大气运动非线性稳定性研究中的能量-Casimir方法

介绍使用能量－Ｃａｓｉｍｉｒ方法（Ａｒｎｏｌ＇ｄ方法）研究大气与海洋运动非线性稳定性所取得的若干新进展，建立了适用于有限振幅、任意空间结构扰动的非线性稳定性判据．用初始状态给出了扰动场在任意时刻的上界与下界估计，提供了关于扰动变化性态的有关信息．对该领域理论研究与应用的深化与发展问题也作了讨论． 

ENERGY CASIMIR METHOD IN THE STUDY OF NONLINEAR STABILITY OF THE ATMOSPHERIC MOTIONS

This paper summarizes some recent advances in the study of nonlinear instability of the atmospheric and oceanic motions by using energy Casimir method(Arnol'd's method). Nonlinear stability criteria established for finite amplitude disturbance due to an arbitrary spatial structure are presented. Upper and lower bounds of the disturbance field in terms of the initial state are obtained,which provide the information on the behaviour of the evolution of the disturbance. The prospects of the further developmen...