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For the barotropic fluid, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous Boussinesq equation including topographic forcing and an external source is derived by employing the perturbation method and stretching transform of time and space. Through inspection of the evolution of the amplitude of the Rossby wave, it is found that Coridis effect, topography effect and an external source are the key inducing factors of the solitary Rossby wave if the basic stream function has a shear flow. Assuming that there is a balance between nonlinear and topography effects, an inhomogeneous Boussinesq equation is derived. The results show that the topography and the Rossby wave interact in the barotropic flow. The inhomogeneous Boussinesq equation describing the evolution of the amplitude of solitary Rossby waves with the change of Rossby parameter β(y) with latitude β, topographic forcing and the external source is obtained.
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Keywords:
- inhomogeneous Boussinesq equation /
- β effect /
- topography /
- an external source
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[2] Benney D J 1966 J.Math. Phys. 45 52
[3] Larsen L N 1965 J.Atmos. Sci. 22 222
[4] Clarke A 1971 Geophys. Fluid Dyn. 2 343
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[10] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181(in Chinese)[封国林、董文杰、贾晓静、曹鸿兴 2002 51 1181]
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[12] Boyd J P 1983 J.Phys. Oceanogr. 13 428
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[14] Luo D H 1991 Acta Meteor. Sin. 5 587
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[19] Song J, Yang L G, Da C J, Zhang H Q 2009 Atmos. Ocea. Sci. Letters 2 18
[20] Song J, Yang L G 2009 Chin. Phys. B 18 2873
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[22] Song J, Yang L G 2010 Acta Phys. Sin. 59 3309 (in Chinese)[宋 健、杨联贵 2010 59 3309]
[23] Zhang L, Zhang L F, Wu H Y, Li G 2010 Acta Phys. Sin. 59 44 (in Chinese)[张 亮、张立凤、吴海燕、李 刚2010 59 44]
[24] Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese)[汪 萍、戴新刚 2005 54 4961]
[25] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353(in Chinese)[范恩贵、张鸿庆 1998 47 353]
[26] Fan E G, Zhang H Q 2000 Acta Phys. Sin. 49 1409 (in Chinese)[范恩贵、张鸿庆 2000 49 1409 ]
[27] Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[28] Zhu H P, Zheng C L 2006 Acta Phys. Sin. 55 4999(in Chinese)[朱海平、郑春龙 2006 55 4999]
[29] Mo J Q, Zhang W J, Chen X F 2009 Acta Phys. Sin. 58 7397(in Chinese)[莫嘉琪、张伟江、陈贤峰 2009 58 7397]
[30] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049(in Chinese)[毛杰健、杨建荣 2007 56 5049]
[31] Liu S D, Fu Z T, Liu S K, Zhao Q 2002 Acta Phys. Sin. 51 718(in Chinese)[刘式达、付遵涛、刘式适、赵 强 2002 51 718]
[32] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923(in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 51 1923]
[33] Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[34] Warn T, Brasnett B 1982 J. Atmos. Sci. 40 28
[35] Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.)pp256—266
[36] Kou H L 1949 J. Meteor. 6 105
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[1] Long R 1964 J.Atmos. Sci. 21 197
[2] Benney D J 1966 J.Math. Phys. 45 52
[3] Larsen L N 1965 J.Atmos. Sci. 22 222
[4] Clarke A 1971 Geophys. Fluid Dyn. 2 343
[5] Redekopp L G 1977 J. Fluid Mech. 82 725
[6] Wadati M 1973 J.Phy. Soc. Japan 34 1289
[7] Redekopp L G, Weidman P D 1978 J.Atmos. Sci. 35 790
[8] Maslowe S A, Redekopp L G 1980 J. Fluid Mech. 101 321
[9] Charney J G, Straus D M 1980 J.Atmos. Sci. 37 1157
[10] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181(in Chinese)[封国林、董文杰、贾晓静、曹鸿兴 2002 51 1181]
[11] Boyd J P 1980 J. Phys. Oceanogr. 10 1699
[12] Boyd J P 1983 J.Phys. Oceanogr. 13 428
[13] Liu S K, Tan B K 1992 Appl.Math. Mech. 13 35(in Chinese)[刘式适、谭本馗 1922 应用数学和力学 13 35]
[14] Luo D H 1991 Acta Meteor. Sin. 5 587
[15] Luo D H 1995 J.Appl.Meteor. 6 220(in Chinese)[罗德海 1995 应用气象学报 6 220]
[16] Zhao Q 1997 J.Trop. Meteor. 13 140(in Chinese)[赵 强 1997 热带气象学报 13 140]
[17] Meng L, Lu K L 2000 Chin. J.Compu. Phys. 17 259
[18] Da C J, Chou J F 2008 Acta Phys. Sin. 57 2595(in Chinese)[达朝究、丑纪范 2008 57 2595]
[19] Song J, Yang L G, Da C J, Zhang H Q 2009 Atmos. Ocea. Sci. Letters 2 18
[20] Song J, Yang L G 2009 Chin. Phys. B 18 2873
[21] Song J, Yang L G 2010 Prog. Geophy. 25 543 (in Chinese)[宋 健、杨联贵 2010 地球物理学进展 25 543]
[22] Song J, Yang L G 2010 Acta Phys. Sin. 59 3309 (in Chinese)[宋 健、杨联贵 2010 59 3309]
[23] Zhang L, Zhang L F, Wu H Y, Li G 2010 Acta Phys. Sin. 59 44 (in Chinese)[张 亮、张立凤、吴海燕、李 刚2010 59 44]
[24] Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese)[汪 萍、戴新刚 2005 54 4961]
[25] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353(in Chinese)[范恩贵、张鸿庆 1998 47 353]
[26] Fan E G, Zhang H Q 2000 Acta Phys. Sin. 49 1409 (in Chinese)[范恩贵、张鸿庆 2000 49 1409 ]
[27] Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[28] Zhu H P, Zheng C L 2006 Acta Phys. Sin. 55 4999(in Chinese)[朱海平、郑春龙 2006 55 4999]
[29] Mo J Q, Zhang W J, Chen X F 2009 Acta Phys. Sin. 58 7397(in Chinese)[莫嘉琪、张伟江、陈贤峰 2009 58 7397]
[30] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049(in Chinese)[毛杰健、杨建荣 2007 56 5049]
[31] Liu S D, Fu Z T, Liu S K, Zhao Q 2002 Acta Phys. Sin. 51 718(in Chinese)[刘式达、付遵涛、刘式适、赵 强 2002 51 718]
[32] Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923(in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 51 1923]
[33] Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[34] Warn T, Brasnett B 1982 J. Atmos. Sci. 40 28
[35] Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.)pp256—266
[36] Kou H L 1949 J. Meteor. 6 105
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