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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.
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Keywords:
- three-layer density-stratified fluid /
- gravity-capillary water waves /
- second-order Stokes solutions /
- small amplitude wave theory
[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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[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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