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In barotropic fluids, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous mKdV-Burgers equation including slowly changing topography and an external source is derived by employing the perturbation method and stretching transforms of time and space. With the inspection of the evolution of the amplitude of Rossby waves, it is found that beta effect, topography effect, slowly changing topography and an external source are all the important factors, and that the solitary Rossby wave is induced thought the basic stream function has a shear flow . On the assumption that the nonlinear and topographic effects are in balance, an inhomogeneous mKdV-Burgers equation is derived, the results show that the topography and Rossby wave interact in the barotropic flows. The inhomogeneous mKdV-Burgers equation describing the evolution of the amplitude of solitary Rossby wave as the change of Rossby parameter β(y) with latitude y, topographic forcing, slowly changing topography and the external source is obtained.
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Keywords:
- inhomogeneous mKdV-Burgers equation /
- β effect /
- slowly changing topography /
- an external source
[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. Phys. 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] 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 物理学报 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 S, Tan B K 1992 Appl. Math. Mech. 13 35 (in Chinese) [刘式适, 谭本馗 1992 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, Lü K L 2000 Chin. J. Compu. Phys. 17 259
[18] 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 物理学报 59 44]
[19] Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese) [汪萍, 戴新刚 2005 物理学报 54 4961]
[20] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆 1998 物理学报 47 353]
[21] Liu S D, Fu Z T, Liu S S, Zhao Q 2002 Acta Phys. Sin. 51 718 (in Chinese) [刘式达, 付遵涛, 刘式适, 赵强 2002 物理学报 51 718]
[22] Liu S S, 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 物理学报 51 1923]
[23] Zhang L H, Yan J, Chang F M 2003 Marine Geol. Lett. 19 14 (in Chinese) [庄丽华, 阎军, 常凤鸣 2003 海洋地质动态 19 14]
[24] Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[25] Warn T, Brasnett B 1982 J. Atmos. Sci. 40 28
[26] Da C J, Chou J F 2008 Acta Phys. Sin. 57 2595 (in Chinese) [达朝究, 丑纪范 2008 物理学报 57 2595]
[27] Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.) pp256-266
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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. Phys. 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] 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 物理学报 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 S, Tan B K 1992 Appl. Math. Mech. 13 35 (in Chinese) [刘式适, 谭本馗 1992 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, Lü K L 2000 Chin. J. Compu. Phys. 17 259
[18] 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 物理学报 59 44]
[19] Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese) [汪萍, 戴新刚 2005 物理学报 54 4961]
[20] Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆 1998 物理学报 47 353]
[21] Liu S D, Fu Z T, Liu S S, Zhao Q 2002 Acta Phys. Sin. 51 718 (in Chinese) [刘式达, 付遵涛, 刘式适, 赵强 2002 物理学报 51 718]
[22] Liu S S, 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 物理学报 51 1923]
[23] Zhang L H, Yan J, Chang F M 2003 Marine Geol. Lett. 19 14 (in Chinese) [庄丽华, 阎军, 常凤鸣 2003 海洋地质动态 19 14]
[24] Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[25] Warn T, Brasnett B 1982 J. Atmos. Sci. 40 28
[26] Da C J, Chou J F 2008 Acta Phys. Sin. 57 2595 (in Chinese) [达朝究, 丑纪范 2008 物理学报 57 2595]
[27] Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.) pp256-266
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