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Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids

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  • Hongwei Yang
  • Baoshu Yin
  • Yunlong Shi
  • Qingbiao Wang

Abstract

The paper presents an investigation of the generation, evolution of Rossby solitary waves generated by topography in finite depth fluids. The forced ILW- (Intermediate Long Waves-) Burgers equation as a model governing the amplitude of solitary waves is first derived and shown to reduce to the KdV- (Korteweg-de Vries-) Burgers equation in shallow fluids and BO- (Benjamin-Ono-) Burgers equation in deep fluids. By analysis and calculation, the perturbation solution and some conservation relations of the ILW-Burgers equation are obtained. Finally, with the help of pseudospectral method, the numerical solutions of the forced ILW-Burgers equation are given. The results demonstrate that the detuning parameter holds important implications for the generation of the solitary waves. By comparing with the solitary waves governed by ILW-Burgers equation and BO-Burgers equation, we can conclude that the solitary waves generated by topography in finite depth fluids are different from that in deep fluids.

Suggested Citation

  • Hongwei Yang & Baoshu Yin & Yunlong Shi & Qingbiao Wang, 2012. "Forced ILW-Burgers Equation as a Model for Rossby Solitary Waves Generated by Topography in Finite Depth Fluids," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, October.
    • Handle: RePEc:hin:jnljam:491343
    DOI: 10.1155/2012/491343
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    Cited by:

    1. Lei Fu & Yaodeng Chen & Hongwei Yang, 2019. "Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    2. Haoyu Dong & Changna Lu & Hongwei Yang, 2018. "The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations," Mathematics, MDPI, vol. 6(10), pages 1-17, October.
    3. Cao, Weiping & Fei, Jinxi & Li, Jiying, 2021. "Symmetry breaking solutions to nonlocal Alice-Bob Kadomtsev-Petviashivili system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Min Guo & Chen Fu & Yong Zhang & Jianxin Liu & Hongwei Yang, 2018. "Study of Ion-Acoustic Solitary Waves in a Magnetized Plasma Using the Three-Dimensional Time-Space Fractional Schamel-KdV Equation," Complexity, Hindawi, vol. 2018, pages 1-17, June.
    5. Zhang, Ruigang & Yang, Liangui & Liu, Quansheng & Yin, Xiaojun, 2019. "Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 666-679.

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