Force solitary Rossby waves with beta effect and topography effect in stratified flows

Song Jian; Yang Lian-Gui

doi:10.7498/aps.59.3309

Abstract

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.

Keywords:

Authors and contacts

Song Jian²,
Yang Lian-Gui¹

(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

References

[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 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 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 物理学报 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 物理学报 59 44］
[23]	］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］
[24]	］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］
[25]	］Fan E G, Zhang H Q 2000 Acta. Phys. Sin. 49 1409 (in Chinese)［范恩贵、张鸿庆 2000 物理学报 49 1409 ］
[26]	］Mao J J, Yang J R 2005 Acta. Phys. Sin. 54 4999 (in Chinese)［毛杰健、杨建荣 2005 物理学报 54 4999］
[27]	］Zhu H P, Zheng C L 2006 Acta. Phys. Sin. 55 4999 (in Chinese) ［朱海平、郑春龙 2006 物理学报 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 物理学报 58 7397］
[29]	］Mao J J, Yang J R 2007 Acta. Phys. Sin. 56 5049 (in Chinese)［毛杰健、杨建荣 2007 物理学报 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 物理学报 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 物理学报 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

Cited By

[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 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 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 物理学报 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 物理学报 59 44］
[23]	］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］
[24]	］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］
[25]	］Fan E G, Zhang H Q 2000 Acta. Phys. Sin. 49 1409 (in Chinese)［范恩贵、张鸿庆 2000 物理学报 49 1409 ］
[26]	］Mao J J, Yang J R 2005 Acta. Phys. Sin. 54 4999 (in Chinese)［毛杰健、杨建荣 2005 物理学报 54 4999］
[27]	］Zhu H P, Zheng C L 2006 Acta. Phys. Sin. 55 4999 (in Chinese) ［朱海平、郑春龙 2006 物理学报 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 物理学报 58 7397］
[29]	］Mao J J, Yang J R 2007 Acta. Phys. Sin. 56 5049 (in Chinese)［毛杰健、杨建荣 2007 物理学报 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 物理学报 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 物理学报 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

[1]	Wu Chao-Jun, Fang Li-Yi, Yang Ning-Ning. Dynamic analysis and experiment of chaotic circuit of non-homogeneous fractional memristor with bias voltage source. Acta Physica Sinica, 2024, 73(1): 010501. doi: 10.7498/aps.73.20231211
[2]	Li Jing-He, He Zhan-Xiang, Meng Shu-Jun, Yang Jun, Li Wen-Jie, Liao Xiao-Qian. Domain decomposition based integral equation modeling of 3-dimensional topography in frequency domain for well electromagnetic field. Acta Physica Sinica, 2019, 68(14): 140202. doi: 10.7498/aps.68.20190330
[3]	Fu Yuan-Guang, Deng Li, Li Gang. Preliminary study on numerical solver of inhomogeneous burnup equations. Acta Physica Sinica, 2018, 67(17): 172802. doi: 10.7498/aps.67.20172650
[4]	Ma Yan, Lin Shu-Yu, Xu Jie, Tang Yi-Fan. Influnece of nonspherical effects on the secondary Bjerknes force in a strong acoustic field. Acta Physica Sinica, 2017, 66(1): 014302. doi: 10.7498/aps.66.014302
[5]	Li Shao-Feng, Yang Lian-Gui, Song Jian. Nonlinear solitary Rossby waves with external heating source and effect topographic effect in stratified flows described by the inhomogeneous Schrdinger equation. Acta Physica Sinica, 2015, 64(19): 199201. doi: 10.7498/aps.64.199201
[6]	Du Hui, Wei Gang, Zhang Yuan-Ming, Xu Xiao-Hui. Experimental investigations on the propagation characteristics of internal solitary waves over a gentle slope. Acta Physica Sinica, 2013, 62(6): 064704. doi: 10.7498/aps.62.064704
[7]	Zhao Long. Robust inertial terrain aided navigation algorithm. Acta Physica Sinica, 2012, 61(10): 104301. doi: 10.7498/aps.61.104301
[8]	Song Jian, Liu Quan-Sheng, Yang Lian-Gui. Beta effect and slowly changing topography Rossby waves in a shear flow. Acta Physica Sinica, 2012, 61(21): 210510. doi: 10.7498/aps.61.210510
[9]	Yang Lian-Gui, Jiang Nan, Song Jian. Equatorial Rossby envelope solitary waves with β effect in a shear flow. Acta Physica Sinica, 2011, 60(2): 024701. doi: 10.7498/aps.60.024701
[10]	Song Jian, Yang Lian-Gui, Liu Quan-Sheng. Nonlinear Rossby envelope waves under the influence of forcing dissipation and effect topographic effect. Acta Physica Sinica, 2011, 60(10): 104701. doi: 10.7498/aps.60.104701
[11]	Song Jian, Lai Jun-Feng. Forced solitary Rossby wave with beta effect and topography effect in barotropic flows. Acta Physica Sinica, 2010, 59(7): 4756-4760. doi: 10.7498/aps.59.4756
[12]	Da Chao-Jiu, Chou Ji-Fan. KdV equation with a forcing term for the evolution of the amplitude of Rossby waves along a slowly changing topography. Acta Physica Sinica, 2008, 57(4): 2595-2599. doi: 10.7498/aps.57.2595
[13]	Zheng Ying-Hui, Zeng Zhi-Nan, Li Ru-Xin, Xu Zhi-Zhan. Nondipole effects in high-order harmonic generation induced by extreme ultraviolet attosecond pulse. Acta Physica Sinica, 2007, 56(4): 2243-2249. doi: 10.7498/aps.56.2243
[14]	Han Ding-An, Guo Hong, Sun Hui, Bai Yan-Feng. The frequency modulation effects of the probe field in three level Λ-system. Acta Physica Sinica, 2004, 53(6): 1793-1798. doi: 10.7498/aps.53.1793
[15]	Tang Jia-Shi, Liu Zhu-Yong, Li Xue-Ping. The quasi-wavelet solutions of MKdV equations. Acta Physica Sinica, 2003, 52(3): 522-525. doi: 10.7498/aps.52.522
[16]	LI HUA-BING, HUANG PING-HUA, LIU MU-REN, KONG LING-JIANG. SIMULATION OF THE MKDV EQUATION WITH LATTICE BOLTZMANN METHOD. Acta Physica Sinica, 2001, 50(5): 837-840. doi: 10.7498/aps.50.837
[17]	ZHAO YONG-MING, YAN JIA-REN. THE THEORY OF THE PERTURBATION EQUATION OF MKdV. Acta Physica Sinica, 1999, 48(11): 1976-1982. doi: 10.7498/aps.48.1976
[18]	FAN EN-GUI, ZHANG HONG-QING. THE HOMOGENEOUS BALANCE METHOD FOR SOLVING NONLINEAR SOLITON EQUATIONS. Acta Physica Sinica, 1998, 47(3): 353-362. doi: 10.7498/aps.47.353
[19]	CHEN YONG-QING. HOMOGENEOUS AND INHOMOGENEOUS DIFFERENTAIL REALIZATIONS AND BOSON-FERMION REALIZATIONS OF THE SPL(2,1) SUPERALGEBRA. Acta Physica Sinica, 1993, 42(8): 1199-1204. doi: 10.7498/aps.42.1199
[20]	Xiang Yuan-hai, Zhu Xi-wen, Deng Jin-quan, Tan Yong-fang. STUDY OF THE EFFECTS OF THE LIGHT INTENSITY AND TEMPERATURE ON THE FREQUENCY OF THE Rb MASER. Acta Physica Sinica, 1991, 40(5): 726-730. doi: 10.7498/aps.40.726

Catalog

Vol. 59, Issue 5 - 2010-03-05

Metrics

Abstract views: 7182
PDF Downloads: 674
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板