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地球流体力学的不稳定性理论告诉我们,如果基流不稳定,那么叠加于其上的扰动可能要增长,对于不考虑粘性与外强迫的保守系统,这种增长是有限度的,这就是不稳定的饱和(Sat-uration).如何给出此类扰动的能量与位涡拟能(非平凡的)增长的上界估计,是一个重要问题.Shepherd提出了一种方法来研究这个问题:首先选择一族稳定基流,然后把叠加于不稳定基流之上的扰动分解成两部分:一部分是对选定的稳定基流的扰动,另一部分是选定的稳定基流对不稳定基流的偏差;利用对应于Arnol’d第一定理的稳定性判据及有关估计,再经过
The instability theory of the geodynamics of the earth tells us that if the base flow is not stable, the disturbance superimposed on it may increase, and this growth is limited for conservative systems that do not consider viscous and external coercion Sat-uration. How to give an estimate of the upper bound of the potential energy (non-trivial) growth of a potential vortex is an important issue. Shepherd proposed a method to study this problem: first A family of stable base flows is selected and then the perturbation superimposed on the unstable base flows is decomposed into two parts: one is the disturbance to the selected steady-state base flow and the other is the selected steady-state base flow to the unstable base flow Deviation; By using the stability criterion corresponding to Arnol’d’s first theorem and related estimates,