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

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.