无限深水中具有指数密度变率的周期性永形内波渐进解析解

邹丽; 宗智; 王振; 赵勇; 梁辉

doi:10.3879/j.issn.1000-0887.2015.01.009

无限深水中具有指数密度变率的周期性永形内波渐进解析解

doi: 10.3879/j.issn.1000-0887.2015.01.009

邹丽^1,2,
宗智^1,2,
王振^3,4,
赵勇⁵,
梁辉^1,2

¹工业装备结构分析国家重点实验室,辽宁大连 116024;²大连理工大学船舶工程学院,辽宁大连 116024;³大连理工大学数学科学学院,辽宁大连 116024;⁴伦敦大学学院机械工程学院,英国伦敦 WCE1 6BT;⁵大连海事大学交通运输装备与海洋工程学院,辽宁大连 116026

基金项目: 国家重点基础研究发展计划（973计划）（2013CB036101）；国家自然科学基金（51109031; 51379033; 51221961; 51309040; 51279030，51239002）

详细信息

作者简介:
邹丽（1981—），女，辽宁盘锦人，副教授，博士(通讯作者. Tel: +86-411-84706373; E-mail: lizou@dlut.edu.cn).

中图分类号: O242.1
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- 文章访问数: 1131
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出版历程
- 收稿日期: 2014-10-14
- 修回日期: 2014-12-17
- 刊出日期: 2015-01-15

Analytical Solutions of Periodic Stationary Internal Waves in Infinitely Deep Water With Exponential Vertical Density Distribution

ZOU Li^1,2,
ZONG Zhi^1,2,
WANG Zhen^3,4,
ZHAO Yong⁵,
LIANG Hui^1,2

¹State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian, Liaoning 116024, P.R.China;²School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;³School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;⁴Department of Mechanical Engineering, University College London, London WC1E 6BT, UK;⁵Transportation Equipment & Ocean Engineering College, Dalian Maritime University, Dalian, Liaoning 116026, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2013CB036101）；The National Natural Science Foundation of China（51109031; 51379033; 51221961; 51309040; 51279030，51239002）

摘要

摘要: 采用同伦分析方法研究了一系列有限振幅的周期深水驻波问题.水密度在垂直方向的分布可以是变化的，假设为指数连续分布.提出一种新形式的偏微分方程作为辅助方程，获得解的新的表达形式来满足底部的边界条件和无限大的刚性假设.给出了解的表达式中系数的递推关系和周期海洋内波形成的永久驻波的显式表达式.得到垂直方向和水平方向的全局收敛解，揭示了密度变量和内波幅度间的关系.同伦分析方法对求解具有指数密度率周期性的永形波解是一致有效的.
- 内波 /
- 深水波 /
- 非线性 /
- 指数密度
Abstract: A train of periodic deep water stationary waves with finite amplitudes were investigated analytically with the homotopy analysis method. The vertical distribution of water density was considered as variable in a continuous exponential trend. A new form of partial differential equations were proposed as the auxiliary equations and the new-form solution expressions were obtained in order to match the level boundary condition at the bottom and the hypothetical infinitely rigid condition. The detailed recursive relation of the coefficient in the solution expression was given and the explicit expressions of the permanent stationary periodic internal waves were presented. The convergent series solutions were obtained for the global domain both in vertical and horizontal directions. The relation between the density variable and the internal wave amplitude was revealed.
- internal wave /
- deep water wave /
- nonlinearity /
- exponential density

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参考文献(19)

[1]	Keulegan G H.Characteristics of internal solitary waves[J].Journal of Research of the National Bureau of Standards,1953,51(3): 133-140.
[2]	Long R R. Solitary waves in the one- and two-fluid systems[J].Tellus,1956,8(4): 460-471.
[3]	Peters A S, Stoker J J. Solitary waves in liquids having non-constant density[J].Communications on Pure and Applied Mathematics,1960,13(1): 115-164.
[4]	Ter-Krikorov A M. Théorie exact des ondes longues stationnaires dans un liquide hétéogéne[J].J Mécanique,1963,2: 351-376.
[5]	Bona J L, Bose D K, Turner R E L. Finite amplitude steady waves in stratified fluids[J].Journal de Mathématiques Pures et Appliquées,1983,62(4): 389-439.
[6]	Benjamin T B. Internal waves of finite amplitude and permanent form[J].J Fluid Mech,1966,25(2): 241-270.
[7]	Benjamin T B. Internal waves of permanent form in fluids of great depth[J]. J Fluid Mech,1967,29(3): 559-592.
[8]	King S E, Carr M, Dritschel D G. The steady-state form of large-amplitude internal solitary waves[J].J Fluid Mech,2011,666: 477-505.
[9]	Helfrich K R, Melville W K. Longnonlinear internal waves[J].Annual Review of Fluid Mechanics,2006,38: 395-425.
[10]	Lamb H.Hydrodynamics[M]. Cambridge: Cambridge University Press, 1932.
[11]	Camassa R, Rusas P O, Saxena A, Tiron R. Fully nonlinear periodic internal waves in a two-fluid system of finite depth[J].Journal of Fluid Mechanics,2010,652: 259-298.
[12]	Broeck V J M, Turner R E L. Long periodic internal waves[J].Phys Fluids A,1929,4(9): 1929-1935.
[13]	Turner R E L. Internal waves in fluids with rapidly varying density[J].Annali Della Scuola Normale Superiore di Pisa-Classe di Scienze,1981,8(4): 513-573.
[14]	Cheng J, Cang J, Liao S J. On the interaction of deep water waves and exponential shear currents[J].Z Angew Math Phys,2009,60(3): 450-478.
[15]	Long R R. Some aspects of the flow of stratified fluids[J].Tellus,1953,5(1): 42-57.
[16]	Dubreil-Jacotin M L. Sur les théorèmes d’existence relatifs aux ondes permanents périodiques à deux dimensions dans les liquids hétérogènes[J].Journal de Mathématiques Pures et Appliquées,1937,19: 43-67.
[17]	Abarbanel H D I, Holm D D, Marsden J E, Ratiu T. Richardson number criterion for the nonlinear stability of three-dimensional stratified flow[J].Physical Review Letters,1984,52(26): 2352-2355.
[18]	Liao S J.Beyond Perturbation: Introduction to the Homotopy Analysis Method [M]. London: Chapman & Hall/ CRC Press, 2003.
[19]	Schwartz L W. Computer extension and analytic continuation of Stoke’s expansion for gravity waves[J].J Fluid Mech,1974,62(3): 553-578.

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无限深水中具有指数密度变率的周期性永形内波渐进解析解

doi: 10.3879/j.issn.1000-0887.2015.01.009

作者简介:
邹丽（1981—），女，辽宁盘锦人，副教授，博士(通讯作者. Tel: +86-411-84706373; E-mail: lizou@dlut.edu.cn).

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Analytical Solutions of Periodic Stationary Internal Waves in Infinitely Deep Water With Exponential Vertical Density Distribution

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留言板

无限深水中具有指数密度变率的周期性永形内波渐进解析解

doi: 10.3879/j.issn.1000-0887.2015.01.009

作者简介: 邹丽（1981—），女，辽宁盘锦人，副教授，博士(通讯作者. Tel: +86-411-84706373; E-mail: lizou@dlut.edu.cn).

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出版历程

Analytical Solutions of Periodic Stationary Internal Waves in Infinitely Deep Water With Exponential Vertical Density Distribution

计量

出版历程

目录

作者简介:
邹丽（1981—），女，辽宁盘锦人，副教授，博士(通讯作者. Tel: +86-411-84706373; E-mail: lizou@dlut.edu.cn).