旋转层结流体中垂直切变基本流、β效应、地形效应和强迫耗散共同作用下的Rossby波  

Rossby Waves Under the Influence of the Vertical Shear of Basic Flow Beta Effect Forcing Dissipation and Topographic Effect in the Rotational Stratified Fluid

作　　者：赵波[1] 杨联贵[1] 宋健[2] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古自治区呼和浩特010021 [2]内蒙古工业大学理学院,内蒙古自治区呼和浩特010051

出　　处：《应用数学》2017年第2期424-433,共10页Mathematica Applicata

基　　金：国家自然科学基金(11362012);国家自然科学基金青年科学基金(11202092,11301259);内蒙古工业大学科学研究基金(ZD201411)

摘　　要：本文运用摄动法和WKB方法(多尺度方法),从位涡守恒方程出发,分析旋转层结大气中基本流有垂直切变以及层结效应对β效应、地形效应和强迫耗散共同作用下的Rossby波的影响,得到一个非标准形式的非线性Schr?dinger方程,而在水平波数小于3时该方程有包络孤立波解;又进一步说明基本流的垂直切变对包络Rossby孤立波的波速的影响;强迫耗散对包络Rossby孤立波稳定度的影响.另外,本文还应用常数变异法求解了非齐次的Bessel方程,得到包络Rossby孤立波的经向结构.In this paper, based on perturbation method and WKB method as well as the quasigeostrophic potential vorticity equation, we analyze the influence of the vertical shear of basic flow and stratification effect on Rossby waves including forcing dissipation and beta effect topographic effect in the rotational stratified atmosphere. As a consequence, we obtain a nonlinear nonstandard Schr¨odinger equation. There is an envelope solitary wave solution when the wavenumber of Rossby envelope solitary waves is less than 3. Thus, we obtain that the vertical shear of basic flow had an influence on the wave velocity of Rossby envelope solitary waves and that the forcing dissipation on the stability of Rossby envelope solitary waves. We also obtain the longitude structure of Rossby envelope solitary waves from nonhomogeneous Bessel equation by using constant variation method.

关 键 词：非线性SCHRODINGER方程 包络Rossby孤立波 基本流垂直切变 层结效应 

分 类 号：O368[理学—流体力学]