A Quantitative Scaling Theory for Meridional Heat Transport in Planetary Atmospheres and Oceans

Abstract

The external fluid layers of planets and their satellites are subject to meridionally dependent heating due to incoming radiation from a distant star, or intrinsic heat fluxes emanating from the planetary interior. On a rocky planet without an atmosphere, such a heat source would induce a strong difference in surface temperature between the equator and the poles. The presence of an atmosphere and/or an ocean strongly mitigates that temperature difference: the meridional temperature gradient induces turbulence in these external fluid layers through a process called baroclinic instability. This baroclinic turbulence, much like a giant stirring spoon or convection in a heated pot of water, greatly enhances heat transport from the equator to the poles, thus reducing the emergent meridional temperature gradient. Predicting the equilibrated meridional temperature profile of these external fluid layers is arguably one of the central questions that a theory of climate should address. As shown in Figure 1, baroclinic turbulence is visible on the surface of Jupiter, where it takes the form of isolated vortices in the polar regions (panel 1a) while inducing coherent zonal jets at mid-latitude (panel 1b). This coexistence of jets and vortices also arises in the Southern Ocean, where baroclinic turbulence results from the instability of the meridional temperature gradient associated with the Antarctic Circumpolar Current: in the near-surface velocity map of panel 1c, ring-shaped structures correspond to isolated vortices, while the zonally elongated features correspond to zonal jets.The images in Figure 1 show that the equilibrated state of baroclinic turbulence consists of a turbulent flow whose energy containing scale-roughly estimated as the inter-vortex or inter-jet distance-is small

Turbulence Theory: Imperfect, but Necessary

“…For smaller scales (where planetary curvature is unimportant), the authors invoke ideas from vortex gas theory, whereas at larger scales the flow transitions into a regime of alternating zonal jets in which the meridional heat transport is rather inefficient. Combining these ideas (along with friction where necessary), Gallet and Ferrari (2021) arrive at a quantitative prediction of an eddy diffusivity that agrees very well with the simulations presented, albeit with the help of some empirical parameters. And along the way they provide a quantitative estimate of how effective the turbulence is at quenching the instabilities that give rise to it-the "supercriticality" of the flow, a previously rather controversial topic.…”

“…For smaller scales (where planetary curvature is unimportant), the authors invoke ideas from vortex gas theory, whereas at larger scales the flow transitions into a regime of alternating zonal jets in which the meridional heat transport is rather inefficient. Combining these ideas (along with friction where necessary), Gallet and Ferrari (2021) arrive at a quantitative prediction of an eddy diffusivity that agrees very well with the simulations presented, albeit with the help…”

“…But simulating individual weather systems is an inefficient way to proceed, for it is ludicrous to think we can predict individual systems a hundred years hence. One would prefer to predict the bulk properties of turbulence, just as we use statistical mechanics to predict the properties of an ideal gas, and that is what Gallet and Ferrari (2021) try to do.…”

“…In fact, the very nature of turbulence is that it involves multiple scales, for this is a consequence of the nonlinearity of the equations of motion: flow at one scale begets flow at another scale, be it bigger or smaller. Perhaps the most striking example of turbulence at large scales can be seen in the beautiful images from Juno, a space probe orbiting the giant planet Jupiter, as in Figure 1 of Gallet and Ferrari (2021).…”

“…If that inverse cascade is halted, either by frictional effects or by Rossby waves, before it reaches the scale of the mean flow then there is a scale separation and a diffusive theory becomes applicable. In common with previous investigators (notably Held & Larichev, 1996; Salmon, 1980), Gallet and Ferrari (2021) use a two‐layer quasi‐geostrophic model to investigate the problem, but their approach differs in how they treat the important aspect of the halting scale of the inverse cascade. For smaller scales (where planetary curvature is unimportant), the authors invoke ideas from vortex gas theory, whereas at larger scales the flow transitions into a regime of alternating zonal jets in which the meridional heat transport is rather inefficient.…”