Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

doi:10.1088/1674-1056/22/5/050204

中国物理B ›› 2013, Vol. 22 ›› Issue (5): 50204-050204.doi: 10.1088/1674-1056/22/5/050204

Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

刘萍^a, 李子良^b

a College of Electron and Information Engineering, University of Electronic Scienceand Technology of China Zhongshan Institute, Zhongshan 528402, China;
b Physical Oceanography Laboratory, College of Physical and Environment Oceanography, Ocean University of China, Qingdao 266100, China

收稿日期:2012-08-25 修回日期:2012-11-15 出版日期:2013-04-01 发布日期:2013-04-01
基金资助:
Projet supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 10452840301004616 and S2011040000403), the National Natural Science Foundation of China (Grant No. 41176005), and the Science and Technology Project Foundation of Zhongshan, China (Grnat No. 20123A326).

Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

Liu Ping (刘萍)^a, Li Zi-Liang (李子良)^b

a College of Electron and Information Engineering, University of Electronic Scienceand Technology of China Zhongshan Institute, Zhongshan 528402, China;
b Physical Oceanography Laboratory, College of Physical and Environment Oceanography, Ocean University of China, Qingdao 266100, China

Received:2012-08-25 Revised:2012-11-15 Online:2013-04-01 Published:2013-04-01
Contact: Li Zi-Liang E-mail:liuping49@126.com
Supported by:
Projet supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 10452840301004616 and S2011040000403), the National Natural Science Foundation of China (Grant No. 41176005), and the Science and Technology Project Foundation of Zhongshan, China (Grnat No. 20123A326).

摘要/Abstract

摘要： The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe the atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.

关键词: (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations, atmospheric gravity waves, symmetries, exact solutions

Abstract: The symmetries and the exact solutions of the (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations, which describe the atmospheric gravity waves, are studied in this paper. The calculation on symmetry shows that the equations are invariant under the Galilean transformations, the scaling transformations, and the space-time translations. Three types of symmetry reduction equations and similar solutions for the (3+1)-dimensional INHB equations are proposed. Traveling and non-traveling wave solutions of the INHB equations are demonstrated. The evolutions of the wind velocities in latitudinal, longitudinal, and vertical directions with space-time are demonstrated. The periodicity and the atmosphere viscosity are displayed in the (3+1)-dimensional INHB system.

Key words: (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations, atmospheric gravity waves, symmetries, exact solutions

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Hj (Classical groups) 02.20.Sv (Lie algebras of Lie groups) 92.60.hh (Acoustic gravity waves, tides, and compressional waves)

刘萍, 李子良. Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations[J]. 中国物理B, 2013, 22(5): 50204-050204.

Liu Ping (刘萍), Li Zi-Liang (李子良). Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations[J]. Chin. Phys. B, 2013, 22(5): 50204-050204.

参考文献 11

[1]	Li Z L 2008 J. Phys. A: Math. Theor. 41 145206
[2]	Li Z L 2009 Chin. Phys. B 18 4074
[3]	Qing J R, Chen S M, Li D W, Liang B and Liu B W 2012 Chin. Phys. B 21 089401
[4]	Liu P, Li Z L and Lou S Y 2010 Applied Mathematics and Mechanics 31 1383
[5]	McWilliams J C 2006 Fundamentals of Geophysical Fluid Dynamics (London: Cambridge University Press)
[6]	Olver P 1986 Applications of Lie Group to Differential Equations (New York: Spring-Verlag)
[7]	Bluman G W and Kumei S 1989 Symmetries and Differential Equations (New York: Spring-Verlag)
[8]	Wang X X, Sun X T, Zhang M L, Han Y L and Jia L Q 2012 Chin. Phys. B 21 050201
[9]	Wang X Z, Fu H and Fu J L 2012 Chin. Phys. B 21 040201
[10]	Liu P and Fu P K 2011 Chin. Phys. B 20 090203
[11]	Liu P and Lou S Y 2009 Commun. Theor. Phys. 51 27

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Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

Exact solutions of (3+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq equations

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