大尺度浅水波方程中相互调制的非线性波  

Nonlinear intermodulation waves of large-scale shallow water equations

作　　者：毛杰健[1] 杨建荣[1] 

机构地区：[1]上饶师范学院物理与电子系,上饶334001

出　　处：《物理学报》2013年第13期47-51,共5页Acta Physica Sinica

基　　金：江西省自然科学基金(批准号:2009GZW0026);国家自然科学基金(批准号:10905038;11275123)资助的课题~~

摘　　要：基于一般的浅水波方程,根据大尺度正压大气的特点,得到无量纲的控制大尺度大气的动力学非线性方程组.利用多尺度法,由无量纲的动力学方程组导出了扰动位势的非线性控制方程.采用椭圆方程构造该扰动位势控制方程的解,获得了扰动位势和速度的多周期波与冲击波(爆炸波)并存的解析解.扰动位势的解表明经向和纬向具有不同周期和波长的周期波,且都受纬向孤波的调制;速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象.According to the general shallow water equations, the nondimensional nonlinear dynamic equations are obtained that can describe large-scale barotropic atmosphere. Using multi-scale method, a nonlinear controlling equation for disturbed height （or pressure） field is deduced. Applying elliptic equation to construct the solutions of the controlling equation, the analytic solutions of the disturbed height field and velocity are obtained, which include the multiply periodic waves and shock （explosive） waves. The solutions of the disturbed height field present periodic waves with different periodicity and wavelength along longitude and latitude, which are modulated by the solitary waves of latitude. The velocity solutions display that in the large-scale air flows exist periodic distribution phenomena of cyclone and anticyclone.

关 键 词：浅水波方程 大尺度正压大气 解析解 非线性波 

分 类 号：O175[理学—数学]