缓变下垫面和耗散作用的非线性Rossby波

宋健; 杨联贵; 刘全生

doi:10.7498/aps.63.060401

摘要

从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在缓变下垫面和耗散共同作用的Rossby代数孤立波方程，得到Rossby波振幅满足带有缓变下垫面的非齐次Benjamin-Davis-Ono-Burgers（BDO-Burgers）方程的结论. 指出地形效应和耗散是诱导非线性Rossby 波产生的重要因素，说明了在缓变下垫面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BDO-Burgers方程，给出在切变基本气流下缓变下垫面和正压流体中Rossby波的相互作用.

关键词:

Abstract

An inhomogeneous Benjamin-Davis-Ono-Burgers (BDO-Burgers) equation including underlying surface, slowly changing underlying surface and turbulent dissipation is derived in terms of quasi-geostrophic vorticity equation by employing the singular perturbation method. An inhomogeneous BDO-Burgers equation describing the evolution of the amplitude of solitary Rossby waves is investigated.

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（批准号：11362012）、国家自然科学基金青年科学基金（批准号：11202092，11301259）、中国科学院海洋环流与波动重点实验室开放研究基金（批准号：KLOCAW1108）、内蒙古自然科学基金（批准号：2011MS0112，2012MS0107，2013MS0105）和内蒙古自治区研究生教育创新计划研究生科研创新资助项目（批准号：1402020201-01007，1402020201-01006）资助的课题.

Authors and contacts

1.
School 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 of China (Grant No. 11362012), the National Natural Science Foundation for Young Scholars of China (Grant Nos. 11202092, 11301259), Open Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences (Grant No. KLOCAW1108) the Natural Foundation Inner Mongolia, China (Grant Nos. 2011MS0112, 2012MS0107, 2013MS0105) and the Inner Mongolia Autonomous Region Graduate Education Innovation Research Plan Research and Innovation Project, China (Grant Nos. 1402020201-01007, 1402020201-01006).

参考文献

[1]	Zhang Z Q, Sun C Q 1999 Chin. Sci. Bull. 44 464 (in Chinese) [张志强, 孙成权 1999 科学通报 44 464]
[2]	Sha W Y, Shao X M, Huang M 2002 Sci. Sin. Terrae 32 317 (in Chinese) [沙万英, 邵雪梅, 黄玫 2002 中国科学 (D 辑) 32 317]
[3]	Liu S Y, Ding Y J, Li J, Shangguan D H, Zhang Y 2006 Quaternary Sciences 26 762 (in Chinese) [刘时银, 丁永建, 李晶, 上官冬辉, 张勇 2006 第四纪研究 26 762]
[4]	Zhou G S, Wang Y H 1999 J. Natural Resources 14 318 (in Chinese) [周广胜, 王玉辉 1999 自然资源学报 14 318]
[5]	Wang C H, Dong W J, Wei Z G 2001 Acta Geog. Sin. 56 523 (in Chinese) [王澄海, 董文杰, 韦志刚 2001 地理学报 56 523]
[6]	Yang G S, Shi Y F 1995 Acta Geog. Sin. 50 302 (in Chinese) [杨桂山, 施雅风 1995 地理学报 50 302]
[7]	Shi Y F 1996 J. Natural Disasters 5 106 (in Chinese) [施雅风 1996 自然灾害学报 5 106]
[8]	L X M, Wu S H, Yang Q Y 2003 Progress in Geography 22 260 (in Chinese) [吕新苗, 吴绍洪, 杨勤业 2003 地理科学进展 22 260]
[9]	Nezlin M V, Snezhkin E N 1993 Rossby Vortices, Spiral Structures, Solitons (Heidelberg: Springer-Verlag)
[10]	Maxworthy T, Redekopp L G 1976 Nature 260 509
[11]	Maxworthy T, Redekopp L G 1976 Icarus 29 261
[12]	Maxworthy T, Redekopp L G, Weidman P D 1978 Icarus 33 388
[13]	Long R R 1964 J. Atmos. Sci. 21 197
[14]	Benney D J 1966 J. Math. Phys. 45 52
[15]	Larsen L N 1965 J. Atmos. Sci. 22 222
[16]	Clarke A 1971 Geophys. Fluid Dyn. 2 343
[17]	Redekopp L G 1977 J. Fluid Mech. 82 725
[18]	Wadati M 1973 J. Phys. Soc. Japan 34 1289
[19]	Redekopp L G, Weidman P D 1978 J. Atmos. Sci. 35 790
[20]	Maslowe S A, Redekopp L G 1980 J. Fluid Mech. 101 321
[21]	Chraney J G, Straus D M 1980 J. Atmos. Sci. 37 1157
[22]	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]
[23]	Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[24]	Benjamin T B 1967 J. Fluid Mech. 29 559
[25]	Davis R E, Acrivos A 1967 J. Fluid Mech. 29 593
[26]	Ono H 1975 J. Phys. Soc. Japan 39 1082
[27]	Ono H 1982 J. Phys. Soc. Japan 50 2757
[28]	Meng L, L K L 2002 Chin. J. Comput. Phys. 19 159
[29]	Yu X, Zhao Q 2009 Chin. Phys. Lett. 26 039201
[30]	Yang J, Zhang Q 2010 Acta Phys. Sin. 59 750 (in Chinese) [杨洁, 赵强 2010 59 750]
[31]	Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese) [汪萍, 戴新刚 2005 54 4961]
[32]	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]
[33]	Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin. Phys. 15 2202
[34]	Berkir A, Gner Ö 2013 Chin. Phys. B 22 110202
[35]	Falaye B J, Oyewumi K J, Abbas M 2013 Chin. Phys. B 22 110301
[36]	Yin J L, Ding S Y 2013 Chin. Phys. B 22 060205
[37]	Liu Y Q, Cheng R J, Ge H X 2013 Chin. Phys. B 22 10024
[38]	Huang L Y, Jiao Y D, Liang D M 2013 Chin. Phys. B 22 070201
[39]	Pedlosky J 1981 J. Atmos. Sci. 38 2626
[40]	Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[41]	Warn T, Brasnett B 1983 J. Atmos. Sci. 40 28
[42]	Da C J, Chou J F 2008 Acta. Phys. Sin. 57 2595 (in Chinese) [达朝究, 丑纪范 2008 57 2595]
[43]	Da C J, Feng A X, Gong Z Q, Song J 2013 Acta Phys. Sin. 62 039202 (in Chinese) [达朝究, 冯爱霞, 龚志强, 宋健 2013 62 039202]
[44]	Yang H W, Yin B S, Yang D Z, Xu Z H 2011 Chin. Phys. B 20 12021
[45]	Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.) pp22–26
[46]	Zhu B Z, Jin F F, Liu Z Y 1991 An Introduction to The Nonlinear Dynamics of The Atmosphere and Ocean (Beijing: China Ocean Press) pp75–96 (in Chinese) [朱抱真, 金飞飞, 刘征宇 1991 大气和海洋的非线性动力学概论 (北京: 海洋出版社) 第75–96页]
[47]	Luo D H 1999 Envelope Rossby Solitons in the Large-Scale Atmosphere and Blocking Circulations (Beijing: China Meteorological Press) (in Chinese) [罗德海 2000 大气中大尺度包洛孤立子理论与阻塞环流 (北京: 气象出版社)]
[48]	Luo D H 2000 Nonlinear Dynamics of Blockings (Beijing: China Meteorological Press) (in Chinese) [罗德海 2000 阻塞非线性动力学(北京: 气象出版社)]
[49]	Luo D H 2005 J. Atmos. Sci. 62 5

施引文献

[1]	Zhang Z Q, Sun C Q 1999 Chin. Sci. Bull. 44 464 (in Chinese) [张志强, 孙成权 1999 科学通报 44 464]
[2]	Sha W Y, Shao X M, Huang M 2002 Sci. Sin. Terrae 32 317 (in Chinese) [沙万英, 邵雪梅, 黄玫 2002 中国科学 (D 辑) 32 317]
[3]	Liu S Y, Ding Y J, Li J, Shangguan D H, Zhang Y 2006 Quaternary Sciences 26 762 (in Chinese) [刘时银, 丁永建, 李晶, 上官冬辉, 张勇 2006 第四纪研究 26 762]
[4]	Zhou G S, Wang Y H 1999 J. Natural Resources 14 318 (in Chinese) [周广胜, 王玉辉 1999 自然资源学报 14 318]
[5]	Wang C H, Dong W J, Wei Z G 2001 Acta Geog. Sin. 56 523 (in Chinese) [王澄海, 董文杰, 韦志刚 2001 地理学报 56 523]
[6]	Yang G S, Shi Y F 1995 Acta Geog. Sin. 50 302 (in Chinese) [杨桂山, 施雅风 1995 地理学报 50 302]
[7]	Shi Y F 1996 J. Natural Disasters 5 106 (in Chinese) [施雅风 1996 自然灾害学报 5 106]
[8]	L X M, Wu S H, Yang Q Y 2003 Progress in Geography 22 260 (in Chinese) [吕新苗, 吴绍洪, 杨勤业 2003 地理科学进展 22 260]
[9]	Nezlin M V, Snezhkin E N 1993 Rossby Vortices, Spiral Structures, Solitons (Heidelberg: Springer-Verlag)
[10]	Maxworthy T, Redekopp L G 1976 Nature 260 509
[11]	Maxworthy T, Redekopp L G 1976 Icarus 29 261
[12]	Maxworthy T, Redekopp L G, Weidman P D 1978 Icarus 33 388
[13]	Long R R 1964 J. Atmos. Sci. 21 197
[14]	Benney D J 1966 J. Math. Phys. 45 52
[15]	Larsen L N 1965 J. Atmos. Sci. 22 222
[16]	Clarke A 1971 Geophys. Fluid Dyn. 2 343
[17]	Redekopp L G 1977 J. Fluid Mech. 82 725
[18]	Wadati M 1973 J. Phys. Soc. Japan 34 1289
[19]	Redekopp L G, Weidman P D 1978 J. Atmos. Sci. 35 790
[20]	Maslowe S A, Redekopp L G 1980 J. Fluid Mech. 101 321
[21]	Chraney J G, Straus D M 1980 J. Atmos. Sci. 37 1157
[22]	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]
[23]	Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[24]	Benjamin T B 1967 J. Fluid Mech. 29 559
[25]	Davis R E, Acrivos A 1967 J. Fluid Mech. 29 593
[26]	Ono H 1975 J. Phys. Soc. Japan 39 1082
[27]	Ono H 1982 J. Phys. Soc. Japan 50 2757
[28]	Meng L, L K L 2002 Chin. J. Comput. Phys. 19 159
[29]	Yu X, Zhao Q 2009 Chin. Phys. Lett. 26 039201
[30]	Yang J, Zhang Q 2010 Acta Phys. Sin. 59 750 (in Chinese) [杨洁, 赵强 2010 59 750]
[31]	Wang P, Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese) [汪萍, 戴新刚 2005 54 4961]
[32]	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]
[33]	Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin. Phys. 15 2202
[34]	Berkir A, Gner Ö 2013 Chin. Phys. B 22 110202
[35]	Falaye B J, Oyewumi K J, Abbas M 2013 Chin. Phys. B 22 110301
[36]	Yin J L, Ding S Y 2013 Chin. Phys. B 22 060205
[37]	Liu Y Q, Cheng R J, Ge H X 2013 Chin. Phys. B 22 10024
[38]	Huang L Y, Jiao Y D, Liang D M 2013 Chin. Phys. B 22 070201
[39]	Pedlosky J 1981 J. Atmos. Sci. 38 2626
[40]	Patione A, Warn T 1982 J. Atmos. Sci. 39 1018
[41]	Warn T, Brasnett B 1983 J. Atmos. Sci. 40 28
[42]	Da C J, Chou J F 2008 Acta. Phys. Sin. 57 2595 (in Chinese) [达朝究, 丑纪范 2008 57 2595]
[43]	Da C J, Feng A X, Gong Z Q, Song J 2013 Acta Phys. Sin. 62 039202 (in Chinese) [达朝究, 冯爱霞, 龚志强, 宋健 2013 62 039202]
[44]	Yang H W, Yin B S, Yang D Z, Xu Z H 2011 Chin. Phys. B 20 12021
[45]	Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.) pp22–26
[46]	Zhu B Z, Jin F F, Liu Z Y 1991 An Introduction to The Nonlinear Dynamics of The Atmosphere and Ocean (Beijing: China Ocean Press) pp75–96 (in Chinese) [朱抱真, 金飞飞, 刘征宇 1991 大气和海洋的非线性动力学概论 (北京: 海洋出版社) 第75–96页]
[47]	Luo D H 1999 Envelope Rossby Solitons in the Large-Scale Atmosphere and Blocking Circulations (Beijing: China Meteorological Press) (in Chinese) [罗德海 2000 大气中大尺度包洛孤立子理论与阻塞环流 (北京: 气象出版社)]
[48]	Luo D H 2000 Nonlinear Dynamics of Blockings (Beijing: China Meteorological Press) (in Chinese) [罗德海 2000 阻塞非线性动力学(北京: 气象出版社)]
[49]	Luo D H 2005 J. Atmos. Sci. 62 5

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