一类完整Coriolis力作用下的高阶非线性Schr?dinger方程的推导

Derivation of a Higher Order Nonlinear Schr?dinger Equation with Complete Coriolis Force

在正压流体中,从含有完整Coriolis力的准地转位涡方程出发,采用摄动展开的方法推导了,一类新的高阶非线性Schr?dinger方程,用于描述地球流体力学中的非线性调制Rossby波.从方程中,讨论了调制波列.结果表明,完整Coriolis力下的水平分量和地形会影响均匀Rossby波调制不稳定,并且不稳定.区域也会随着改变.此外,均匀基本流也是影响Rossby孤立波调制不稳定性的的重要因素.

In this paper, based on the barotropic potential vorticity equation with complete Coriolis force, a new higher order nonlinear Schrodinger equation is derived by using perturbation expansion method to describe nonlinear modulated Rossby waves in the geophysical fluid. From this equation, the modulational wave trains are discussed. It is found that the horizontal component term of Coriolis force and the topography term has an effect on the uniform Rossby wave trains and the instability region have changed. In addition, the uniform background basic flow does affect the modulational instability of solitary Rossby wave train.