切变纬向流中β效应与缓变地形Rossby波

宋健; 刘全生; 杨联贵

doi:10.7498/aps.61.210510

摘要

正压流体中, 从有外源的准地转位涡方程出发, 采用摄动方法和时空伸长变换推导了具有β效应、缓变地形和外源的Rossby孤立波方程, 得到Rossby波振幅满足带有缓变地形与外源强迫的非齐次 mKdV-Burgers方程的结论. 通过分析孤立Rossby波振幅的演变,指出了β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素; 说明了在缓变地形强迫效应和非线性作用相平衡的假定下, Rossby孤立波振幅的演变满足非齐次mKdV-Burgers方程; 给出在切变基本气流下缓变地形和正压流体中Rossby波的相互作用关系.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
内蒙古大学数学科学学院, 呼和浩特 010021;

2.
内蒙古工业大学理学院, 呼和浩特 010051

基金项目: 国家自然科学基金青年科学基金(批准号: 11202092)和内蒙古自然科学基金(批准号: 2011MS0112, 2012MS0107)资助的课题.

Authors and contacts

1.
College of Mathematical Science, Inner Mongolia University, Hohhot 010021, China;

2.
College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China

Funds: Project supported by the National Natural Science Foundation for Young Scholars of China (Grant No. 11202092) and the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2011MS0112, 2012MS0107).

参考文献

[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 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 59 44]
[19]	Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese) [汪萍, 戴新刚 2005 54 4961]
[20]	Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆 1998 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 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 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 57 2595]
[27]	Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.) pp256-266

施引文献

[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 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 59 44]
[19]	Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese) [汪萍, 戴新刚 2005 54 4961]
[20]	Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) [范恩贵, 张鸿庆 1998 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 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 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 57 2595]
[27]	Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.) pp256-266

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