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Angular Momentum and Temperature Homogenization in the Symmetric Circulation of the Atmosphere

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  • 1 Scripps Institution of Oceanography, La Jolla, California
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Abstract

The axisymmetric model of the Hadley circulation can be systematically reduced in the limit of small Rossby number to a simpler one-dimensional system. The reduced system governs the nonlinear evolution of the surface angular momentum and the vertically averaged potential temperature. The meridional transports of heat and angular momentum take the form of downgradient nonlinear diffusion, which acts to homogenize laterally the angular momentum and the potential temperature within the meridional Hadley cells. The diffusivities for both quantities are proportional to the square of the latitudinal gradient of potential temperature. The reduced system is amenable to analytic exploration and allows the explicit determination of the extent and strength of the meridional circulation in terms of the parameters of the problem, such as the Rossby number, the stratification imposed by the radiative–convective equilibrium, and the surface drag. The reduced system also shows that surface easterlies at the equator are possible even when the heating distribution is latitudinally symmetric, as long as the surface drag or the imposed stratification are small.

* Additional affiliation: Instituto FISBAT–CNR, Bologna, Italy.

Corresponding author address: Dr. Paola Cessi, Scripps Institution of Oceanography, UCSD-0230, La Jolla, CA 92093-0230.

Email: cessi@hank.ucsd.edu

Abstract

The axisymmetric model of the Hadley circulation can be systematically reduced in the limit of small Rossby number to a simpler one-dimensional system. The reduced system governs the nonlinear evolution of the surface angular momentum and the vertically averaged potential temperature. The meridional transports of heat and angular momentum take the form of downgradient nonlinear diffusion, which acts to homogenize laterally the angular momentum and the potential temperature within the meridional Hadley cells. The diffusivities for both quantities are proportional to the square of the latitudinal gradient of potential temperature. The reduced system is amenable to analytic exploration and allows the explicit determination of the extent and strength of the meridional circulation in terms of the parameters of the problem, such as the Rossby number, the stratification imposed by the radiative–convective equilibrium, and the surface drag. The reduced system also shows that surface easterlies at the equator are possible even when the heating distribution is latitudinally symmetric, as long as the surface drag or the imposed stratification are small.

* Additional affiliation: Instituto FISBAT–CNR, Bologna, Italy.

Corresponding author address: Dr. Paola Cessi, Scripps Institution of Oceanography, UCSD-0230, La Jolla, CA 92093-0230.

Email: cessi@hank.ucsd.edu

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