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

摘要/Abstract

摘要：

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Schrödinger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.

关键词: 完整Coriolis力, Rossby波, 高阶非线性Schrödinger方程, 调制不稳定性

Abstract:

In this paper, based on the barotropic potential vorticity equation with complete Coriolis force, a new higher order nonlinear Schrödinger 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.

Key words: Complete Coriolis force, Rossby waves, Higher order nonlinear Schrödinger equation, Modulational disturbances

中图分类号:

P315

王丹妮,杨红丽,杨联贵. 一类完整Coriolis力作用下的高阶非线性Schrödinger方程的推导[J]. 数学物理学报, 2018, 38(5): 883-892.

Danni Wang,Hongli Yang,Liangui Yang. Derivation of a Higher Order Nonlinear Schrödinger Equation with Complete Coriolis Force[J]. Acta mathematica scientia,Series A, 2018, 38(5): 883-892.

图/表 2

参考文献 34

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