摘要
7 分层流模式 假设有J薄层均匀流体,其上边界面、密度和速度分别由Z_k;ρ_k和V_k表示,k=1,2,…,J(图3)。我们有如下的基本方程组 (曾庆存,1979):
Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is Universal for obtaining criteria of instability in ail models with all possible basic flows. For example, the model can be barotropic or baroclinic, layered or continuous, quasi-geostrophic or primitive equations! the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows show a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. It should be mentioned here that the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the end the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy,hence the variational principle can not be directly applied. However, a generalized Liapounoff norm can still be obtained on the basis of variationul consideration.
出处
《力学进展》
EI
CSCD
北大核心
1991年第1期70-82,共13页
Advances in Mechanics
关键词
大气运动
不稳定
变分原理
atmospheric motions
vanalional principle
instability
