Abstract. Baroclinic and barotropic instabilities are well known as the mechanisms responsible for the production of the dominant energy-containing eddies in the atmospheres of Earth and several other planets, as well as Earth's oceans. Here we consider insights provided by both linear and nonlinear instability theories into the conditions under which such instabilities may occur, with reference to forced and dissipative flows obtainable in the laboratory, in simplified numerical atmospheric circulation models and in the planets of our solar system. The equilibration of such instabilities is also of great importance in understanding the structure and energetics of the observable circulation of atmospheres and oceans. Various ideas have been proposed concerning the ways in which baroclinic and barotropic instabilities grow to a large amplitude and saturate whilst also modifying their background flow and environment. This remains an area that continues to challenge theoreticians and observers, though some progress has been made. The notion that such instabilities may act under some conditions to adjust the background flow towards a critical state is explored here in the context of both laboratory systems and planetary atmospheres. Evidence for such adjustment processes is found relating to baroclinic instabilities under a range of conditions where the efficiency of eddy and zonal-mean heat transport may mutually compensate in maintaining a nearly invariant thermal structure in the zonal mean. In other systems, barotropic instabilities may efficiently mix potential vorticity to result in a flow configuration that is found to approach a marginally unstable state with respect to Arnol'd's second stability theorem. We discuss the implications of these findings and identify some outstanding open questions.

中文翻译：

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行星大气中的斜压和正压不稳定性：能量学、平衡和调整

摘要。众所周知，斜压和正压不稳定性是在地球和其他几个行星的大气层以及地球海洋中产生占主导地位的含能量涡流的机制。在这里，我们考虑了线性和非线性不稳定性理论提供的对可能发生这种不稳定性的条件的见解，参考了在实验室、简化的大气环流数值模型和太阳系行星中可获得的强迫和耗散流。这种不稳定性的平衡对于理解大气和海洋可观测环流的结构和能量学也非常重要。关于斜压和正压不稳定性增长到大振幅和饱和的方式，同时还改变了它们的背景流和环境，已经提出了各种想法。尽管已经取得了一些进展，但这仍然是一个继续挑战理论家和观察家的领域。此处在实验室系统和行星大气的背景下探讨了这种不稳定性可能会在某些条件下将背景流调整为临界状态的概念。发现这种调整过程的证据与一系列条件下的斜压不稳定性有关，在这些条件下，涡流和纬向平均热传输的效率可以相互补偿，以维持纬向平均值中几乎不变的热结构。在其他系统中，正压不稳定性可以有效地混合势涡，以产生一种流动配置，该配置被发现接近于 Arnol'd 第二稳定性定理的边缘不稳定状态。我们讨论了这些发现的含义并确定了一些悬而未决的开放性问题。