Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment

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.

Temperature Structures Associated with Different Components of the Atmospheric Circulation on Tidally Locked Exoplanets

“…f r and f d are computed from the time-resolved model output, but time-averaged diagnostics are presented for simplicity. Time averaging means the effect of transient eddies (potentially arising due to barotropic and/or baroclinic instabilities; Read et al 2020) on the decomposed height fields is not shown in our analysis. However, we would like to stress that the nonlinear balance given by Equation (19) holds locally in time.…”

Exploring Jupiter's Polar Deformation Lengths with High-resolution Shallow Water Modeling

“…Andrews (1984) found that Arnol'd-type stability can only occur for zonally symmetric cases. However, Carnevale & Shepherd (1990) and Mu & Wu (2001) provided further extensions to the theorem, although the restrictions are nontrivial (Read et al 2020). Here we only include this analysis as a means to study the stable or unstable behavior of the long-term trends in our simulations.…”

Barotropic instability of a time-dependent parallel flow

“…Pedlosky 1987; Vallis 2006; Read et al. 2020). No attempt is made to review the entire field and the following discussion is focused on a subset of results that pertain directly to the present investigation.…”