Fully nonlinear (2+1)-dimensional displacement shallow water wave equation

doi:10.1088/1674-1056/26/5/054501

中国物理B ›› 2017, Vol. 26 ›› Issue (5): 54501-054501.doi: 10.1088/1674-1056/26/5/054501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Fully nonlinear (2+1)-dimensional displacement shallow water wave equation

Feng Wu(吴锋), Zheng Yao(姚征), Wanxie Zhong(钟万勰)

1 State Key Laboratory of Structural Analysis of Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116023, China;
2 Transportation Equipments and Ocean Engineering College, Dalian Maritime University, Dalian 116026, China

收稿日期:2016-11-04 修回日期:2016-12-20 出版日期:2017-05-05 发布日期:2017-05-05
通讯作者: Zheng Yao E-mail:yaozheng@dlmu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272076 and 51609034) and China Postdoctoral Science Foundation (Grant No. 2016M590219).

Fully nonlinear (2+1)-dimensional displacement shallow water wave equation

Feng Wu(吴锋)¹, Zheng Yao(姚征)², Wanxie Zhong(钟万勰)¹

1 State Key Laboratory of Structural Analysis of Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116023, China;
2 Transportation Equipments and Ocean Engineering College, Dalian Maritime University, Dalian 116026, China

Received:2016-11-04 Revised:2016-12-20 Online:2017-05-05 Published:2017-05-05
Contact: Zheng Yao E-mail:yaozheng@dlmu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272076 and 51609034) and China Postdoctoral Science Foundation (Grant No. 2016M590219).

摘要/Abstract

摘要： Recently, a new (2+1)-dimensional displacement shallow water wave equation (2DDSWWE) was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach. Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear (2+1)-dimensional displacement shallow water wave equation (FN2DDSWWE). The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.

关键词: shallow water system, Hamilton variational principle, displacement, solitary wave

Abstract: Recently, a new (2+1)-dimensional displacement shallow water wave equation (2DDSWWE) was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach. Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear (2+1)-dimensional displacement shallow water wave equation (FN2DDSWWE). The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.

Key words: shallow water system, Hamilton variational principle, displacement, solitary wave

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

94.05.Fg (Solitons and solitary waves) 95.30.Lz (Hydrodynamics) 47.10.-g (General theory in fluid dynamics)

吴锋, 姚征, 钟万勰. Fully nonlinear (2+1)-dimensional displacement shallow water wave equation[J]. 中国物理B, 2017, 26(5): 54501-054501.

Feng Wu(吴锋), Zheng Yao(姚征), Wanxie Zhong(钟万勰). Fully nonlinear (2+1)-dimensional displacement shallow water wave equation[J]. Chin. Phys. B, 2017, 26(5): 54501-054501.

参考文献 36

[1]	Khan A A and Lai W C 2014 Modeling Shallow Water Flows Using the Discontinuous Galerkin Method (New York: CRC Press) p. 49
[2]	Vreugdenhil C B 1994 Numerical Methods for Shallow-Water Flow (Netherlands: Springer) p. 1
[3]	Kinnmark I 1986 The Shallow Water Wave Equations: Formulation, Analysis and Application (Berlin: Springer) p. 1
[4]	Eleuterio F T 2001 Shock-Capturing Methods for Free-Surface Shallow Flows (New York: Wiley) p. 15
[5]	Lamb H 1975 Hydrodynamics (6th Edn.) (New York: Cambridge University Press) p. 250
[6]	Warren B A and Wunsch C 1981 Evolution of Physical Oceanography (Cambridge: MIT Press) p. 292
[7]	Le Méhauté B 1976 An Introduction to Hydrodynamics and Water Waves (New York: Springer) p. 9
[8]	Schwámmle V and Herrmann H J 2003 Nature 426 619
[9]	Dumbser M and Facchini M 2016 Appl. Math. Comput. 272 336
[10]	Berloff N G 2005 Phys. Rev. Lett. 94 120401
[11]	Sokolow A, Bittle E G and Sen S 2007 Europhys. Lett. 77 24002
[12]	Goodman R H 2008 Chaos 18 270
[13]	Teng M H 1997 Journal of Waterway Port Coastal & Ocean Engineering 123 138
[14]	Zou L, Zong Z, Wang Z and Tian S 2010 Phys. Lett. A 374 3451
[15]	Boussinesq J 1872 Journal of Mathematics Pure and Applied 17 112
[16]	Remoissenet M 1996 Waves Called Solitons: Concepts and Experiments (3rd Edn.) (Berline: Springer) p. 60
[17]	Shen S F 2006 Acta Phys. Sin. 55 1016 (in Chinese)
[18]	Wang Y U and Chen Y 2013 Chin. Phys. B 22 241
[19]	Jian M J and Rong Y J 2013 Acta Phys. Sin. 62 130201 (in Chinese)
[20]	Li D L and Zhao J X 2009 Chin. Phys. Lett. 26 54701
[21]	Wei G, Kirby J T, Grilli S T and Subramanya R 1995 J. Fluid Mech. 294 71
[22]	Madsen P A and Schaffer H A 1998 Philos. T. R. Soc. A 356 3123
[23]	Krishnan E V, Kumar S and Biswas A 2012 Nonlinear Dynam. 70 1213
[24]	Wang J and Zho Z P 2011 Port & Waterway Engineering 11 (in Chinese)
[25]	Zhang B S, Lu D Q, Dai S Q and Chen Y L 1998 Advances in Mechanics 28 521
[26]	Dong J Z 2011 Methods for Analysing Nonlinear Waves in Shallow Water under Hamiltonian System (Ph.D. Dissertation) (Dalian: Dalian University of Technology) (in Chinese)
[27]	Luke J C 1967 J. Fluid Mech. 27 395
[28]	Whitham G B 1967 Proceedings of The Royal Society of London Series A-Mathematical and Physical Sciences 299 6
[29]	Zakharov V E 1968 Journal of Applied Mechanics & Technical Physics 9 190
[30]	Lu D Q, Dai S Q and Zhang B S 1999 Applied Mathematics and Mechanics 20 331
[31]	Miles J W 1977 J. Fluid Mech. 83 153
[32]	Liu P, Li Z and Luo R 2012 Appl. Math. Comput. 219 2149
[33]	Liu P and Lou S Y 2008 Chinese Phys. Lett. 25 3311
[34]	Zhong W and Yao Z 2006 Journal of Dalian University of Technology 46 151 (in Chinese)
[35]	Yao Z and Zhong W 2016 Computer Aided Engineering 25 21 (in Chinese)
[36]	Liu P and Fu P K 2011 Chin. Phys. B 20 90203

Fully nonlinear (2+1)-dimensional displacement shallow water wave equation

Fully nonlinear (2+1)-dimensional displacement shallow water wave equation

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