Abstract
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.
Highlights
One of the great achievements of the past 100 years in fluid dynamics has been the development of a theory of dynamical instability, both linear and nonlinear
Even though the equilibrated time-averaged flow continues to satisfy the Charney–Stern– Pedlosky (CSP) condition for instability, it has effectively stabilised the flow to a configuration that is close to marginal stability with regard to Arnol’d’s second stability condition, as a result of a process which can be regarded as a form of barotropic adjustment
Mars is arguably the most Earth-like planet elsewhere in the solar system, at least so far as its atmosphere and climate are concerned. It is roughly half the linear size of Earth with a rotation period of just over 24 h. It lies at a distance of around 1.3–1.5 astronomical units (AU) with an orbital period of around 687 d, and with a rotation axis tilted by approximately 25◦ from the perpendicular to its orbit, it experiences a strong seasonal cycle much like Earth
Summary
One of the great achievements of the past 100 years in fluid dynamics has been the development of a theory of dynamical instability, both linear and nonlinear. This has led to a quantitative understanding of a variety of phenomena, including the processes that lead to the development of large-scale energetic eddies in rotating, stratified atmospheres and oceans These instabilities, known as 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. In general they occur in flows for which background rotation plays an important role, while baroclinic instabilities require statically stable stratification.
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