Planetary Circulations: 1. Barotropic Representation of Jovian and Terrestrial Turbulence

Gareth P. Williams Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, NJ 08540

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Abstract

We seek the formative processes of the planetary circulations of Jupiter and Saturn. The study concentrates on examining whether processes known to control the terrestrial circulation, namely, two-dimensional turbulence and baroclinic instability, can produce Jovian circulations under Jovian conditions. The first numerical model involves a spherical barotropic vorticity equation subjected to a stochastic representation of baroclinic processes. The resulting solutions suggest that a strong affinity exists between the Jovian and terrestrial circulations. This leads to a reevaluation of terrestrial circulation theory from the broader perspective of parameter space.

The solutions in the Jovian regime support the hypothesis that a variation of the Rhines effect—an interaction of the two-dimensional turbulence cascade and Rossby wave propagation—creates the pseudoaxisymmetry and scale Lβ=π(2U/β)½ of the bands (U is the rms zonal velocity, and β the northward gradient of the Coriolis force). The anisotropy of the interaction produces zonally oriented flows, composed of a series of alternating easterly and westerly jets, between which lie characteristic ovals. Equatorial jets occur readily when vorticity sources that lie symmetrically about the equator act on the atmosphere. Frictionally induced Ekman circulations provide a possible mechanism for cloud formation.

Integrations with terrestrial parameters support Kuo’s (1951) forced vorticity-transfer theory for the Earth’s circulation: westerly jets form in the forced midlatitude zones, and Rossby-wave propagation from those zones causes the broad easterly trade winds. Enstrophy cascade and β effects control the formation of momentum converging eddy patterns. Lβ also provides a measure of the width of the terrestrial jet. Cascade blocking by a stronger surface drag prevents terrestrial flows from approaching the same degree of zonality as Jovian ones.

Jupiter also appears to be dynamically equivalent to a hypothetical (or primeval) global ocean that has neither continental boundaries nor surface winds.

Abstract

We seek the formative processes of the planetary circulations of Jupiter and Saturn. The study concentrates on examining whether processes known to control the terrestrial circulation, namely, two-dimensional turbulence and baroclinic instability, can produce Jovian circulations under Jovian conditions. The first numerical model involves a spherical barotropic vorticity equation subjected to a stochastic representation of baroclinic processes. The resulting solutions suggest that a strong affinity exists between the Jovian and terrestrial circulations. This leads to a reevaluation of terrestrial circulation theory from the broader perspective of parameter space.

The solutions in the Jovian regime support the hypothesis that a variation of the Rhines effect—an interaction of the two-dimensional turbulence cascade and Rossby wave propagation—creates the pseudoaxisymmetry and scale Lβ=π(2U/β)½ of the bands (U is the rms zonal velocity, and β the northward gradient of the Coriolis force). The anisotropy of the interaction produces zonally oriented flows, composed of a series of alternating easterly and westerly jets, between which lie characteristic ovals. Equatorial jets occur readily when vorticity sources that lie symmetrically about the equator act on the atmosphere. Frictionally induced Ekman circulations provide a possible mechanism for cloud formation.

Integrations with terrestrial parameters support Kuo’s (1951) forced vorticity-transfer theory for the Earth’s circulation: westerly jets form in the forced midlatitude zones, and Rossby-wave propagation from those zones causes the broad easterly trade winds. Enstrophy cascade and β effects control the formation of momentum converging eddy patterns. Lβ also provides a measure of the width of the terrestrial jet. Cascade blocking by a stronger surface drag prevents terrestrial flows from approaching the same degree of zonality as Jovian ones.

Jupiter also appears to be dynamically equivalent to a hypothetical (or primeval) global ocean that has neither continental boundaries nor surface winds.

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