基于导数展开法的非线性Rossby波动力学

TIAN Hongxiao; ZHANG Ruigang; LIU Quansheng

doi:10.21656/1000-0887.460159

基于导数展开法的非线性Rossby波动力学

doi: 10.21656/1000-0887.460159

1.
内蒙古科技大学理学院, 内蒙古包头 014010
2.
内蒙古大学数学科学学院, 呼和浩特 010021

基金项目: 国家自然科学基金(12262025);内蒙古自然科学基金(2020LH01006)

详细信息

作者简介:

中图分类号: O357.41
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- 被引次数: 0
出版历程
- 收稿日期: 2025-09-03
- 修回日期: 2025-12-18
- 刊出日期: 2026-03-01

Dynamics of Nonlinear Rossby Waves With the Derivative-Expansion Method

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

More Information

Corresponding author: 刘全生(1979—), 男, 教授, 博士(通信作者. E-mail: smslqs@imu.edu.cn)

摘要

摘要: 非线性Rossby波是大尺度大气及海洋的典型波动现象. 由于所涉及问题的非线性, 主要考虑利用弱非线性方法-导数展开法, 研究广义β效应和基本流效应下的Rossby波动. 利用导数展开法能够同时抓住波动过程多尺度性的优点, 在微扰展开与久期项无关的情形下, 得到了刻画非线性波动振幅演化的非线性方程, 如Korteweg-de Vries方程、Boussinesq方程及Zakharov-Kuznetsov方程. 定性与定量分析表明, 广义β效应是诱导Rossby孤立波演化的关键因素.
- Rossby波 /
- 广义β效应 /
- 导数展开法 /
- 非线性方程
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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Figure 1. Evolutions of the total flow field with ν=0.254, k=2.5, $\epsilon$=0.3, $\bar{u}_0$=0.5, c₀=0.3 (KdV, case 1)

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Figure 2. Evolutions of the total flow field with k=2.5, $\epsilon$=0.3, $\bar{u}_0$=0.5, c₀=0.3 and different ν (KdV, case 1)

Note For color interpretation, refer to the online version. Hereafter the same.

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Figure 3. Evolutions of the total flow field with a₁=0.1, k=2, $\epsilon$=0.6, $\bar{u}_0$=0.7, c₀=0.3 (KdV, case 2)

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Figure 4. Evolutions of the total flow field with k=2, $\epsilon$=0.6, $\bar{u}_0$=0.7, c₀=0.3 and different a₁ (KdV, case 2)

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Figure 5. Evolutions of the total flow field with ν=0.254, A₀=4, $\epsilon$=0.6, $\bar{u}_{0}$=0.7, c₀=0.3 (mKdV, case 1)

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Figure 6. Evolutions of the total flow field with A₀=4, $\epsilon$=0.6, $\bar{u}_{0}$=0.7, c₀=0.3 and different ν (mKdV, case 1)

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Figure 7. Evolutions of the total flow field with A₀=1.5, a₁=0.1, $\epsilon$=0.3, $\bar{u}_{0}$=0.7, c₀=0.3 (mKdV, case 2)

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Figure 8. Evolutions of the total flow field with A₀=1.5, $\epsilon$=0.3, $\bar{u}_{0}$=0.7, c₀=0.3 and different a₁ (mKdV, case 2)

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Figure 9. Evolutions of the total flow field with ν=0.254, k=2.5, $\epsilon$=0.3, $\bar{u}_{0}$=0.5, c₀=0.3 (Boussinesq, case 1)

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Figure 10. Evolutions of the total flow field with k=2.5, $\epsilon$=0.3, $\bar{u}_{0}$=0.5, c₀=0.3 and different ν (Boussinesq, case 1)

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Figure 11. Evolutions of the total flow field with a₁=0.1, k=1, $\epsilon$=0.35, $\bar{u}_{0}$=0.7, c₀=0.3 (Boussinesq, case 2)

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Figure 12. Evolutions of the total flow field with k=1, $\epsilon$=0.35, $\bar{u}_{0}$=0.7, c₀=0.3 and different a₁ (Boussinesq, case 2)

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Figure 13. Evolutions of the total flow field with ν=0.254, k=1.5, ω=1.5, l=0.01, $\epsilon$=0.4, $\bar{u}_{0}$=0.7, c₀=0.3 (ZK, case 1)

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Figure 14. Evolutions of the total flow field with k=1.5, ω=1.5, l=0.01, $\epsilon$=0.4, $\bar{u}_{0}$=0.7, c₀=0.3 and different ν (ZK, case 1)

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Figure 15. Evolutions of the total flow field with a₁=0.1, k=1.5, ω=1.5, l=0.01, $\epsilon$=0.3, $\bar{u}_{0}$=0.9, c₀=0.3 (ZK, case 2)

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Figure 16. Evolutions of the total flow field with k=1.5, ω=1.5, l=0.01, $\epsilon$=0.3, $\bar{u}_{0}$=0.9, c₀=0.3 and different a₁ (ZK, case 2)

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