Communications in Theoretical Physics ›› 2022, Vol. 74 ›› Issue (7): 075002. doi: 10.1088/1572-9494/ac65ec
• Mathematical Physics • Previous Articles Next Articles
Cong Wang(王丛), Jingjing Li(李晶晶), Hongwei Yang(杨红卫)()
Received:
2022-01-20
Revised:
2022-03-15
Accepted:
2022-04-11
Published:
2022-07-01
Contact:
Hongwei Yang(杨红卫)
E-mail:hwyang1979@163.com
Cong Wang(王丛), Jingjing Li(李晶晶), Hongwei Yang(杨红卫), Commun. Theor. Phys. 74 (2022) 075002.
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Figure 1.
(a) Modulational instability gain G and (b) regions of modulational instability (MI) and modulational stability (MS) of Rossby waves at 60 °N for $k=3/(6.371\cos 60^\circ )$, K = 1, l = 1, Ly = 5, B0 = 0.5, and u = 1. Here, only the dependence of the instability on the wavenumber p in the x direction is considered, with the dependence on the wavenumber q in the y direction being ignored."
Figure 2.
(a) Modulational instability gain G of Rossby waves at 60 °N for q = 0 (blue curve), q = 0.2 (red curve), and q = 0.5 (green curve) for $k=3/(6.371\cos 60^\circ )$, K = 1, l = 1, Ly = 5, B0 = 0.5, and u = 1. (b) Magnified view of part of the plot in (a)."
Figure 5.
(a) Modulational instability gain G and (b) regions of modulational instability of Rossby waves at 60 °N for $k=3/(6.371\cos 60^\circ )$, K = 1, l = 1, Ly = 5, B0 = 0.5, and u = 1. Here, the dependences of the instability on both the wavenumbers p and q in the x and y directions, respectively, are considered."
1 |
Maxworthy T Redekopp L G 1976 New theory of the Great Red Spot from solitary waves in the Jovian atmosphere Nature 260 509 511
doi: 10.1038/260509a0 |
2 |
Chen L G Yang L G Zhang R G 2020 A (2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution Commun. Theor. Phys. 72 045004
doi: 10.1088/1572-9494/ab7703 |
3 |
Yang Y Song J 2021 On the generalized eigenvalue problem of Rossby waves vertical velocity under the condition of zonal mean flow and topography Appl. Math. Lett. 121 107485
doi: 10.1016/j.aml.2021.107485 |
4 |
Strong C Magnusdottir G 2010 The role of Rossby wave breaking in shaping the equilibrium atmospheric circulation response to north atlantic boundary forcing J. Clim. 23 192 202
doi: 10.1175/2009JCLI2676.1 |
5 |
Song J Yang L G 2009 mKdV equation for the amplitude of solitary Rossby waves in stratified shear flows with a zonal shear flow Atmos. Ocean. Sci. Lett. 02 18 23
doi: 10.1080/16742834.2009.11446771 |
6 |
Shi L Yang D Yin B 2020 The effect of background flow shear on the topographic Rossby wave J. Oceanoge. 76 1 4
doi: 10.1007/s10872-020-00546-6 |
7 |
Xu Z Wang Y Liu Z Mcwilliams J C Gan J 2021 Insight into the dynamics of the radiating internal tide associated with the kuroshio current J. Geophys. Res.—Oceans 126 e2020JC017018
doi: 10.1029/2020JC017018 |
8 |
Holbrook N J Goodwin I D 2011 ENSO to multi-decadal time scale changes in East Australian current transports and Fort Denison sea level: Oceanic Rossby waves as the connecting mechanism Deep-Sea Res. II 58 547 558
doi: 10.1016/j.dsr2.2010.06.007 |
9 |
Cane M A Zebiak S E 1985 Theory for El Niño and the southern oscillation Science 228 1085 1087
doi: 10.1126/science.228.4703.1085 |
10 |
Long R R 1964 Solitary waves in the westerlies J. Atmos. Sci. 21 197 200
doi: 10.1175/1520-0469(1964)021<0197:SWITW>2.0.CO;2 |
11 |
Benny D J 1966 Long non-linear waves in fluid flows Stdu. Appl. Math. 45 52 63
doi: 10.1002/sapm196645152 |
12 |
Wadati Miki 1973 The modified korteweg-de vries equation J. Phys. Soc. Japan. 34 1289
doi: 10.1143/JPSJ.34.1289 |
13 |
Lou S Y Tong B Hu H C Tang X Y 2006 Coupled KdV equations derived from two-layer fluids J. Phys. A Math. Gen. 39 513 527
doi: 10.1088/0305-4470/39/3/005 |
14 |
Liu Q S Zhang Z Y Zhang R G Huang C X 2019 Dynamical analysis and exact solutions of a new (2+1)-dimensional generalized boussinesq model equation for nonlinear Rossby waves Commun. Theor. Phys. 71 1054 1062
doi: 10.1088/0253-6102/71/9/1054 |
15 |
Benny D J 1979 Large amplitude Rossby waves Stud. Appl. Math. 60 1 10
doi: 10.1002/sapm19796011 |
16 |
Yamagata T 1980 The stability, modulation and long wave resonance of a planetary wave in a rotating, two-layer fluid on a channel beta-plane J. Meteorol. Soc. Japan. 58 160 171
doi: 10.2151/jmsj1965.58.3_160 |
17 |
Luo D 1996 Envelope solitary Rossby waves and modulational instabilities of uniform Rossby wave trains in two space dimensions Wave Motion 24 315 325
doi: 10.1016/S0165-2125(96)00025-X |
18 |
Luo D 2001 Derivation of a higher order nonlinear Schrödinger equation for weakly nonlinear Rossby waves Wave Motion 33 339 347
doi: 10.1016/S0165-2125(00)00073-1 |
19 |
Huang F Tang X Y Lou S Y 2006 Exact solutions for a higher-order nonlinear Schrödinger equation in atmospheric dynamics Commun. Theor. Phys. 45 573
doi: 10.1088/0253-6102/45/3/039 |
20 |
Benjamin T B Feir J E 1967 The disintegration of wave trains on deep water: I. Theory J. Fluid. 27 417 430
doi: 10.1017/S002211206700045X |
21 |
Taniuti T Washimi H 1968 Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma Phys. Rev. Lett. 21 209 212
doi: 10.1103/PhysRevLett.21.209 |
22 |
Kibler B Chabchoub A Gelash A 2015 Superregular breathers in optics and hydrodynamics: omnipresent modulation instability beyond simple periodicity Phys. Rev. X 5 041026
doi: 10.1103/PhysRevX.5.041026 |
23 |
Wang D S Guo B Wang X 2019 Long-time asymptotics of the focusing Kundu CEckhaus equation with nonzero boundary conditions J. Differ. Equ. 266 5209 5253
doi: 10.1016/j.jde.2018.10.053 |
24 |
Guo L Wang L Cheng Y 2019 Higher-order rogue waves and modulation instability of the two-component derivative nonlinear Schrödinger equation Commun. Nonlinear Sci. 79 104915
doi: 10.1016/j.cnsns.2019.104915 |
25 |
Baronio F Chen S H Grelu P 2015 Baseband modulation instability as the origin of rogue waves Phys. Rev. A 91 033804
doi: 10.1103/PhysRevA.91.033804 |
26 |
Chen J Feng B Maruno K I 2019 High-order rogue waves of a long-wave-short-wave model of Newell type Phys. Rev. E 100 052216
doi: 10.1103/PhysRevE.100.052216 |
27 |
Xu L Wang D S Wen X Jiang Y 2020 Exotic localized vector waves in a two-component nonlinear wave system J. Nonlinear Sci. 30 537 564
doi: 10.1007/s00332-019-09581-0 |
28 |
Lu D Seadawy A R Wang J Arshad M Farooq U 2019 Soliton solutions of the generalised third-order nonlinear Schrödinger equation by two mathematical methods and their stability Pramana 93 44
doi: 10.1007/s12043-019-1804-5 |
29 |
Yue Y Huang L Chen Y 2020 Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrödinger equation Commun. Nonlinear Sci. Numer. Simul. 89 105284
doi: 10.1016/j.cnsns.2020.105284 |
30 |
Li S Song J Cao A 2020 Gravity-capillary waves modulated by linear shear flow in arbitrary water depth Chin. Phys. B 29 406 415
doi: 10.1088/1674-1056/abb3e4 |
31 |
Zhang P Xu Z Li Q 2018 The evolution of mode-2 internal solitary waves modulated by background shear currents Nonlinear Proc. Geoph. 25 441 455
doi: 10.5194/npg-25-441-2018 |
32 |
Bi Y Liu Q Wang L 2020 Bifurcation and potential landscape of p53 dynamics depending on PDCD5 level and ATM degradation rate Int. J. Bifurcat. Chaos 30 2050134
doi: 10.1142/S0218127420501345 |
33 |
Bi Y Zhang Z Liu Q Liu T 2021 Research on nonlinear waves of blood flflow in arterial vessels Commun. Nonlinear Sci. Numer. Simul. 102 105918
doi: 10.1016/j.cnsns.2021.105918 |
34 |
Adem A R Ntsime B P Biswas A Asma M Belic M R 2020 Stationary optical solitons with Sasa-Satsuma equation having nonlinear chromatic dispersion Phys. Lett. A 384 126721
doi: 10.1016/j.physleta.2020.126721 |
|
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