雅可比椭圆函数在大气和海洋动力学中的应用:二维非线性Rossby波研究  

Application of Jacobi elliptic functions in the atmospheric and oceanic dynamics: studies on two-dimensional nonlinear Rossby waves

作　　者：赵强[1] 刘式适[1] 

机构地区：[1]北京大学物理学院大气科学系,北京100871

出　　处：《地球物理学报》2006年第4期965-970,共6页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(40475023)资助

摘　　要：提出了扩展雅可比椭圆函数方法,来求得Petviashvili方程的精确解析解.Petviashvili方程被视为正压准地转位涡度方程的非地转扩展,应用该方法可以得到很多二维非线性Rossby波的周期波解,在取极限情况下,也可以得到二维Rossby孤立子解.The two-dimensional （2-D） nonlinear Rossby waves described by the Petviashvili equation, which has been invoked as an ageostrophic extension of the barotropic quasi-geostrophic potential vorticity equation, can be studied by the exact periodic-wave solutions for the Petviashvili equation. The exact analytical periodic-wave solutions to the Petviashvili equation are obtained by using our extended generalization of Jacobi elliptic function expansion method. It is shown that more periodic-wave 2-D Rossby solutions can be obtained by this method. In the limit case, the 2-D Rossby soliton solutions can also be obtained.

关 键 词：Petviashvili方程 雅可比椭圆函数 ROSSBY波 

分 类 号：P433[天文地球—大气科学及气象学]