Ocean Notions for Jovian Motions
Jupiter's multiple wind currents, observed in December 2000 by the Cassini spacecraft, pose an outstanding puzzle for the theory of planetary fluid dynamics. Winds at the equator blow steadily eastward in excess of 200mph, while higher latitudes show an alternating pattern of westward and eastward jet streams of some 50-100mph. Jupiter's ammonia ice clouds, visible near the 1-bar level (at pressures similar to those at Earth's surface), are almost ideally marked with spots, waves, and eddies which can be tracked, timed, and plotted as wind maps. Yet the brightly reflective ammonia deck, variably colored with sulfides or other trace compounds, almost completely obscures the temperature, composition, and meteorology at deeper levels where the circulation is likely to be driven, perhaps over 100 miles below the level of visible features.
Unlike the Earth and the other inner planets of the Solar System, Jupiter has no solid surface, and emits more heat from its gravitationally contracting interior than its cloud-tops absorb from the sun. This internal heating likely causes Jupiter's deep atmosphere to be turbulent, like a heated pot of water on a stove. The upper weather layer directly under the visible cloud-tops may be padded, however, by a stable layer beneath it, imposed either by thermal radiation welling up from below or by the heat released at deep levels where water vapor changes to a liquid. Consistent with this view, data transmitted by the Galileo atmospheric probe during its 1995 descent into Jupiter's equatorial zone indicated a trend toward more stable layering with increasing depth, as well as a larger-downward abundance of detected water, but only at levels just above the termination of its mission.
Our attempt to understand the maintenance and deep structure of Jupiter's cloud-top wind currents must therefore confront a dilemma comparable to that of dynamical oceanographers working in the first half of the twentieth century. Lacking detailed and extensive measurements of the deep temperature, flow and composition, our models must begin with some restrictive assumptions about the deep circulation as it connects to the observed levels at the top. Encouraged by the oceanographic example, I have taken for my study of the Jovian circulation a page from the dynamical lore of the mid-Atlantic Gulf Stream, as modeled with an assumed smoothing of a special quantity called the "potential vorticity."
Potential vorticity (PV) measures the combined effects of thermal layering and rotation on observed fluid motions. For the ocean, the PV can be represented as the total fluid rotation, including the local vertical component of the planet's spin, divided by the thickness of an upper moving layer. The depth of the rapidly moving, relatively warm Gulf Stream, specifically the uppermost layer warmer than about 63°F, increases from nearly zero some twenty miles off the Carolina shore, to roughly 1600ft one hundred miles to the east, out toward the Sargasso Sea. The region of rapidly varying, downward-colder temperature just below the Stream is called the thermocline. The westward decrease of its upper-layer thickness, with a stronger-vertical layering of temperature toward the shore, appears to be compensated by a westward increase in the northward current speed. As pointed out by the famous oceanographer Henry Stommel in 1965, to the extent that the PV is nearly uniform across the stream, its variable depth can be mathematically related to the measured current speed, in good agreement with deep soundings of the thermocline by survey ships.
This kind of relationship between deep temperatures and currents would also be helpful in understanding the motion of Jupiter's atmosphere, where it is difficult to see through the upper cloud deck. I have constructed a mathematical example of this idea, assuming a simple vertical-latitudinal arrangement of the Jupiter thermocline, consistent with an assumed deep wind layer above a convectively turbulent interior, and a smooth equator-to-pole variation of the associated PV. The results of the model calculation are shown in Figure 2, which charts Jupiter's latitude and depth structure in terms of color-shaded surfaces of "potential temperature" (with blue the atmospheric analog to cold water). The super-imposed solid contours, deeply graded toward the equator, represent the calculated current speeds, with winds stronger-upward by a fixed amount from one curve to the next. As with Stommel's model for the Gulf Stream, regions of stronger deep layering coincide with stronger flow, with a horizontal scale of variation directly related to the deep thermal contrast.
Someday, these ideas could be tested with a light-weight spacecraft equipped with a multi-channel microwave sensor. Since Jupiter's thermal radiation at 10-100 cm wavelengths originates at levels below the cloud-tops, such an instrument could effectively "see" the variable structure of the planet's deep flowing thermocline.
Allison, M. 2000. A similarity model for the windy Jovian thermocline. Planet. Space Sci. 48, 753-774.
Stommel, H. 1965. The Gulf Stream: A Physical and Dynamical Description. Univ. of California Press.
Please address all inquiries about this research to Dr. Michael Allison.