THERMAL SCIENCE

International Scientific Journal

Bao-Jun Zhao

,

Jia-Xin Wang

,

Li Cheng

,

Chen-Juan Jiang

VARIABLE COEFFICIENT KDV SYSTEM FOR THE NON-LINEAR ROSSBY WAVES

ABSTRACT
The paper deals with a non-linear barotropic vorticity equation in a shear flow, the model is applied to get the non-linear Rossby solitary wave with the effects of topography and other external forcing. Basing on the perturbation method, the variable coefficient KdV equation is derived for Rossby waves. The periodic-like solution for the equation is obtained with the help of Jacobi elliptic functions, the solitary solutions can also be obtained in the limit case. The analysis indicates that the wave amplitude and velocity will be related to the topography effect. It is also shown that the external forcing plays an important role in evolution of the waves.
KEYWORDS
Rossby solitary wave, Jacobi elliptic function, variable coefficient KdV
PAPER SUBMITTED: 2021-06-18
PAPER REVISED: 2021-07-16
PAPER ACCEPTED: 2021-07-25
PUBLISHED ONLINE: 2022-04-09
DOI REFERENCE: https://doi.org/10.2298/TSCI2202123Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 2, PAGES [1123 - 1130]
REFERENCES
  1. Fu, Z. T., et al., Equatorial Rossby Solitary Wave under the External Forcing, Communications in Theoretical Physics, 43 (2005), 1, pp. 45-48
  2. Tang, X. Y., et al., Variable Coefficient, Non-Linear Systems Derived from an Atmospheric Dynamical System, Chinese Physics B, 18 (2009), 11, pp. 4622-4635
  3. Pedlosky, J., The Destabilization of Shear Flow by Topography, Journal of Physical Oceanography, 10 (1980), 11, pp. 1877-1879
  4. Yang, Y. Y., et al., On the Generalized Eigenvalue Problem of Rossby Waves Vertical Velocity under the Condition of Zonal Mean Flow and Topography, Applied Mathematics Letters, 121 (2021), ID 107485
  5. Bi, Y. H., et al., Research on Non-Linear Waves of Blood Flow in Arterial Vessels, Communications in Nonlinear Science and Numerical Simulation, 102 (2021), ID 105918
  6. Bekir, A., On Traveling Wave Solutions to Combined KdV-mKdV Equation and Modified Burgers-KdV Equation, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 4, pp. 1038-1042
  7. Huang, Y., et al., All Exact Traveling Wave Solutions of the Combined KdV-mKdV Equation, Advances in Difference Equations, 2014 (2014), 1, 261 Zhao, B.-J.,
  8. Alam, M. N., Akbar, M. A., Some New Exact Traveling Wave Solutions to the Simplified MCH Equa-tion and the (1+1)-Dimensional Combined KdV-mKdV Equations, Journal of the Association of Arab Universities for Basic and Applied Sciences, 17 (2015), Apr., pp. 6-13
  9. Zhang, H., et al., N-Lump and Interaction Solutions of Localized Waves to the (2+1)-Dimensional Gen-eralized KP Equation, Results in Physics, 25 (2021), 5, ID 104168
  10. Zhang, W. J., et al., Solitary Wave, M-Lump and Localized Interaction Solutions to the (4+1)-Dimen-sional Fokas Equation, Physica Scripta, 95 (2020), 4, ID 045217
  11. Fu, Z. T., et al., Structures of Equatorial Envelope Rossby Wave under the Influence of New Type of Diabatic Heating, Chaos, Solitons and Fractals, 22 (2004), 22, pp. 335-340
  12. Zhao, Q., et al., Two-Dimensional Rossby Waves: Exact Solutions to Petviashvili Equation, Communi-cations in Theoretical Physics, 45 (2006), 3, pp. 414-416
  13. Pedlosky, J., Geophysical Fluid Dynamics second edition, Springer, New York, USA, 1987
  14. Liu, S. K., et al., Solution by Using the Jacobi Elliptic Function Expansion Method for Variable-Coef-ficient Non-Linear Equations, Acta Physica Sinica-Chinese Edition, 51 (2002), 19, pp. 1923-1926
PDF VERSION [DOWNLOAD]
Variable coefficient KdV system for the non-linear Rossby waves

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence