| 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 |
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| 引用本文： | 赵强,刘式适.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[J].地球物理学报,2006,49(4):965-970. |
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| 作者姓名： | 赵强 刘式适 |
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| 作者单位： | 北京大学物理学院大气科学系，北京 100871 |
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| 基金项目： | 国家自然科学基金项目（40475023）资助. |
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| 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.
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| 关 键 词： | Petviashvili方程 雅可比椭圆函数 Rossby波 |
| 文章编号： | 0001-5733（2006）04-0965-06 |
| 收稿时间： | 2005-03-07 |
| 修稿时间： | 2005-03-072006-02-10 |
Application of Jacobi elliptic functions in the atmospheric and oceanic dynamics: studies on two-dimensional nonlinear Rossby waves |
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| ZHAO Qiang,LIU Shi-Kuo.Application of Jacobi elliptic functions in the atmospheric and oceanic dynamics: studies on two-dimensional nonlinear Rossby waves[J].Chinese Journal of Geophysics,2006,49(4):965-970. |
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| Authors: | ZHAO Qiang LIU Shi-Kuo |
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| Institution: | Department of Atmospheric Sciences, School of Physics, Peking University, Beijing 100871, China |
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| Abstract: | 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. |
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| Keywords: | Petviashvili equation Jacobi elliptic function Rossby wave |
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