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大尺度正压大气环流的波动特征对理解气候变化具有重要的意义，而非线性浅水波方程组是描述大尺度正压大气环流的原始控制方程. 本文对线性方程的复变函数解，通过二次适当的移植，求得浅水波方程组的发展方程的扰动位势 的实变函数解，该实变函数解析解由基流项和波动项两部分组成. 其中基流由波数、波速、β效应、变形半径和时间的任意函数共同决定；波动项与β效应有关. 分析表明，在大尺度正压大气环流中扰动位势存在曲面的周期波和孤波的现象，周期波与孤波相互调制而呈现不稳定性；当多个周期孤波同时出现时，则彼此独立传播；扰动位势波动项中的时间任意函数对曲面周期孤波的波幅有调制作用，可控制波的产生、发展和消失. 所得结果对研究大气波动现象和气候变化具有一定的理论参考价值.The wave motion characteristic of large-scale barotropic atmospheric circulation, which can be described by the original nonlinear shallow water equations, is important for comprehending the climatic change. Employing the complex solution of linear equation, and transplanting it twice, the new analytic solution of disturbed height field of the nonlinear evolution equation is obtained which is constructed by the basic flow term and fluctuation term. The basic flow is codetermined by the wave number, wave velocity, β effect, radius of deformation and arbitrary function of time. The fluctuation term is related to β effect, and displays that in the disturbed height field there exist the periodic wave and solitary wave of curved face, which modulate each other and present instability; several periodic-solitary waves can propagate independently when they appear simultaneously; the arbitrary function of time in the fluctuation term has a modulation effect on the amplitude of periodic-solitary wave, and can control the occurrence, development and vanishing of wave. The results have a certain theoretical reference value for studying the atmospheric fluctuation phenomena and climatic change.
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Keywords:
- large-scale barotropic atmosphere /
- nonlinear shallow water equations /
- wave of curved face /
- period-solitary wave
[1] Vincent H C 2010 J. Hydro-Enviro. Res. 3 173
[2] Callaghan T G, Forbes L K 2006 J. Comput. Phys. 217 845
[3] Phillips N A 1959 Mon. Weather Rev. 87 333
[4] Williamson D L, Drake J B, Hack J J, Jakob R, Swarztrauber P N 1992 J. Comput. Phys. 102 211
[5] Thuburn J, Li Y 2000 Tellus A 52 181
[6] Baines P G 1976 J. Fluid Mech. 73 193
[7] Mao J J, Yang J R 2013 Acta Phys. Sin. 62 130205(in Chinese)[毛杰健, 杨建荣 2013 62 130205]
[8] Pinilla C, Chu V H 2008 J. Coastal Res. 52 207
[9] He J R, Li H M 2011 Phys. Rev. E 83 066607
[10] Yang J R, Mao J J 2008 Commun. Theor. Phys. 49 22
[11] Yang J R, Mao J J 2008 Chin. Phys. B 17 4337
[12] Yang J R, Mao J J, Tang X Y 2013 Chin. Phys. B 22 115203
[13] Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999(in Chinese)[毛杰健, 杨建荣 2005 54 4999]
[14] Mao J J, Yang J R 2006 Chin. Phys. 15 2804
[15] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049(in Chinese)[毛杰健, 杨建荣 2007 56 5049]
[16] Lou S Y, Jia M, Huang F, Tang X Y 2007 J. Theor. Phys. 46 2082
[17] Lou S Y, Jia M, Tang X Y, Huang F 2007 Phys. Rev. E 75 056318
[18] Tang X Y, Shukla P K 2007 J. Phys. A: Math. Theor. 40 5921
[19] Tang X Y, Shukla P K 2007 Phys. Scr. 76 665
[20] Lou S Y, Tang X Y, Lin J 2000 J. Math. Phys. 41 8286
[21] Lou S Y, Li Y Q, Tang X Y 2013 Chin. Phys. Lett. 30 080202
[22] Luo D H 2005 J. Atmos. Sci. 62 3202
[23] Huang F, Tang X Y, Lou S Y, Lu C H 2007 J. Atmos. Sci. 64 52
[24] Chow K W 2002 Wave Motion 35 71
[25] Ma W X 2002 Phys. Lett. A 301 35
[26] Luo D H 1996 Wave Motion 24 315
[27] Steinbock O, Zykov V S, Muller S C 1993 Phys. Rev. E 48 3295
[28] Gao X, Zhang H, Zykov V, Bodenschatz E 2014 New J. Phys. 16 033012
[29] Barboza R, Bortolozzo U, Assanto G, Vidal-Henriquez E, Clerc M G, Residori S 2012 Phys. Rev. Lett. 109 143901
[30] Uchida S 1956 J. Aeronaut. Sci. 23 830
[31] Mitria F G, Fellahb Z E A 2011 Ultrasonics 51 523
[32] Zhao X F, Huang S X 2013 Acta Phys. Sin. 62 099204(in Chinese)[赵小峰, 黄思训 2013 62 099204]
[33] Karimian A, Yardim C, Gerstoft P, Hodgkiss W S, Barrios A E 2012 IEEE Trans. 60 4408
[34] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computa Tional Ocean Acoustics (2nd Ed.) (New Yark: Springer-Verlag)
-
[1] Vincent H C 2010 J. Hydro-Enviro. Res. 3 173
[2] Callaghan T G, Forbes L K 2006 J. Comput. Phys. 217 845
[3] Phillips N A 1959 Mon. Weather Rev. 87 333
[4] Williamson D L, Drake J B, Hack J J, Jakob R, Swarztrauber P N 1992 J. Comput. Phys. 102 211
[5] Thuburn J, Li Y 2000 Tellus A 52 181
[6] Baines P G 1976 J. Fluid Mech. 73 193
[7] Mao J J, Yang J R 2013 Acta Phys. Sin. 62 130205(in Chinese)[毛杰健, 杨建荣 2013 62 130205]
[8] Pinilla C, Chu V H 2008 J. Coastal Res. 52 207
[9] He J R, Li H M 2011 Phys. Rev. E 83 066607
[10] Yang J R, Mao J J 2008 Commun. Theor. Phys. 49 22
[11] Yang J R, Mao J J 2008 Chin. Phys. B 17 4337
[12] Yang J R, Mao J J, Tang X Y 2013 Chin. Phys. B 22 115203
[13] Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999(in Chinese)[毛杰健, 杨建荣 2005 54 4999]
[14] Mao J J, Yang J R 2006 Chin. Phys. 15 2804
[15] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049(in Chinese)[毛杰健, 杨建荣 2007 56 5049]
[16] Lou S Y, Jia M, Huang F, Tang X Y 2007 J. Theor. Phys. 46 2082
[17] Lou S Y, Jia M, Tang X Y, Huang F 2007 Phys. Rev. E 75 056318
[18] Tang X Y, Shukla P K 2007 J. Phys. A: Math. Theor. 40 5921
[19] Tang X Y, Shukla P K 2007 Phys. Scr. 76 665
[20] Lou S Y, Tang X Y, Lin J 2000 J. Math. Phys. 41 8286
[21] Lou S Y, Li Y Q, Tang X Y 2013 Chin. Phys. Lett. 30 080202
[22] Luo D H 2005 J. Atmos. Sci. 62 3202
[23] Huang F, Tang X Y, Lou S Y, Lu C H 2007 J. Atmos. Sci. 64 52
[24] Chow K W 2002 Wave Motion 35 71
[25] Ma W X 2002 Phys. Lett. A 301 35
[26] Luo D H 1996 Wave Motion 24 315
[27] Steinbock O, Zykov V S, Muller S C 1993 Phys. Rev. E 48 3295
[28] Gao X, Zhang H, Zykov V, Bodenschatz E 2014 New J. Phys. 16 033012
[29] Barboza R, Bortolozzo U, Assanto G, Vidal-Henriquez E, Clerc M G, Residori S 2012 Phys. Rev. Lett. 109 143901
[30] Uchida S 1956 J. Aeronaut. Sci. 23 830
[31] Mitria F G, Fellahb Z E A 2011 Ultrasonics 51 523
[32] Zhao X F, Huang S X 2013 Acta Phys. Sin. 62 099204(in Chinese)[赵小峰, 黄思训 2013 62 099204]
[33] Karimian A, Yardim C, Gerstoft P, Hodgkiss W S, Barrios A E 2012 IEEE Trans. 60 4408
[34] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computa Tional Ocean Acoustics (2nd Ed.) (New Yark: Springer-Verlag)
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