切变基本纬向流中β效应的赤道Rossby孤立波包

宋健; 姜楠; 杨联贵

doi:10.7498/aps.60.024701

摘要

从描写赤道Rossby 波的正压大气位涡方程出发,采用多重尺度摄动方法推导出在切变基本纬向流中具有β效应的非线性赤道Rossby波包演变满足非线性Schrdinger方程,并得到单个包络孤立子波解,分析了基本切变流,β效应对非线性赤道Rossby波的影响.

关键词:

With a simple model of shallow-water on an equatorial beta plane, the nonlinear equatorial Rossby waves in a shear flow with beta effect are investigated by the asymptotic method of multiple scales. The nonlinear Schrdinger equation, satisfied by large amplitude Rossby envelope solitary waves in shear basic flow with beta effect, is derived. The effects of basic flow shear and beta effect on the nonlinear equatorial Rossby waves are also analyzed.

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; (3)天津大学机械学院,天津 300072

基金项目: 内蒙古自然科学重点基金(批准号: 2009ZD01)和内蒙古教育厅基金(批准号: NJZY08005)资助的课题.

Authors and contacts

(1)College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China; (2)School of Mathematical Science, Inner Mongolia University, Hohhot 010021, China; (3)School of Mechanical Engineering, Tianjin University, Tianjin 300072, China

参考文献

[1]	Matsuno T 1966 J.Meteor. Soc. Japan 44 25
[2]	Domaracki A, Loesch A Z 1977 J.Atmos. Sci. 34 486
[3]	Ripa P 1982 J.Phys.Oceanogr. 12 97
[4]	Body J P 1980a J.Phys. Oceanogr. 10 1
[5]	Body J P 1980b J.Phys. Oceanogr. 10 1699
[6]	Body J P 1984 Dyn.Atmos.Oceans 8 173
[7]	Body J P 1985 J.Phys.Oceanogr. 15 46
[8]	Body J P 1983 J.Phys.Oceanogr. 13 428
[9]	Zhao Q, Liu S K 2001 Chin. J. Atmos. Sci. 25 133(in Chinese)[赵强、刘式适 2001 大气科学 25 133]
[10]	Zhao Q, Fu Z T, Liu S K 2001 Adv. Sci. 18 418
[11]	Chraney J G, Straus D M 1980 J. Atmos. Sci. 37 1157
[12]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese)[封国林、戴新刚、王爱慧、丑纪范 2001 50 606]
[13]	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]
[14]	Feng G L, Gao X Q, Dong W J, Li J P 2008 Chaos Solitons and Fractals 37 487
[15]	Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[16]	Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese)[封国林、王启光、侯威、龚志强、支蓉 2009 58 2853]
[17]	Da C J, Chou J F 2008 Acta Phys. Sin. 57 2595 (in Chinese)[达朝究、丑纪范 2008 57 2595]
[18]	Song J, Yang L G, Da C J, Zhang H Q 2009 Atmos. Ocea. Sci. Lett. 2 18
[19]	Song J, Yang L G 2009 Chin. Phys. B 18 2873
[20]	Song J, Yang L G 2009 Proc. Geophys. 25 543 (in Chinese) [宋健、杨联贵 2010 地球物理学进展 25 543]
[21]	Song J, Yang L G 2010 Acta Phys. Sin. 59 383(in Chinese) [宋健、杨联贵 2010 59 383]
[22]	Song J, Lai J F 2010 Acta Phys. Sin 59 4756 (in Chinese) [宋健、赖俊峰 2010 59 4756] 〖23] Song J, Yang L G 2010 Plateau Meteor. 29 1137
[23]	Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、张鸿庆 1998 47 353]
[24]	Fan E G, Zhang H Q 2000 Acta Phys. Sin. 49 1409 (in Chinese)[范恩贵、张鸿庆 2000 49 1409 ]
[25]	Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999 (in Chinese)[毛杰健、杨建荣 2005 54 4999]
[26]	Zhu H P, Zheng C L 2006 Acta Phys. Sin. 55 4999 (in Chinese)[朱海平、郑春龙 2006 55 4999]
[27]	Chen X F, Mo J Q, Zhang W J 2009 Acta Phys. Sin. 58 7397 (in Chinese)[陈贤峰、莫嘉琪、张伟江 2009 58 7397]
[28]	Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese)[毛杰健、杨建荣 2007 56 5049]
[29]	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]
[30]	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 He W P, Feng G L, Dong W J, Li J P 2004 Acta Phys. Sin. 53 3258 (in Chinese)〖何文平、封国林、董文杰、李建平 2004 53 3258]
[31]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Pro. Geophys. 15 601
[32]	Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese)[周磊、龚志强、支蓉、封国林 2008 57 7380]
[33]	Charney J G 1963 J.Atmos. Sci. 20 607
[34]	Gill A E 1982 Atmosphere-Oean Dynamics (San Diego: Academic Press) pp444—447
[35]	Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.)pp256—266
[36]	Kuo H L 1949 J. Meteor. 6 105

施引文献

[1]	Matsuno T 1966 J.Meteor. Soc. Japan 44 25
[2]	Domaracki A, Loesch A Z 1977 J.Atmos. Sci. 34 486
[3]	Ripa P 1982 J.Phys.Oceanogr. 12 97
[4]	Body J P 1980a J.Phys. Oceanogr. 10 1
[5]	Body J P 1980b J.Phys. Oceanogr. 10 1699
[6]	Body J P 1984 Dyn.Atmos.Oceans 8 173
[7]	Body J P 1985 J.Phys.Oceanogr. 15 46
[8]	Body J P 1983 J.Phys.Oceanogr. 13 428
[9]	Zhao Q, Liu S K 2001 Chin. J. Atmos. Sci. 25 133(in Chinese)[赵强、刘式适 2001 大气科学 25 133]
[10]	Zhao Q, Fu Z T, Liu S K 2001 Adv. Sci. 18 418
[11]	Chraney J G, Straus D M 1980 J. Atmos. Sci. 37 1157
[12]	Feng G L, Dai X G, Wang A H, Chou J F 2001 Acta Phys. Sin. 50 606 (in Chinese)[封国林、戴新刚、王爱慧、丑纪范 2001 50 606]
[13]	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]
[14]	Feng G L, Gao X Q, Dong W J, Li J P 2008 Chaos Solitons and Fractals 37 487
[15]	Feng G L, Gong Z Q, Zhi R, Zhang D Q 2008 Chin. Phys. B 17 2745
[16]	Feng G L, Wang Q G, Hou W, Gong Z Q, Zhi R 2009 Acta Phys. Sin. 58 2853 (in Chinese)[封国林、王启光、侯威、龚志强、支蓉 2009 58 2853]
[17]	Da C J, Chou J F 2008 Acta Phys. Sin. 57 2595 (in Chinese)[达朝究、丑纪范 2008 57 2595]
[18]	Song J, Yang L G, Da C J, Zhang H Q 2009 Atmos. Ocea. Sci. Lett. 2 18
[19]	Song J, Yang L G 2009 Chin. Phys. B 18 2873
[20]	Song J, Yang L G 2009 Proc. Geophys. 25 543 (in Chinese) [宋健、杨联贵 2010 地球物理学进展 25 543]
[21]	Song J, Yang L G 2010 Acta Phys. Sin. 59 383(in Chinese) [宋健、杨联贵 2010 59 383]
[22]	Song J, Lai J F 2010 Acta Phys. Sin 59 4756 (in Chinese) [宋健、赖俊峰 2010 59 4756] 〖23] Song J, Yang L G 2010 Plateau Meteor. 29 1137
[23]	Fan E G, Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)[范恩贵、张鸿庆 1998 47 353]
[24]	Fan E G, Zhang H Q 2000 Acta Phys. Sin. 49 1409 (in Chinese)[范恩贵、张鸿庆 2000 49 1409 ]
[25]	Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999 (in Chinese)[毛杰健、杨建荣 2005 54 4999]
[26]	Zhu H P, Zheng C L 2006 Acta Phys. Sin. 55 4999 (in Chinese)[朱海平、郑春龙 2006 55 4999]
[27]	Chen X F, Mo J Q, Zhang W J 2009 Acta Phys. Sin. 58 7397 (in Chinese)[陈贤峰、莫嘉琪、张伟江 2009 58 7397]
[28]	Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese)[毛杰健、杨建荣 2007 56 5049]
[29]	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]
[30]	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 He W P, Feng G L, Dong W J, Li J P 2004 Acta Phys. Sin. 53 3258 (in Chinese)〖何文平、封国林、董文杰、李建平 2004 53 3258]
[31]	He W P, Feng G L, Wu Q, Wan S Q, Chou J F 2008 Non. Pro. Geophys. 15 601
[32]	Zhou L, Gong Z Q, Zhi R, Feng G L 2008 Acta Phys. Sin. 57 7380 (in Chinese)[周磊、龚志强、支蓉、封国林 2008 57 7380]
[33]	Charney J G 1963 J.Atmos. Sci. 20 607
[34]	Gill A E 1982 Atmosphere-Oean Dynamics (San Diego: Academic Press) pp444—447
[35]	Jeffrey A, Kawahara T 1982 Asymptotic Methods in Nonlinear Waves Theory (Melbourne: Pitman Publishing Inc.)pp256—266
[36]	Kuo H L 1949 J. Meteor. 6 105

[1]	潘楠, 黄平, 黄龙刚, 雷鸣, 刘文军. 非均匀光纤中暗孤子传输特性研究. , 2015, 64(9): 090504. doi: 10.7498/aps.64.090504
[2]	李少峰, 杨联贵, 宋健. 层结流体中在热外源和效应地形效应作用下的非线性Rossby孤立波和非齐次Schrdinger方程. , 2015, 64(19): 199201. doi: 10.7498/aps.64.199201
[3]	罗晓华. Schrödinger方程的一般解与超晶格多量子阱的电子跃迁. , 2014, 63(1): 017302. doi: 10.7498/aps.63.017302
[4]	孙庆华, 潘楠, 雷鸣, 刘文军. 色散渐变光纤中相移控制研究. , 2014, 63(15): 150506. doi: 10.7498/aps.63.150506
[5]	李帮庆, 马玉兰, 王聪, 徐美萍, 李阳. 耦合Schrödinger系统的周期振荡折叠孤子. , 2011, 60(6): 060203. doi: 10.7498/aps.60.060203
[6]	钱存, 王亮亮, 张解放. 变系数非线性Schrödinger方程的孤子解及其相互作用. , 2011, 60(6): 064214. doi: 10.7498/aps.60.064214
[7]	宋健, 赖俊峰. 正压流体中具有β效应与地形效应的强迫Rossby孤立波. , 2010, 59(7): 4756-4760. doi: 10.7498/aps.59.4756
[8]	张民仓, 皇甫国庆. 环状非有心势场中Schr?dinger方程的精确解. , 2010, 59(10): 6819-6823. doi: 10.7498/aps.59.6819
[9]	程雪苹, 林机, 韩平. 三维非线性Schr?dinger方程的直接微扰方法. , 2010, 59(10): 6752-6756. doi: 10.7498/aps.59.6752
[10]	宋健, 杨联贵. 层结流体中具有β效应与地形效应的强迫Rossby孤立波. , 2010, 59(5): 3309-3314. doi: 10.7498/aps.59.3309
[11]	高斌, 刘式达, 刘式适. Davey-Stewartson方程组的包络周期解和孤立波解. , 2009, 58(4): 2155-2158. doi: 10.7498/aps.58.2155
[12]	罗香怡, 刘学深, 丁培柱. 立方非线性Schr?dinger方程的动力学性质研究及其解模式的漂移. , 2007, 56(2): 604-610. doi: 10.7498/aps.56.604
[13]	宗丰德, 戴朝卿, 杨琴, 张解放. 光纤中变系数非线性Schr?dinger方程的孤子解及其应用. , 2006, 55(8): 3805-3812. doi: 10.7498/aps.55.3805
[14]	蒲利春, 林宗兵, 张雪峰, 王本菊, 姜毅, 严天艳. 非线性Schr?dinger方程组的精确解组. , 2005, 54(10): 4472-4477. doi: 10.7498/aps.54.4472
[15]	陆法林, 陈昌远. 非球谐振子势Schr?dinger方程的精确解. , 2004, 53(3): 688-692. doi: 10.7498/aps.53.688
[16]	沈守枫, 潘祖梁, 张隽, 叶彩儿. Manakov型非线性Schr?dinger方程的Jacobi椭圆函数包络解. , 2004, 53(7): 2056-2059. doi: 10.7498/aps.53.2056
[17]	李向正, 张金良, 王跃明, 王明亮. 非线性Schr?dinger方程的包络形式解. , 2004, 53(12): 4045-4051. doi: 10.7498/aps.53.4045
[18]	曹庆杰, 张天德, 李久平, G.W.PRICE, K.DJIDJELI, E.H.TWIZELL. 一类广义N维非线性Schr?dinger方程的孤子解及其性质研究. , 1997, 46(11): 2166-2173. doi: 10.7498/aps.46.2166
[19]	段一士, 俞重远, 吴振森. 双折射光纤中非线性耦合Schr?dinger方程的小振幅孤波解. , 1997, 46(12): 2359-2362. doi: 10.7498/aps.46.2359
[20]	刘中柱, 黄念宁. 用广田直接法求带高阶修正的扩充的非线性Schr?dinger方程的孤子解. , 1991, 40(1): 1-7. doi: 10.7498/aps.40.1

计量

文章访问数: 9428
PDF下载量: 762
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板