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Dynamics of nonlinear Rossby waves in zonally varying flow with spatial-temporal varying topography

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  • Zhang, Ruigang
  • Yang, Liangui
  • Liu, Quansheng
  • Yin, Xiaojun

Abstract

In the present work, we investigate the dynamics of nonlinear Rossby waves in zonally varying background current under generalized beta approximation. The effects of the zonally varying background current, the spatial-temporal varying topography, the potential forcing and the dissipation on nonlinear Rossby waves are all taken into consideration. We derive a new modified Korteweg–deVries equation with variable coefficients for the Rossby wave amplitude with the help of multiple scales method and perturbation expansions. Based on the obtained model equation, the physical mechanisms of nonlinear Rossby waves are analyzed. Within the present selected parameter ranges, the qualitative results demonstrate that the generalized beta and basic topography are essential factors in exciting the nonlinear Rossby solitary waves. In addition, the zonally varying flow affects the linear phase speed and the linear growth or decay characteristics of the waves. The results also show that the spatial-temporal slowly varying topography, which represents an unstable mechanism for the evolution of Rossby solitary waves, is a factor in linear growth or decay. Furthermore, to validate the efficiency of the obtained model equation, a weakly nonlinear method and numerical simulation are adopted to solve the obtained equation and the results indicate the consistency between the qualitative analysis and the quantitative solutions in explaining the present equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:666-679
    DOI: 10.1016/j.amc.2018.10.084
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    References listed on IDEAS

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    1. 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.
    2. Zeidan, D., 2016. "Assessment of mixture two-phase flow equations for volcanic flows using Godunov-type methods," Applied Mathematics and Computation, Elsevier, vol. 272(P3), pages 707-719.
    3. Minhajul, & Zeidan, D. & Raja Sekhar, T., 2018. "On the wave interactions in the drift-flux equations of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 117-131.
    4. 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.
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    Cited by:

    1. Zhang, Jiaqi & Zhang, Ruigang & Yang, Liangui & Liu, Quansheng & Chen, Liguo, 2021. "Coherent structures of nonlinear barotropic-baroclinic interaction in unequal depth two-layer model," Applied Mathematics and Computation, Elsevier, vol. 408(C).

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