切变纬向流中β效应与缓变地形Rossby波  

Beta effect and slowly changing topography Rossby waves in a shear flow

作　　者：宋健[1,2] 刘全生[1] 杨联贵[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古工业大学理学院,呼和浩特010051

出　　处：《物理学报》2012年第21期140-144,共5页Acta Physica Sinica

基　　金：国家自然科学基金青年科学基金(批准号:11202092);内蒙古自然科学基金(批准号:2011MS0112;2012MS0107)资助的课题~~

摘　　要：正压流体中,从有外源的准地转位涡方程出发,采用摄动方法和时空伸长变换推导了具有β效应、缓变地形和外源的Rossby孤立波方程,得到Rossby波振幅满足带有缓变地形与外源强迫的非齐次mKdV-Burgers方程的结论.通过分析孤立Rossby波振幅的演变,指出了β效应、地形效应以及外源都是诱导Rossby孤立波产生的重要因素;说明了在缓变地形强迫效应和非线性作用相平衡的假定下,Rossby孤立波振幅的演变满足非齐次mKdV-Burgers方程;给出在切变基本气流下缓变地形和正压流体中Rossby波的相互作用关系.In barotropic fluids, based on the quasi-geostrophic potential vorticity equation, an inhomogeneous mKdV-Burgers equation including slowly changing topography and an external source is derived by employing the perturbation method and stretching transforms of time and space. With the inspection of the evolution of the amplitude of Rossby waves, it is found that beta effect, topography effect, slowly changing topography and an external source are all the important factors, and that the solitary Rossby wave is induced thought the basic stream function has a shear flow. On the assumption that the nonlinear and topographic effects are in balance, an inhomogeneous mKdV-Burgers equation is derived, the results show that the topography and Rossby wave interact in the barotropic flows. The inhomogeneous mKdV-Burgers equation describing the evolution of the amplitude of solitary Rossby wave as the change of Rossby parameterβ（y） with latitude y, topographic forcing, slowly changing topography and the external source is obtained.

关 键 词：非齐次mKdV-Burgers方程 β效应 缓变地形 外源 

分 类 号：O35[理学—流体力学]