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For the stratified fluids, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous modified Korteweg-de Vried (mKdV) equation including topographic forcing is derived by employing the perturbation method and stretching transforms of time and space. With inspection of the evolution of the amplitude of Rossby waves, it is found that Coridis effect, topography effect and Vaisala-Brunt frequency are the important factors, that induce the solitary Rossby wave, and it is induced even though the basic stream function has not a shear. Assuming that there is a balance between nonlinear and topographic effects, an inhomogeneous mKdV equation is derived, the results show that the topography and Rossby waves interact in the stratified flows. The inhomogeneous mKdV equation describing the evolution of the amplitude of solitary Rossby waves as a function of the change of Rossby parameter β(y) with latitude y, topographic forcing and the Vaisala-Brunt frequency is obtained.
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Keywords:
- inhomogeneous mKdV equation /
- β effect /
- topographic /
- Vaisala-Brunt frequency
[1] ［1］Long R 1964 J. Atmos. Sci. 21 197
[2] ［2］Benney D J 1966 J. Math. Phys. 45 52
[3] ［3］Larsen L N 1965 J. Atmos. Sci. 22 222
[4] ［4］Clarke A 1971 Geophys. Fluid Dyn. 2 343
[5] ［5］Redekopp L G 1977 J. Fluid Mech. 82 725
[6] ［6］Wadati M 1973 J. Phy. Soc. Japan 34 1289
[7] ［7］Redekopp L G, Weidman P D 1978 J. Atmos. Sci. 35 790
[8] ［8］Maslowe S A, Redekopp L G 1980 J. Fluid Mech. 101 321
[9] ［9］Chraney 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] ］Body J P 1980 J. Phys. Oceanogr. 10 1699
[12] ］Body 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] ］Lv K L, Jiang H S 1996 Acta. Meteor. Sin. 54 2597 (in Chinese)［吕克利、 蒋后硕 1996 气象学报 54 2597］
[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 2009 Pro. Geophy. (accepted)
[22] ］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］
[23] ］Wang P, Dai X G 2005 Acta. Phys. Sin. 54 4961 (in Chinese)［汪萍、 戴新刚 2005 54 4961］
[24] ］Fan E G, Zhang H Q 1998 Acta. Phys. Sin. 47 353 (in Chinese)［范恩贵、 张鸿庆 1998 47 353］
[25] ］Fan E G, Zhang H Q 2000 Acta. Phys. Sin. 49 1409 (in Chinese)［范恩贵、 张鸿庆 2000 49 1409 ］
[26] ］Mao J J, Yang J R 2005 Acta. Phys. Sin. 54 4999 (in Chinese)［毛杰健、 杨建荣 2005 54 4999］
[27] ］Zhu H P, Zheng C L 2006 Acta. Phys. Sin. 55 4999 (in Chinese) ［朱海平、 郑春龙 2006 55 4999］
[28] ］ Mo J Q, Chen X F, Zhang W J 2009 Acta. Phys. Sin. 58 7397 (in Chinese) ［莫嘉琪、陈贤峰、 张伟江 2009 58 7397］
[29] ］Mao J J, Yang J R 2007 Acta. Phys. Sin. 56 5049 (in Chinese)［毛杰健、 杨建荣 2007 56 5049］
[30] ］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］
[31] ］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］
[32] ］Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[33] ］Warn T, Brasnett B 1982 J. Atmos. Sci. 40 28
[34] ］Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory （Melbourne: Pitman Publishing Inc.）p256—266
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[1] ［1］Long R 1964 J. Atmos. Sci. 21 197
[2] ［2］Benney D J 1966 J. Math. Phys. 45 52
[3] ［3］Larsen L N 1965 J. Atmos. Sci. 22 222
[4] ［4］Clarke A 1971 Geophys. Fluid Dyn. 2 343
[5] ［5］Redekopp L G 1977 J. Fluid Mech. 82 725
[6] ［6］Wadati M 1973 J. Phy. Soc. Japan 34 1289
[7] ［7］Redekopp L G, Weidman P D 1978 J. Atmos. Sci. 35 790
[8] ［8］Maslowe S A, Redekopp L G 1980 J. Fluid Mech. 101 321
[9] ［9］Chraney 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] ］Body J P 1980 J. Phys. Oceanogr. 10 1699
[12] ］Body 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] ］Lv K L, Jiang H S 1996 Acta. Meteor. Sin. 54 2597 (in Chinese)［吕克利、 蒋后硕 1996 气象学报 54 2597］
[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 2009 Pro. Geophy. (accepted)
[22] ］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］
[23] ］Wang P, Dai X G 2005 Acta. Phys. Sin. 54 4961 (in Chinese)［汪萍、 戴新刚 2005 54 4961］
[24] ］Fan E G, Zhang H Q 1998 Acta. Phys. Sin. 47 353 (in Chinese)［范恩贵、 张鸿庆 1998 47 353］
[25] ］Fan E G, Zhang H Q 2000 Acta. Phys. Sin. 49 1409 (in Chinese)［范恩贵、 张鸿庆 2000 49 1409 ］
[26] ］Mao J J, Yang J R 2005 Acta. Phys. Sin. 54 4999 (in Chinese)［毛杰健、 杨建荣 2005 54 4999］
[27] ］Zhu H P, Zheng C L 2006 Acta. Phys. Sin. 55 4999 (in Chinese) ［朱海平、 郑春龙 2006 55 4999］
[28] ］ Mo J Q, Chen X F, Zhang W J 2009 Acta. Phys. Sin. 58 7397 (in Chinese) ［莫嘉琪、陈贤峰、 张伟江 2009 58 7397］
[29] ］Mao J J, Yang J R 2007 Acta. Phys. Sin. 56 5049 (in Chinese)［毛杰健、 杨建荣 2007 56 5049］
[30] ］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］
[31] ］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］
[32] ］Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[33] ］Warn T, Brasnett B 1982 J. Atmos. Sci. 40 28
[34] ］Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory （Melbourne: Pitman Publishing Inc.）p256—266
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