Skip to main content
SpringerLink
Log in

Theoretical analysis of equatorial near-inertial solitary waves under complete Coriolis parameters

  • Published:
Acta Oceanologica Sinica Aims and scope Submit manuscript

Abstract

An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper. Starting from the basic model equations of oceanic motions, a Korteweg de Vries equation is derived to simulate the evolution of equatorial nonlinear near-inertial waves by using methods of scaling analysis and perturbation expansions under the equatorial beta plane approximation. Theoretical dynamic analysis is finished based on the obtained Korteweg de Vries equation, and the results show that the horizontal component of Coriolis parameters is of great importance to the propagation of equatorial nonlinear near-inertial solitary waves by modifying its dispersion relation and by interacting with the basic background flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Benney D J. 1966. Long non-linear waves in fluid flows. Journal of Mathematics and Physics, 45(1–4): 52–63

    Article  Google Scholar 

  • Caillol P, Grimshaw R H. 2008. Rossby elevation waves in the presence of a critical layer. Studies in Applied Mathematics, 120(1): 35–64

    Article  Google Scholar 

  • Caldwell D R. 1983. Small-scale physics of the ocean. Reviews of Geophysics, 21(5): 1192–1205

    Article  Google Scholar 

  • Fruman M D. 2009. Equatorially bounded zonally propagating linear waves on a generalized β plane. Journal of the Atmospheric Sciences, 66(9): 2937–2945

    Article  Google Scholar 

  • Fu Lei, Chen Yaodeng, Yang Hongwei. 2019. Time-space fractional coupled generalized Zakharov-Kuznetsov equations set for Rossby solitary waves in two-layer fluids, Mathematics, 7(1): 41

    Article  Google Scholar 

  • Fu Lei, Yang Hongwei. 2019. An application of (3+1)-dimensional time-space fractional ZK model to analyze the complex dust acoustic waves. Complexity, 2019: 2806724

    Google Scholar 

  • Gerkema T, Shrira V I. 2005a. Near-inertial waves on the “nontraditional” β plane. Journal of Geophysical Research: Oceans, 110(C1): C01003

    Article  Google Scholar 

  • Gerkema T, Shrira V I. 2005b. Near-inertial waves in the ocean: Beyond the “traditional approximation”. Journal of Fluid Mechanics, 529:195–219

    Article  Google Scholar 

  • Gerkema T, Zimmerman J T F, Maas L R M, et al. 2008. Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Reviews of Geophysics, 46(2): RG2004

    Article  Google Scholar 

  • Grimshaw R H J. 1975. A note on the//-plane approximation. Tellus, 27(4): 351–357

    Article  Google Scholar 

  • Guo Min, Dong Haoyu, Liu Jianxin, et al. 2019. The time-fractional mZK equation for gravity solitary waves and solutions using sech-tanh and radial basic function method. Nonlinear Analysis: Modelling and Control, 24(1): 1–19

    Google Scholar 

  • Hayashi M, Itoh H. 2012. The importance of the nontraditional Coriolis terms in large-scale motions in the tropics forced by prescribed cumulus heating. Journal of the Atmospheric Sciences, 69(9): 2699–2716

    Article  Google Scholar 

  • Helal M A, Seadawy A R. 2012. Benjamin-Feir instability in nonlinear dispersive waves. Computers & Mathematics with Applications, 64(11): 3557–3568

    Article  Google Scholar 

  • Holton J R, Hakim G J. 2013. An Introduction to Dynamic Meteorology. 5th ed. Boston: Academic Press

    Google Scholar 

  • Itano T, Kasahara A. 2011. Effect of top and bottom boundary conditions on symmetric instability under full-component Coriolis force. Journal of the Atmospheric Sciences, 68(11): 2771–2782

    Article  Google Scholar 

  • Kasahara A. 2003. On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the earth’s angular velocity. Journal of the Meteorological Society of Japan. Ser. II, 81(5): 935–950

    Article  Google Scholar 

  • Kasahara A. 2010. A mechanism of deep-ocean mixing due to near-inertial waves generated by flow over bottom topography. Dynamics of Atmospheres and Oceans, 49(2–3): 124–140

    Article  Google Scholar 

  • Khater A H, Callebaut D K, Helal M A, et al. 2006a. Variational method for the nonlinear dynamics of an elliptic magnetic stagnation line. The European Physical Journal D-Atomic, Molecular, Optical and Plasma Physics, 39(2): 237–245

    Google Scholar 

  • Khater A H, Callebaut D K, Seadawy A R. 2006b. General soliton solutions for nonlinear dispersive waves in convective type instabilities. Physica Scripta, 74(3): 384–393

    Article  Google Scholar 

  • Kloosterziel R C, Carnevale G F, Orlandi P. 2007. Inertial instability in rotating and stratified fluids: barotropic vortices. Journal of Fluid Mechanics, 583: 379–412

    Article  Google Scholar 

  • Kloosterziel R C, Carnevale G F, Orlandi P. 2017. Equatorial inertial instability with full Coriolis force. Journal of Fluid Mechanics, 825: 69–108

    Article  Google Scholar 

  • Leibovich S, Lele S K. 1985. The influence of the horizontal component of earth’s angular velocity on the instability of the Ekman layer. Journal of Fluid Mechanics, 150: 41–87

    Article  Google Scholar 

  • Liu Yongjun, Gao Xiaoping, Yu Tianxia, et al. 2015. Influence of complete Coriolis force on the dispersion relation of ocean internal-wave in a background currents field. MATEC Web of Conferences, 25: 01014

    Article  Google Scholar 

  • Long R R. 1964. Solitary waves in the westerlies. Journal of the Atmospheric Sciences, 21(2): 197–200

    Article  Google Scholar 

  • Marshall J, Schott F. 1999. Open-ocean convection: Observations, theory, and models. Reviews of Geophysics, 37(1): 1–64

    Article  Google Scholar 

  • Nezlin M V, Snezhkin E N. 1993. Rossby Vortices, Spiral Structures, Solitons. Berlin: Springer-Verlag

    Book  Google Scholar 

  • Ono H. 1981. Algebraic Rossby wave soliton. Journal of the Physical Society of Japan, 50(8): 2757–2761

    Article  Google Scholar 

  • Pedlosky J. 1987. Geophysical Fluid Dynamics. New York: Springer-Verlag

    Book  Google Scholar 

  • Phillips N A. 1966. The equations of motion for a shallow rotating atmosphere and the “traditional approximation”. Journal of the Atmospheric Sciences, 23(5): 626–628

    Article  Google Scholar 

  • Ren Yanwei, Tao Mengshuang, Dong Huanhe, et al. 2019. Analytical research of (3+1)-dimensional Rossby waves with dissipation effect in cylindrical coordinate based on Lie symmetry approach. Advances in Difference Equations, 2019: 13

    Article  Google Scholar 

  • Satsuma J, Ablowitz M J, Kodama Y. 1979. On an internal wave equation describing a stratified fluid with finite depth. Physics Letters A, 73(4): 283–286

    Article  Google Scholar 

  • Seadawy A R. 2011. New exact solutions for the KdV equation with higher order nonlinearity by using the variational method. Computers & Mathematics with Applications, 62(10): 3741–3755

    Article  Google Scholar 

  • Seadawy A R. 2015. Nonlinear wave solutions of the three-dimensional Zakharov-Kuznetsov-Burgers equation in dusty plasma. Physica A: Statistical Mechanics and its Applications, 439: 124–131

    Google Scholar 

  • Seadawy A R. 2016. Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma. Physica A: Statistical Mechanics and its Applications, 455: 44–51

    Article  Google Scholar 

  • Seadawy A R. 2017a. Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods. The European Physical Journal Plus, 132(12): 518

    Article  Google Scholar 

  • Seadawy A R. 2017b. Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas. Pramana, 89(3): 49

    Article  Google Scholar 

  • Seadawy A R. 2018. Three-dimensional weakly nonlinear shallow water waves regime and its traveling wave solutions, International Journal of Computational Methods, 15(3): 1850017

    Article  Google Scholar 

  • Seadawy A R, Alamri S Z. 2018. Mathematical methods via the nonlinear two-dimensional water waves of Olver dynamical equation and its exact solitary wave solutions. Results in Physics, 8: 286–291

    Article  Google Scholar 

  • Seadawy A R, Lu D C, Yue C. 2017. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability. Journal of Taibah University for Science, 11(4): 623–633

    Article  Google Scholar 

  • Tian Runhua, Fu Lei, Ren Yanwei, et al. 2019. (3+1)-Dimensional time-fractional modified Burgers equation for dust ion-acoustic waves as well as its exact and numerical solutions. Mathematical Methods in the Applied Science, 1–20

  • Tort M, Ribstein B, Zeitlin V. 2016. Symmetric and asymmetric inertial instability of zonal jets on the f-plane with complete Coriolis force. Journal of Fluid Mechanics, 788: 274–302

    Article  Google Scholar 

  • White A A, Bromley R A. 1995. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force. Quarterly Journal of the Royal Meteorological Society, 121(522): 399–418

    Article  Google Scholar 

  • Yang Hongli, Liu Fumei, Wang Danni, et al. 2016. Nonlinear Rossby waves near the equator with complete Coriolis force. Progress in Geophysics (in Chinese), 31(3): 988–991

    Google Scholar 

  • Yang Hongwei, Sun Junchao, Fu Chen. 2019. Time-fractional Benjamin-Ono equation for algebraic gravity solitary waves in baroclinic atmosphere and exact multi-soliton solution as well as interaction. Communications in Nonlinear Science and Numerical Simulation, 71: 187–201

    Article  Google Scholar 

  • Yano J I. 2017. Inertio-gravity waves under the non-traditional f-plane approximation: Singularity in the large-scale limit. Journal of Fluid Mechanics, 810: 475–488

    Article  Google Scholar 

  • Yasuda Y, Sato K. 2013. The effect of the horizontal component of the angular velocity of the earth’s rotation on inertia-gravity waves. Journal of the Meteorological Society of Japan. Ser H, 91(1): 23–41

    Article  Google Scholar 

  • Zhang Xiaoming. 1991. A model of the equatorial deep jets and the role of the horizontal Coriolis parameter [dissertation]. Woods Hole: Woods Hole Oceanographic Institution

    Google Scholar 

  • Zhang Ruigang, Liu Quansheng, Yang Liangui, et al. 2019a. Nonlinear planetary-synoptic wave interaction under generalized beta effect and its solutions. Chaos, Solitons & Fractals, 122: 270–280

    Article  Google Scholar 

  • Zhang Ruigang, Yang Liangui. 2019. Nonlinear Rossby waves in zonally varying flow under generalized beta approximation. Dynamics of Atmospheres and Oceans, 85: 16–27

    Article  Google Scholar 

  • Zhang Ruigang, Yang Liangui, Liu Quansheng, et al. 2019b. Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography. Applied Mathematics and Computation, 346: 666–679

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Ruigang Zhang & Liangui Yang

Authors
  1. Ruigang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liangui Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liangui Yang.

Additional information

Foundation item: The National Natural Science Foundation of China under contract No. 11762011; the Natural Science Foundation of Inner Mongolia Autonomous Region under contract No. 2020BS01002; the Research Program of Science at Universities of Inner Mongolia Autonomous Region under contract No. NJZY20003; the Scientific Starting Foundation of Inner Mongolia University under contract No. 21100-5185105.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, R., Yang, L. Theoretical analysis of equatorial near-inertial solitary waves under complete Coriolis parameters. Acta Oceanol. Sin. 40, 54–61 (2021). https://doi.org/10.1007/s13131-020-1699-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13131-020-1699-5

Key words

Search

Navigation