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According to the general shallow water equations, the nondimensional nonlinear dynamic equations are obtained that can describe large-scale barotropic atmosphere. Using multi-scale method, a nonlinear controlling equation for disturbed height (or pressure) field is deduced. Applying elliptic equation to construct the solutions of the controlling equation, the analytic solutions of the disturbed height field and velocity are obtained, which include the multiply periodic waves and shock (explosive) waves. The solutions of the disturbed height field present periodic waves with different periodicity and wavelength along longitude and latitude, which are modulated by the solitary waves of latitude. The velocity solutions display that in the large-scale air flows exist periodic distribution phenomena of cyclone and anticyclone.
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Keywords:
- shallow water equations /
- large-scale barotropic atmosphere /
- analytic solution /
- nonlinear wave
[1] Vincent H C 2010 J. Hydro-enviro. Res. 3 173
[2] Cullen M J P 2008 Phys. D 237 1461
[3] Agnes H 2008 Comput. Math. Appl. 55 2295
[4] Callaghan T G, Forbes L K 2006 J. Comput. Phys. 217 845
[5] Läuter M, Dörthe H, Natalja R 2007 J. Comput. Phys. 223 609
[6] Frank J, Reich S 2002 J. Comput. Phys. 180 407
[7] Boyd J P 1998 Dyna. Atmosph. Oceans 28 69
[8] Wu J, Lee T S, Shu B 2001 Comput. Methods Appl. Mech. Engrg. 190 2099
[9] Mo J Q, Lin W T 2007 Acta Phys. Sin. 56 3662 (in Chinese) [莫嘉琪, 林万涛 2007 物理学报 56 3662]
[10] Lou S Y, Jia M, Tang X Y, Huang F 2007 Phys. Rev. E 75 056318
[11] Lou S Y, Jia Man, Huang F, Tang X Y 2007 Internat. J. Theor. Phys. 46 C 2007
[12] Yang J R, Mao J J 2009 Acta Phys. Sin. 58 3611 (in Chinese) [杨建荣, 毛杰健 2009 物理学报 58 3611]
[13] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 物理学报 56 5049]
[14] Tang X Y, Shukla P K 2008 Commun. Theor. Phys. (Beijing, China) 49 229
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[1] Vincent H C 2010 J. Hydro-enviro. Res. 3 173
[2] Cullen M J P 2008 Phys. D 237 1461
[3] Agnes H 2008 Comput. Math. Appl. 55 2295
[4] Callaghan T G, Forbes L K 2006 J. Comput. Phys. 217 845
[5] Läuter M, Dörthe H, Natalja R 2007 J. Comput. Phys. 223 609
[6] Frank J, Reich S 2002 J. Comput. Phys. 180 407
[7] Boyd J P 1998 Dyna. Atmosph. Oceans 28 69
[8] Wu J, Lee T S, Shu B 2001 Comput. Methods Appl. Mech. Engrg. 190 2099
[9] Mo J Q, Lin W T 2007 Acta Phys. Sin. 56 3662 (in Chinese) [莫嘉琪, 林万涛 2007 物理学报 56 3662]
[10] Lou S Y, Jia M, Tang X Y, Huang F 2007 Phys. Rev. E 75 056318
[11] Lou S Y, Jia Man, Huang F, Tang X Y 2007 Internat. J. Theor. Phys. 46 C 2007
[12] Yang J R, Mao J J 2009 Acta Phys. Sin. 58 3611 (in Chinese) [杨建荣, 毛杰健 2009 物理学报 58 3611]
[13] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 物理学报 56 5049]
[14] Tang X Y, Shukla P K 2008 Commun. Theor. Phys. (Beijing, China) 49 229
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