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A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids

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  • Hongwei Yang
  • Qingfeng Zhao
  • Baoshu Yin
  • Huanhe Dong

Abstract

From rotational potential vorticity-conserved equation with topography effect and dissipation effect, with the help of the multiple-scale method, a new integro-differential equation is constructed to describe the Rossby solitary waves in deep rotational fluids. By analyzing the equation, some conservation laws associated with Rossby solitary waves are derived. Finally, by seeking the numerical solutions of the equation with the pseudospectral method, by virtue of waterfall plots, the effect of detuning parameter and dissipation on Rossby solitary waves generated by topography are discussed, and the equation is compared with KdV equation and BO equation. The results show that the detuning parameter plays an important role for the evolution features of solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.

Suggested Citation

  • Hongwei Yang & Qingfeng Zhao & Baoshu Yin & Huanhe Dong, 2013. "A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    • Handle: RePEc:hin:jnlaaa:597807
    DOI: 10.1155/2013/597807
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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. 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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