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Propagation and modulational instability of Rossby waves in stratified fluids |
| Xiao-Qian Yang(杨晓倩)1, En-Gui Fan(范恩贵)3, and Ning Zhang(张宁)1,2,† |
1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
2 Department of Fundamental Course, Shandong University of Science and Technology, Tai'an 271019, China;
3 School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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Abstract Perturbation analysis and scale expansion are used to derive the (2+1)-dimensional coupled nonlinear Schrödinger (CNLS) equations that can describe interactions of two Rossby waves propagating in stratified fluids. The (2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately. The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method, and the influence factors of modulational instability are analyzed. The results suggest that, when two Rossby waves with slightly different wave numbers propagate in the stratified fluids, the intensity of bright soliton decreases with the increases of dark soliton coefficients. In addition, the size of modulational instable area is related to the amplitude and wave number in y direction.
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Received: 07 December 2021
Revised: 18 January 2022
Accepted manuscript online: 24 January 2022
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PACS:
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02.30.Jr
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(Partial differential equations)
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03.65.Ge
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(Solutions of wave equations: bound states)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11805114) and the Shandong University of Science and Technology Research Fund (Grant No. 2018TDJH101). |
Corresponding Authors:
Ning Zhang
E-mail: zhangningsdust@126.com
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Cite this article:
Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁) Propagation and modulational instability of Rossby waves in stratified fluids 2022 Chin. Phys. B 31 070202
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[1] Song J 2014 Nonlinear Rossby waves in geophysical fluid (Ph.D. dissertation) (Inner Mongolia:Inner Mongolia University) (in Chinese)
[2] Yang H W 2012 Dynamics research of nonlinear Rossby solitary waves under the influence of unsteady disturbance (Ph.D. dissertation) (Qingdao:Institute of Oceanology of the Chinese Academy of Sciences) (in Chinese)
[3] Battisti D S 2010 J. Phys. Oceanogr. 19 551
[4] Kang I S and An S I 1998 J. Climat. 11 2461
[5] Yang Y Y and Song J 2021 Appl. Math. Lett. 121 107485
[6] Bi Y H, Zhang Z G, Liu Q S and Liu T J 2021 Commun. Nonlinear Sci. Numer. Simul. 102 105918
[7] Liu Q S, Song J and Yang L G 2014 Prog. Geophys. 29 0057 (in Chinese)
[8] Song J 2006 The mKdV equation for the amplitude of Rossby wave in stratified fluid (MS thesis) (Inner Mongolia:Inner Mongolia University) (in Chinese)
[9] Chen L G, Yang L G and Zhang J Q 2020 Math. Appl. 33 373
[10] Yang H W, Chen X, Guo M and Yao D C 2018 Nonlinear Dyn. 91 2019
[11] Tan B K and Boyd J P 2000 Chaos Solitons & Fractals 11 1113
[12] Dysthe K B 1979 Proc. R. Soc. London A 369 105
[13] Haus H A and Wong W S 1996 Rev. Mod. Phys. 68 423
[14] Luo D H 2001 Wave Motion 33 339
[15] Tan B K 1996 J. Atmosph. Sci. 53 1604
[16] Choy Y Y, Tay K G anf Ong C T 2013 Matematika 28 1
[17] Song S Y 2010 The establishment of weak nonlinear model of deep-sea internal wave and its application in the South China Sea (MS thesis) (Qingdao:Ocean University of China, OUC) (in Chinese)
[18] Zhang Y J, Qin Y L, Ren H L and Liu F 2012 Asia-Pacific Youth Conference on Communication and Technology, August 7-9, 2011, Hangzhou, China, pp. 413-416
[19] Liang L W, Li X D and Li Y X 2009 Acta Phys. Sin. 58 2159 (in Chinese)
[20] Liu Y 2012 Application of G'/G-expansion method in solving (2+1) dimensional KP equation (MS thesis) (Sichuan:Sichuan Normal University) (in Chinese)
[21] Pang J, Jin L H and Ying X M 2011 Chin. J. Quantum Electron. 28 674
[22] Zeng X and Zhang H Q 2005 Acta Phys. Sin. 54 1476 (in Chinese)
[23] Shi Y R, Lv K P, Duan W S, Hong X R, Yang H J and Zhao J B 2003 J. Northwest Normal University 39 30
[24] Li Y K 1992 Sci. China A-Math. 22 600 (in Chinese)
[25] Miao J J 2012 Two Classes of Darboux Transformations of (2+1)-dimensional KP Equations (MS thesis) (Henan:Zhengzhou University) (in Chinese)
[26] Gao X Y and Duan W S 2008 J. Northwest Normal University 44 43 (in Chinese)
[27] He X Y, Zhao Z H and Han S 2014 J. Guangxi University of Science and Technology 25 9
[28] Ruan H Y and Chen Y X 2001 Acta Phys. Sin. 50 586 (in Chinese)
[29] Du Z F, Song L J and Wang Y 2019 Laser Optoelectron. Prog. 56 34
[30] Song X and Li H M 2013 J. Zhejiang Normal University 36 294
[31] Zhang Z Q and He Z M 2020 J. At. Mol. Phys. 37 279 (in Chinese)
[32] Chen Z M and Duan W S 2020 Acta Phys. Sin. 69 149 (in Chinese)
[33] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202
[34] Baronio F, Conforti M, Degasperis A, Lombardo S, Onorato M and Wabnitz S 2014 Phys. Rev. Lett. 113 034101
[35] Li S F, Cao A Z, Song J B, Yu C C and Chen J 2020 Phys. Fluids 32 072104
[36] Sun W R 2016 Analytic study on the solitons and rogue waves in some fields such asthe plasmas and optical fiber communications (Ph.D. dissertation) (Beijing:Beijing University of Posts and Telecommunications) (in Chinese)
[37] Qiu J L and Li W B 2017 J. Northwest Normal University 53 48 |
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