孤立Rossby波的fmKdV方程及其解析解  

fmKdV Equation for Solitary Rossby Waves and Its Analytical Solution

作　　者：陈利国 高菲菲 李琳琳 杨联贵[2] CHEN Liguo;GAO Feifei;LI Linlin;YANG Liangui(School of Statistics and Mathematics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China;School of Mathenatical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古财经大学统计与数学学院,内蒙古呼和浩特010070 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2021年第3期566-573,共8页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11762011);Research Program of Science at Universities of Inner Mongolia Autonomous Region,China(NJZY21272)。

摘　　要：本文基于刻画非线性Rossby波浅水模式的准地转位涡方程,利用约化摄动法,推导了强迫的修正Korteweg-de Vries(fm Kd V)方程.通过分析fm Kd V方程,得到基本地形是Rossby孤立波形成的主要因素,缓变地形是外强迫因素.除此之外,推广beta效应和基本剪切流也是孤立波形成重要因素.最后,利用广义形变映射法获得fm Kd V方程的解析解,结果表明缓变地形影响孤立波的速度,而耗散影响孤立波的速度和振幅.In this paper,based on the geostrophic potential vorticity equation of shallow water model describing the nonlinear Rossby wave,we derive a forced modified Korteweg-de Vries(fm Kd V)equation by utilizing the reduced perturbation method.By analyzing the fm Kd V equation,we can explicate the basic topography,which is an important factor for the formation of solitary Rossby waves,while slowly varying topography with time is an external forcing effect.Besides,the generalized bate and basic shear flow effect are also important factors in the generation of solitary waves.Finally,the analytical solution for the fm Kd V equation are presented by the general mapping deformation method.The results show that slowly varying topography with time only affects the speed of Rossby waves,dissipation affects both the amplitude and speed of Rossby waves.

关 键 词：ROSSBY波 fmKdV方程 缓变地形 耗散 广义形变映射法 

分 类 号：O29[理学—应用数学] O175.2[理学—数学]