We have seen that the zonal wind circulation of the giant planets is very vigorous. What is not so clear, however, is how these jets are initiated, maintained, and how deep into the interior these zonal winds extend. In this section we will review some the modeling work that has been done to understand the mean circulation of the giant planet atmospheres.
The Rhines length Lp was introduced in Section 5.3.1, in the context that vortices in a two-dimensional turbulent flow will grow via the inverse energy cascade until they reach a size comparable with the Rhines length, when they are then dissipated by Rossby waves. Rhines (1975) also realized that the variation off with latitude would lead to an elongation of such vortices in the east-west direction and that under certain circumstances the flow reorganizes itself into jets spaced by Lp. This idea has been extended by Vallis and Maltrud (1993).
Theories for the vertical structure of the jets range between two limiting scenarios (Vasavada and Showman, 2005). In one, the jets are modeled as being confined to a shallow "weather layer" near the visible cloud level, where absorption of sunlight and latent heat release from cloud formation would lead to thermal contrasts of the order of 5 K to 10 K, setting up vertical wind shears from the thermal wind equation. In such a model, cyclonic regions must be cold at depth in order to reduce the winds to zero and anticyclonic regions must be warm. This contrasts with the observed behavior above the clouds that cyclonic regions are warm and anticyclonic regions cold. The other limiting scenario for the jets is that they extend thoroughout the entire molecular-hydrogen interior.
To describe fully the various models of the global circulation of Jupiter and the other giant planets is beyond the scope of this book. While the main theories are introduced in the following sections, for a more complete treatment the reader is referred to more detailed works such as Vasavada and Showman (2005).
If the interior of a giant planet rotates at the same rotation rate at all levels then the deep atmosphere may be reasonably approximated as a fixed lower surface since the interior is adiabatic and has a huge mass. Any "weather" arising from differential heating and cooling is likely to be confined to the surface layers. Such shallow-layer models, adapted from terrestrial models, have provided a reasonable first analysis model at interpreting the dynamics of the giant planet atmospheres (e.g., Huang and Robinson, 1998; Williams, 1978, 1979, 1985, 1996, 2002, 2003a, b; Williams and Robinson, 1973). In such models, belts and zones appear spontaneously and there are examples of the kind of vortices found on the giant planets. However, a problem is that such models constantly need "pumping" with energy in order to keep them going, and soon disappear if the forcing is removed. In addition, the calculated outward thermal flux greatly exceeds that actually observed and jets resulting from such models are found to be stable with respect to the barotropic (or Rayleigh-Kuo) stability criterion, whereas the observed jets on Jupiter and Saturn have curvatures exceeding fl by a factor of 2-3. A further shortcoming of shallow-layer models is that they predict equatorial jets with a similar width to midlatitude jets, while the observed equatorial jets of Jupiter and Saturn are approximately twice as wide. Furthermore, the equatorial jets of Jupiter and Saturn are eastwards, while most shallow-layer models produce westward jets.
With all these shortcomings, shallow-layer models are the only models that have an asymmetry in that they favor organized anticyclonic vortices and disorganized cyclonic regions, much as is observed on Jupiter and the other giant planets. Hence, while there is evidence for a deep component to the zonal flow of the giant planets, as outlined in the following sections, some shallow-layer aspects appear to remain and the true flow probably lies somewhere between the shallow-layer and deep models.
While shallow-layer models are reasonably simple and are clearly applicable to the atmospheres of the terrestrial planets, the shallow weather layer theory of Jovian dynamics has suffered two setbacks since space age observation of the planetary atmospheres began. First of all, it is observed that although they experience differential solar heating, the giant planets have very little temperature variation with latitude, and any latitudinal variation that is present rapidly diminishes as the pressure increases. If zonal winds really were confined to the surface weather layer, then there must be large vertical wind shear below the cloud tops, and from the thermal wind equation an accompanying large variation in temperature with latitude, particularly for Saturn and Neptune, which have such high zonal winds. The low-temperature variation actually observed clearly suggests that the zonal wind structure is deep. For Saturn, zonal winds are estimated to extend to pressures of at least 10 bar (Smith et al., 1981). Similar low-temperature variations are found at Jupiter and, in addition, radio tracking of the Galileo entry probe (Young, 2003) allowed the direct determination of the deep wind structure at the edge of the 5 ^m hotspot it entered. Rather than decrease with depth, the winds were found to initially increase with depth and then tend to a constant value. However, this result must be qualified with the fact that the Galileo entry probe entered a somewhat anomalous region of the planet and thus conditions there may not be generally representative. The second major problem with the shallow weather layer model is that for Jupiter and Saturn (but not Uranus and Neptune) the rapidly varying zonal wind structure gives wind curvatures at the eastward jets that violate the barotropic instability (or Rayleigh-Kuo) criterion that fl — uyy should not change sign. Since the zonal wind structure in fact appears very stable, this violation would suggest either that the physical assumptions used in
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Re lot me rVelooty Profile deriving the criterion are invalid for Jovian atmospheres or that the shallow-layer model is not applicable. Hence, the zonal winds of the giant planets would appear to be deep—not shallow—and several other features in the giant planet atmospheres, discussed later, suggest significant coupling between the surface weather layer and the deep interior. Hence, a more complete picture of the giant planet atmospheres would appear to require the consideration of deep interior flows also.
One effect of giant planet rapid rotation on the interior fluid dynamics is the suppression of motion parallel to its rotation axis, known as the Taylor-Proudman effect (Busse, 1976, 1994, 2002; Ingersoll and Pollard, 1982) introduced earlier (Section 5.2.1). This tends to force the fluid to move as semi-rigid columns that are aligned with the rotation axis as shown in Figure 5.8. A remarkable experiment was performed on Spacelab 3 in 1985 (Hart et al., 1986), where a liquid confined between two hemispherical surfaces was spun about its own axis, with an electrostatic field used to simulate gravity. Under certain conditions a clear "banana cell'' convection flow was seen. The oblate-spheroidal shape of giant planets cause such columns to stretch as they move towards or away from the rotation axis and, via the conservation of angular momentum, this vortex tube stretching effect is suggested to give rise to Rossby waves. An obvious consequence of this model is that atmospheric motions should be symmetric about the equator, which to a very good approximation they are. Thus to explain the zonal structure of the giant planet atmospheres it is possible to imagine Taylor-Proudman columns organizing themselves into a number of concentric cylinders, all rotating at slightly different rates. This theory elegantly explained the symmetric zonal structure of the giant planets and was also consistent with the findings of the Voyager missions that the zonal structure broke down at high latitudes and was replaced by chaotic overturning. The latitude where this occurred was found to be close to that where a cylinder just touching the metallic-molecular
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