Charney’s Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

Abstract

The Charney model is reexamined using a new mathematical tool, the multiscale window transform (MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ ≪ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning. The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ ≫ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ ≪ 1, however, barotropic and baroclinic instabilities are of the same order; in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.

摘 要

本研究使用一个新的泛函分析工具——多尺度子空间变换 (MWT) 和基于 MWT 的局地多尺度能量分析法研究了经典Charney模式中的局地稳定性结构和多尺度能量过程。传统上, Charney模式一直被认为是一个纯斜压的模式, 但我们研究发现该模式中实际上存在混合不稳定, 其中斜压不稳定主要位于模式的底层, 而正压不稳定存在于所有层次, 并且在斜压不稳定趋于消失的地方达到最强, 这正好对应着扰动气压场中等位相线由西倾转为垂直的高度。虽然传统的斜压不稳定解释了扰动的底部强化特征, 但扰动场中位于高层的次级中心只能用新发现的正压不稳定来解释 (尤其是当 Charney-Green参数 γ ≪ 1时)。此外, 我们还发现 Charney 模式中正压不稳定和斜压不稳定的相对大小随着参数γ的变化而变化:当 γ ≪ 1时, 正压不稳定与斜压不稳定具有相同量级、甚至超过斜压不稳定;而当 γ ≫ 1时, 正压不稳定可以忽略不计, 此时系统的不稳定性才可以视为是纯斜压的。