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 .

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.