基于导数展开法的非线性Rossby波动力学

田红晓; 张瑞岗; 刘全生

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:
田红晓(1981—)，女，讲师，硕士(E-mail: tianhongxiao@imust.edu.cn)；刘全生(1979—)，男，教授，博士(通信作者. E-mail: smslqs@imu.edu.cn).

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

中图分类号: O357.41
计量
- 文章访问数: 19
- HTML全文浏览量: 4
- PDF下载量: 7
- 被引次数: 0
出版历程
- 收稿日期: 2025-09-03
- 修回日期: 2025-12-18
- 网络出版日期: 2026-04-01
- 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

Funds:

The National Science Foundation of China(12262025)

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

HTML全文

参考文献(32)

[2]WHITHAM G B. Non-linear dispersion of water waves[J].Journal of Fluid Mechanics,1967,27(2): 399-412.

KAWAHARA T. The derivative-expansion method and nonlinear dispersive waves[J].Journal of the Physical Society of Japan,1973,35(5): 1537-1544.

[3]WHITHAM G B. Two-timing, variational principles and waves[J].Journal of Fluid Mechanics,1970,44(2): 373-395.

[4]WHITHAM G B. Variational methods and applications to water waves[J].Proceedings of the Royal Society of London (Series A): Mathematical and Physical Sciences,1967,299(1456): 6-25.

[5]LIGHTHILL M J. Contributions to the theory of waves in non-linear dispersive systems[J].IMA Journal of Applied Mathematics,1965,1(3): 269-306.

[6]DAVEY A. The propagation of a weak nonlinear wave[J].Journal of Fluid Mechanics,1972,53(4): 769-781.

[7]NAYFEH A H. Nonlinear oscillations in a hot electron plasma[J].The Physics of Fluids,1965,8(10): 1896-1898.

[8]PEDLOSKY J.Geophysical Fluid Dynamics[M]. 2nd ed. New York: Springer-Verlag, 1987.

[9]QIU Tianwei, WEI Guangmei, SONG Yuxin, et al. Study on new soliton solutions of KdV class equations based on PINN method[J].Applied Mathematics and Mechanics,2025,46(1): 105-113. (in Chinese)

[10]L K L, JIANG H S. Interaction of topography with solitary Rossby waves in a near-resonant flow[J].Acta Meteorologica Sinica,1997, (2): 204-215.

[11]LUO D H. Solitary Rossby waves with the beta parameter and dipole blocking[J].Journal of Applied Meteorological Science,1995,6(2): 220-227. (in Chinese)

[12]SONG J, YANG L G. Modified KdV equation for solitary Rossby waves with β effect in barotropic fluids[J].Chinese Physics B,2009,18(7): 2873-2877.

[13]LUO D H, JI L R.A theory of blocking formation in the atmosphere[J].Science in China,1989,33(3):323-333.

[14]YANG H, YANG D, SHI Y, et al. Interaction of algebraic Rossby solitary waves with topography and atmospheric blocking[J].Dynamics of Atmospheres and Oceans,2015,71: 21-34.

[15]GOTTWALLD G A. The Zakharov-Kuznetsov equation as a two-dimensional model for nonlinear Rossby wave[PP/OL]. arXin(2003-12-04)[2025-12-18］. https://arXiv.org/abs/nlin/0312009.

[16]WANG J, ZHANG R, YANG L. A Gardner evolution equation for topographic Rossby waves and its mechanical analysis[J].Applied Mathematics and Computation,2020,385: 125426.

[17]YU D, ZHANG Z, YANG H. A new nonlinear integral-differential equation describing Rossby waves and its related properties[J].Physics Letters A,2022,443: 128205.

[18]YU D, FU L, YANG H. A new dynamic model of ocean internal solitary waves and the properties of its solutions[J].Communications in Nonlinear Science and Numerical Simulation,2021,95: 105622.

[19]ZHANG J, ZHANG R, YANG L, et al. Coherent structures of nonlinear barotropic-baroclinic interaction in unequal depth two-layer model[J].Applied Mathematics and Computation,2021,408: 126347.

[20]SUN W, YANG J, TAN W, et al. Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean[J].Acta Oceanologica Sinica,2021,40(10): 1-16.

[21]TIAN R, ZHANG Z, ZHAO B, et al. A kind of new coupled model for rossby waves in two layers fluid[J].IEEE Access,2020,8: 146361-146375.

[22]ZHANG R, YANG L. Theoretical analysis of equatorial near-inertial solitary waves under complete Coriolis parameters[J].Acta Oceanologica Sinica,2021,40(1): 54-61.

[23]ZHAO B, WANG J. Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling[J].Advances in Mechanical Engineering,2023,15: 16878132221140212.

[24]LIU Nan, SONG Jian. Stable radiation baroclinic potential vortices under basic flow zonal shear[J].Applied Mathematics and Mechanics,2024,45(1): 120-126. (in Chinese)

[25]WANG C, LI J J, YANG H W. Modulation instability analysis of Rossby waves based on (2+1)-dimensional high-order Schrodinger equation[J].Communications in Theoretical Physics,2022,74(7): 075002.

[26]JI J, GUO Y, ZHANG L, et al. 3D variable coefficient KdV equation and atmospheric dipole blocking[J].Advances in Meteorology,2018,2018: 4329475.

[27]CHEN W K, YUAN C X. Application of variable coefficient KdV equation to solitary waves in the ocean[J].Periodical of Ocean University of China,2020,50(8): 19-24.

[28]ZHANG Z, CHEN L, ZHANG R, et al. Dynamics of Rossby solitary waves with time-dependent mean flow via Euler eigenvalue model[J].Applied Mathematics and Mechanics (English Edition), 2022,43(10): 1615-1630.

[29]SONG J, LIU Q S, YANG L G. Beta effect and slowly changing topography Rossby waves in a shear flow[J].Acta Physica Sinica,2012,61(21): 210510.

[30]ZHANG R G, YANG L G, SONG J, et al. Nonlinear Rossby waves near the equator with topog-raphy[J].Progress in Geophysics,2017,32(4):1532-1538.

[31]CHEN L, YANG L G. A nonlinear Boussinesq equation with external source and dissipation forcing under generalizedβ-plane approximation and its solitary wave solutions[J].Applied Mathematics and Mechanics,2020,41(1): 98-106. (in Chinese)

[32]YIN X J, YANG L G, LIU Q S, et al. The nonlinear(2+l) dimensional Zakharov-Kuznetsov equation and its solitary solution[J].Journal of Yunnan University(Natural Sciences Edition), 2018,40(4): 619-624.

施引文献

资源附件(0)

访问统计