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

Abstract

The meridional temperature profile of the upper layers of planetary atmospheres is set through a balance between differential radiative heating by a nearby star, or by intrinsic heat fluxes emanating from the deep interior, and the redistribution of that heat across latitudes by turbulent flows. These flows spontaneously arise through baroclinic instability of the meridional temperature gradients maintained by the forcing. When planetary curvature is neglected, this turbulence takes the form of coherent vortices that mix the meridional temperature profiles. However, the curvature of the planet favors the emergence of Rossby waves and zonal jets that restrict the meridional wandering of the fluid columns, thereby reducing the mixing efficiency across latitudes. A similar situation arises in the ocean, where the baroclinic instability of zonal currents leads to enhanced meridional heat transport by a turbulent flow consisting of vortices and zonal jets. A recent scaling theory for the turbulent heat transport by vortices is extended to include the impact of planetary curvature, in the framework of the two‐layer quasi‐geostrophic beta‐plane model. This leads to a quantitative parameterization providing the meridional temperature profile in terms of the externally imposed heat flux in an idealized model of planetary atmospheres and oceans. In addition, it provides a quantitative prediction for the emergent criticality, that is, the degree of instability in a canonical model of planetary atmosphere or ocean.The turbulent motion of planetary atmospheres and oceans is greatly impacted by the curvature of the planet, which favors the emergence of Rossby waves and sharp zonal jets. These structures suppress meridional heat transport and impact the resulting thermal structure of the atmosphere or ocean. A quantitative scaling‐theory is derived that takes planetary curvature into account when predicting the turbulent heat transport. The theory provides a quantitative parameterization to determine the meridional temperature profile in a canonical model of planetary atmosphere or ocean subject to meridionally dependent heating. We derive a scaling theory for meridional heat transport in idealized planetary atmospheres and oceans, including planetary curvature The theory provides a quantitative parameterization to compute the meridional temperature profile in terms of the imposed heat flux The theory provides a quantitative prediction for the emergent criticality, that is, the degree of instability of the atmosphere or ocean