. Phys. B 22 050203
[12]	Tinao I, Porter J, Laverón S A, Fernández J 2014 Phys. Fluids 26 024111

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Catalog

Vol. 63, Issue 14 - 2014-07-20

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