Dynamics of Nonlinear Rossby Waves With the Derivative-Expansion Method

TIAN Hongxiao; ZHANG Ruigang; LIU Quansheng

doi:10.21656/1000-0887.460159

Volume 47 Issue 3

Mar. 2026

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TIAN Hongxiao, ZHANG Ruigang, LIU Quansheng. Dynamics of Nonlinear Rossby Waves With the Derivative-Expansion Method[J]. Applied Mathematics and Mechanics, 2026, 47(3): 313-328. doi: 10.21656/1000-0887.460159

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Dynamics of Nonlinear Rossby Waves With the Derivative-Expansion Method

doi: 10.21656/1000-0887.460159

1.
School of Science, Inner Mongolia University of Science and Technology, Baotou, Inner Mongolia 014010, P.R.China
2.
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China

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Corresponding author: 刘全生(1979—), 男, 教授, 博士(通信作者. E-mail: smslqs@imu.edu.cn)
Received Date: 2025-09-03
Rev Recd Date: 2025-12-18
Publish Date: 2026-03-01

Abstract

Abstract

Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere and ocean. Owing to the nonlinearity of the involved problems, the weakly nonlinear method, ie the derivative expansion method, was mainly used to investigate Rossby waves under the combined effects of the generalized β-effect and the basic flow effect. The derivative expansion method has the advantage of capturing the multi-scale characteristics of wave processes simultaneously. In the case where the perturbation expansion is independent of secular terms, the nonlinear equations describing the amplitude evolution of nonlinear waves were derived, such as the Korteweg-de Vries equation, the Boussinesq equation and Zakharov-Kuznetsov equation. Both qualitative and quantitative analyses indicate that the generalized β-effect is the key factor inducing the evolution of Rossby solitary waves.
- planetary Rossby waves,
- generalized beta effect,
- derivative-expansion method,
- nonlinear equation

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References

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