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以小振幅波理论为基础，利用摄动方法研究了三层密度分层流体的毛细重力波，给出了三层成层状态下各层流体速度势的二阶渐近解及毛细重力波波面位移的二阶Stokes波解. 结果表明：一阶解及二阶解除了依赖于各层流体的厚度及密度，与表面张力也有很重要的关系.
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关键词:
- 三层密度分层流体 /
- 毛细重力波 /
- 二阶Stokes波解 /
- 小振幅波理论
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:
- 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 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 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
-
[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 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 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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