一般多层准地转基本流的扰动发展与非线性稳定性  

Disturbance Evolution and Nonlinear Stability for a General Multilayer Quasi-Geostrophic Model

作　　者：宋士吉[1] 刘家琦[2] 刘秦玉[3] 

机构地区：[1]东南大学自动化研究所,南京210096 [2]哈尔滨工业大学数学系,哈尔滨150001 [3]青岛海洋大学物理海洋研究所,青岛266003

出　　处：《大气科学》2000年第3期412-426,共15页Chinese Journal of Atmospheric Sciences

摘　　要：考察了一般多层准地转模式中初值与参数共同扰动的情形。在初始扰动场仅依赖于初始扰动位势涡度、初始扰动边界速度环量与扰动参数的条件下 ,给出了扰动能量、扰动位涡拟能发展上 (下 )界精细的显式估计。进而在Lyapunov意义下广义非线性稳定性概念的基础上 ,得到了对应于Arnold第二定理的非线性稳定性判据。本文工作推广了仅考虑模式中初值扰动情形所得到的相应结果。The status of disturbance of both initial values and parameters in the model is investigated, and the exact estimations of the disturbance energy and disturbance potential enstrophy are given, when the initial disturbance fields depend only on the initial disturbance enstrophy, initial disturbance velocity circulation along the boundary, and the disturbance parameters. And based on the concept of generalized nonlinear stability in the sense of Lyapunov, the nonlinear stability criteria paralleling to Arnold's second theorem are obtained. The results of this paper generalize the findings, in which only the initial value disturbances are considered.

关 键 词：准地转运动 初值 扰动 非线性稳定性 位势涡度 

分 类 号：P433[天文地球—大气科学及气象学]