Equilibration of a Baroclinic Planetary Atmosphere toward the Limit of Vanishing Bottom Friction

Junyi Chai Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, New Jersey

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Malte Jansen Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois

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Geoffrey K. Vallis Department of Mathematics, University of Exeter, Exeter, United Kingdom

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Abstract

This paper discusses whether and how a baroclinic atmosphere can equilibrate with very small bottom friction in a dry primitive equation general circulation model. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and it is damped by a linear friction near the lower boundary. When friction is decreased by four orders of magnitude, kinetic energy dissipation by friction gradually becomes negligible, while “energy recycling” becomes dominant. In this limit kinetic energy is converted back into potential energy at the largest scales, thus closing the energy cycle without significant frictional dissipation. The momentum fluxes are of opposite sign in the upper and lower atmosphere: in the upper atmosphere, eddies converge momentum into the westerly jets; however, in the lower atmosphere, the eddies diverge momentum out of the westerly jets. The secondary circulation driven by the meridional eddy momentum fluxes thus acts to increase the baroclinicity of the westerly jet. This regime may be relevant for the Jovian atmosphere, where the frictional time scale may be much larger than the radiative damping time scale.

Corresponding author address: Junyi Chai, Atmospheric and Oceanic Sciences Program, Princeton University, 300 Forrestal Road, Sayre Hall, Princeton, NJ 08544. E-mail: junyic@princeton.edu

Abstract

This paper discusses whether and how a baroclinic atmosphere can equilibrate with very small bottom friction in a dry primitive equation general circulation model. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and it is damped by a linear friction near the lower boundary. When friction is decreased by four orders of magnitude, kinetic energy dissipation by friction gradually becomes negligible, while “energy recycling” becomes dominant. In this limit kinetic energy is converted back into potential energy at the largest scales, thus closing the energy cycle without significant frictional dissipation. The momentum fluxes are of opposite sign in the upper and lower atmosphere: in the upper atmosphere, eddies converge momentum into the westerly jets; however, in the lower atmosphere, the eddies diverge momentum out of the westerly jets. The secondary circulation driven by the meridional eddy momentum fluxes thus acts to increase the baroclinicity of the westerly jet. This regime may be relevant for the Jovian atmosphere, where the frictional time scale may be much larger than the radiative damping time scale.

Corresponding author address: Junyi Chai, Atmospheric and Oceanic Sciences Program, Princeton University, 300 Forrestal Road, Sayre Hall, Princeton, NJ 08544. E-mail: junyic@princeton.edu
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