Equation (5.59) may be solved for V to give
This is the gradient wind approximation and by convention V is taken as positive for cyclonic motion, negative for anticyclonic motion, and R is positive and measured from the center of curvature. This equation has one cyclonic solution (low pressure in the center) and thus dp/dR is positive, but three anticyclonic solutions, two of which have high pressures in the center of the cyclone, but one that has low pressure at the center. Hence, by including the acceleration term, the symmetry between cyclones and anticyclones is broken, although it is not known if this also accounts for the observed cyclonic/anticyclonic asymmetry on the giant planets. Another reason for the greater number of anticyclones than cyclones might be that anticyclones are more stable under Jovian conditions and thus that cyclones rapidly become disrupted and break up. One reason for this may be that cyclones are more susceptible than anticyclones to moist convection (Dowling, 1997). As discussed in Section 5.2.2, the extra mass of an anticyclone depresses the atmospheric layers beneath it, whereas cyclones have the opposite effect and can raise deep moist air beyond its lifting condensation level. Hence, moist convection may be triggered which, if vigorous enough, may disrupt organized cyclonic circulation.
Much modeling has been done on long-lived eddies and, in addition, laboratory studies have been conducted with rotating annulus experiments (Section 5.4.1) to simulate a range of driving conditions (Read, 1986; Read and Hide, 1983, 1984). The GRS on Jupiter is the largest of the long-lived anticyclones observed on the giant planets and the way it is driven and sustained is the source of much debate. There are at least four possible driving mechanisms that have been considered: (1) barotropic shear; (2) baroclinic shear; (3) local forcing (e.g., moist convection, ortho-para conversion); and (4) capture and absorption of smaller eddies. Unfortunately the precise forcing mechanism is unclear, although the capture of smaller eddies would lead to the deposition of their momentum in the outer annulus of the GRS, whose observed width of roughly 300 km to 500 km is consistent with the smallest scale of observed eddies, and may be equal to the radius of deformation for Jupiter. While many studies concentrate on how such flows may be maintained against dissipation, another possibility is that the GRS is a "free mode" of the Jovian circulation system and thus needs very little driving against dissipative effects. If frictional forces on the giant planets really are as low as they appear to be then such vortices may appear spontaneously and be naturally long-lived (Lewis, 1988). Hence, for example, the GRS can be considered to be a giant "flywheel" which, rather than being difficult to drive, is actually rather difficult to stop!
The GRS may be a special case, but in a number of numerical simulations (e.g., Vasavada and Showman, 2005), jet instabilities can lead to the formation of up to — 10 mid-size vortices, which then undergo mergers to form fewer larger vortices. Such behavior is remarkably consistent with how Jupiter's white ovals were observed to form in 1939 (Section 5.5.2).
Once initiated, because of the ft-effect isolated vortices should be dispersed by Rossby waves, but this may be halted by their position between jets, from which some models suggest they may draw their energy (Achterberg and Ingersoll, 1994). Near the equator, where ft is greatest, the dispersion is so strong that vortices generally cannot survive (Showman and Dowling, 2000) and no vortices are seen within 10° of the equators of any of the giant planets.
In theoretical studies (e.g., Achterberg and Ingersoll, 1994; Yamazaki et al., 2004), isolated vortices tend to drift westwards, and in the absence of strong background winds, also drift equatorwards. Such equatorwards drifting is seen on Neptune (Section 5.8.2), but not on Jupiter, where such motion may be inhibited by the jet system. Furthermore, some studies show that thin vortices migrate more slowly than thick vortices and are more easily confined by jets (Williams, 1996). A small thickness would be more consistent with the observed dynamical lifetimes of most large vortices, and some studies (Dritschel et al., 1999) suggest that vortices are baroclinically unstable if their thickness exceeds their width by more than the order of f /NB, where f is the Coriolis parameter and NB is the Brunt-Vaisala frequency (Section 5.3.1). Putting in typical values for the Jovian atmosphere suggests that the GRS and white ovals extend no more than —500 km below the clouds.
While some vortices such as the GRS certainly appear to be isolated, other examples of ovals, such as the brown barges of Jupiter (discussed in Section 5.5.2), appear in regular chains suggesting a link with planetary-scale Rossby waves, perhaps through the Rhines effect (Section 5.3.1). Another example was the North Polar Spot (NPS) observed by Voyager 2 on Saturn and its associated North Polar Hexagon (NPH) wave. While it initially appeared as though the wave arose through deflection of the mean flow around the NPS, followed by subsequent oscillation, it may be that the NPS was just a manifestation of a global series of cyclones and anticyclones at this latitude with an accompanying, apparently wave-like flow around them. While the NPH has been seen again by Cassini (Baines et al., 2007b; Fletcher et al, 2008a), Cassini has not detected any associated North Polar spot during the current epoch. We will return to this topic is Section 5.6.3.
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