The Jovian atmosphere contains numerous examples of waves on a wide range of lengthscales. At the smallest scale, Flasar and Gierasch (1986) discovered waves in the equatorial region in Voyager images traveling east-west at the cloud tops with wavelengths of ^300 km, gathered together in wave packets of length ^ 1,300 km in the meridional direction and 3,000 km to 13,000 km in the zonal direction. These were interpreted as equatorially trapped modes with smaller gravity waves superimposed on them, perhaps generated by Kelvin-Helmholtz instabilities (Bosak and Ingersoll, 2002), and were most apparent at the edges of the equatorial jet at ±8°. A later Galileo observation of these waves (Belton et al., 1996) is shown in Figure 5.20. The interpretation of these features led to the suggestion of a statically stable duct beneath the NH3 cloud deck and this hypothesis was later supported by Galileo probe temperature measurements (Seiff et al., 1998), although the Galileo probe entered a 5 ^m hotspot, which may not be very representative of mean near-equatorial conditions. These mesoscale gravity waves were observed again during the New Horizons flyby throughout the equatorial region within about 5° of the equator, during a time when the equatorial region was unusually cloud-free. By assessing their visibility in different spectral channels it is possible to conclude that they are formed at altitudes above the 600 mbar level. Their wavelength was measured to be 330 km, consistent with earlier determinations and they have a phase speed of ~250ms-1. Unfortunately this speed is inconsistent with current theories of how they are formed!

At larger, planetary scales, waves have been detected in both thermal maps of Jupiter (Deming et al., 1989, 1997; Magalhaes et al., 1989, 1990; Orton et al., 1991, 1994) and in the planetary variation of cloud opacity as determined by emission at 5 ^m (Harrington et al., 1996; Ortiz et al., 1998). A near-stationary wavenumber-9 wave was discovered by Magalhaes et al. (1989, 1990) from Voyager IRIS data in the upper troposphere at 270 mbar near 15°N, and a similar wavenumber-11 wave was observed at 20°N at 45 ^m (which sounds down to 1 bar in the absence of clouds). Similar wavenumber-10 waves were observed by Deming et al. (1989) from ground-based observations (8-13 ^m), again at 20°N and also at the equator. Ground-based observations at 7.8 ^m (Orton et al., 1991), sounding temperatures at ~20mbar, found near-stationary waves at ±20°, which were interpreted as planetary waves generated by instabilities in the strong cloud top prograde jets at ±18°. The near-stationary appearance of these waves with respect to System III implies some sort of dynamical link with the interior bulk rotation of the planet. Observations by Orton et al. (1994) at 18 ^m, which sounds the 250 mbar temperatures, found waves at 13°N in the NEB at the same time as the wave previously mentioned in the stratosphere near 20°N. Both disturbances appeared to have a zonal group velocity of -5.5ms"1 with respect to System III longitude and there appeared to be some correlation with height implying vertical propagation of a Rossby wave. A later study by Deming et al. (1997) found such waves to be ubiquitous at near-equatorial latitudes with wave-numbers anywhere between 2 and 15. The amplitude of thermal waves in the lower stratosphere (20 mbar) sounded at 7.8 ^m was found to be roughly 3x greater than thermal waves in the upper troposphere (250 mbar), sounded at 18 ^m. The waves at these two altitudes appear to be correlated and the amplitude growth is consistent with a p-11/2-dependence expected for vertically propagating Rossby gravity waves. By analyzing the amplitude of these stationary Rossby waves, Deming et al. (1997) infer latitudinal deflections of only 1°, which may arise from interaction with the interior "banana cell" (Section 5.4.1) convective structure or through interaction with

Figure 5.20. Two images of Jupiter's atmosphere recorded by Galileo SSI with the "violet" filter in 1996, centered at 15°S and 307°W. The pixel resolution is approximately 30 km. Mesoscale Kelvin-Helmholtz gravity waves can just be seen in the center of the upper image where they appear as a series of about 15 nearly vertical north-south stripes. The combined wave packet is about 300 km long and is aligned in the east-west direction. In the lower image, recorded 9 hours later, there is no indication of the waves, though the clouds appear to have been disturbed. Such waves were also seen by the Voyager spacecraft in 1979. Courtesy of NASA.

Figure 5.20. Two images of Jupiter's atmosphere recorded by Galileo SSI with the "violet" filter in 1996, centered at 15°S and 307°W. The pixel resolution is approximately 30 km. Mesoscale Kelvin-Helmholtz gravity waves can just be seen in the center of the upper image where they appear as a series of about 15 nearly vertical north-south stripes. The combined wave packet is about 300 km long and is aligned in the east-west direction. In the lower image, recorded 9 hours later, there is no indication of the waves, though the clouds appear to have been disturbed. Such waves were also seen by the Voyager spacecraft in 1979. Courtesy of NASA.

vortices, which are themselves moving slowly with respect to System III, sandwiched between easterly and westerly flow regions.

Waves have also been detected in ground-based images of Jupiter recorded at 5 ^m, a wavelength sensitive to the total cloud opacity above the warm 5 bar to 8 bar pressure regions and thus sensitive to the opacity of the expected ammonium hydro-sulfide and ammonia cloud decks. A number of waves were discovered at many latitudes (Harrington et al., 1996) including near-stationary Wavenumber-10 features at 7°N-8°N and eastward-propagating Wavenumber-4 waves at the equator. The former wave appears to be associated with the 5 ^m hotspots at the southern edge of the NEB, which appear to be distributed semi-uniformly with longitude, and are interspersed by highly reflective equatorial plumes lying between the hotspots and slightly to the south. These hotspots were studied by Ortiz et al. (1998) who concluded that they were manifestations of equatorially trapped Rossby waves. The 5 ^m hotspots are regions of very low cloud cover, which makes them appear very bright at IR wavelengths and dark at visible wavelengths. For some time these features were interpreted as being regions of rapid downdraft, which would explain their low cloud cover and also the observed depletion of volatiles such as ammonia and water. However, such models required excessive downdraft velocities and also predicted that the abundance of volatiles such as ammonia, water vapor, and hydrogen sulfide should all return to their "deep" abundances at roughly the same pressure level. Instead, the Galileo entry probe, which sampled just such a 5 ^m hotspot, found that the abundance of ammonia increased first as the probe descended, then H2S, then H2O which was still increasing at 20 bar when communication with the probe was lost. Hence, an alternative theory, that these hotspots are associated with a planetary-wave system that alternately compresses and expands the vertical air column, has been developed and extended with nonlinear modeling (Friedson, 1999; Showman and Dowling, 2000) and is currently the favored explanation. In this model, the bright anticyclonic regions (equatorial plumes) appear on the upward portion of the planetary wave concentrating volatiles at high altitudes, where they condense to form bright white clouds. The 5 ^m hotspots then appear on the downward portion of the wave, where the statically stable air column is vertically stretched, increasing the base pressure by a factor of almost 2. The accompanying adiabatic heating forces the clouds to sublimate and reduces the apparent volatile abundances, but retains the relative abundances of H2O, H2S, and NH3, which thus increase towards their deep values at different rates as observed by the Galileo probe. Showman and Dowling (2000) found that their modeled waves were only stable if large initial pressure perturbations were assumed, suggesting that nonlinear effects are central to the stability of this wave. Furthermore, the authors found that the zonal wind profile measured by the Galileo entry probe (Atkinson et al., 1998), which implies static stability in the troposphere consistent with the probe's atmospheric temperature experiment (Seiff et al., 1998), may in fact be a local effect. The vertical negative wind shear (winds decreasing with height) was reproduced by Showman and Dowling's model at the southern edge of their simulated hotspots (where the probe entered), but was zero in the center and positive at the northern edge implying that the measured wind profile may owe more to local dynamical effects than to the general zonal wind structure. The spectral signature of pure ammonia ice has been observed in the equatorial plumes (and in localized thunderstorm clouds seen in other cyclonic regions; Baines et al., 2002), which is not generally seen elsewhere. This is interpreted as being due to the rapid condensation of new ''fresh'' ammonia crystals in these regions, which are then subsequently degraded or coated with chromophores after a few days. A link between these waves and upper tropospheric properties was observed by Cassini ISS and can be seen in Figure 5.16 where a wavenumber-16 wave is clearly seen at 9°N-19°N in both the strong methane-absorbing band at 0.89 ^m and also in the accompanying UV image. Hence, the wave clearly extends into the upper troposphere and has an effect on either the abundance or reflecting properties of the haze particles (Porco et al., 2003). Several wavelike features were also visible in Cassini CIRS observations of atmospheric temperature (Flasar et al., 2004b). In the troposphere, within 15° of the equator, a weak variation of temperature with longitude has been seen, which may be associated with the waves thought to be driving the QQO, introduced in Section 5.3.2. Farther away from the equator, numerous chains of warm features are seen at a variety of latitudes. These features, below the tropopause, seem to be almost stationary with respect to the interior, and their cause is not known. At higher altitudes, in the stratosphere, many thermal waves were seen, some in the southern hemisphere with westward zonal velocity, suggesting that these are caused by planetary Rossby waves. Stratospheric waves are probably initiated by disturbances in the troposphere, but waves propagating vertically upwards should, to a first order, retain their zonal velocity. Hence, how westward-moving stratospheric waves are related to tropospheric stationary disturbances is mysterious.

One of the most striking features of Jovian stratospheric temperatures observed by Orton et al. (1991) was a periodic, approximately 4-year variation of the zonal temperature at 20mbar, known as the Quasi-Quadrennial Oscillation or QQO. This feature, which has been continuously observed since 1978, takes the form of a periodic warming of the equator and simultaneous cooling of latitudes between ±(15-30°), followed by a cooling of the equator and warming of the ±(15-30°) latitude band, with a period of between 2 and 5 years and an amplitude of 1 K to 2 K. During the cool equatorial phase, longitudinal structure has been observed in the northern band, which are the thermal waves mentioned earlier. The oscillation has also been observed in the upper troposphere (250 mbar) at equatorial latitudes by Orton et al. (1994), where the temperature oscillation is found to be roughly 180° out of phase with the stratosphere. Leovy et al. (1991) likened this variability to variation in the Earth's equatorial stratosphere known as the QBO (discussed in Section 5.3.2). However, Friedson (1999) found that this analysis underestimated the vertical and horizontal averaging of ground-based observations and that Leovy's identification of the driving waves as alternating equatorially trapped Kelvin and mixed Rossby gravity waves was not able to account for the amplitude of the oscillation observed. Instead, Friedson (1999) considered a wide range of equatorially trapped modes and found that forcing of the upper-tropospheric flow and lower-stratospheric flow by smaller scale internal gravity waves produced temperature variations much closer to those seen. However, Li and Read (2000) also modeled the QQO and found that the effect was sufficiently well modeled by alternating wavenumber 8-11 waves with an equatorial Rossby mode moving eastwards at around 100 m s-1 (or perhaps a Kelvin mode) and a mixed Rossby gravity wave stationary with respect to System III, apparently excited by a wave source moving with the zonal wind in the deep atmosphere. While these studies appear inconsistent, Li and Read (2000) did find that the identification of wave mode depended substantially on model assumptions and thus that more detailed nonlinear modeling might be necessary. Hence, while it seems likely that Jupiter's QQO is substantially like the Earth's QBO, the precise identification of the wave motions forcing it remains elusive.

Cassini CIRS made temperature measurements in the upper troposphere and stratosphere (Flasar et al., 2004b), which can be used with the thermal wind equation to probe winds in the stratosphere, providing we fix winds at the cloud top level to those determined by cloud tracking. Cassini CIRS found that the winds decrease with altitude in the upper troposphere as was previously determined by Voyager. However, at some latitudes (23°N, the equator, and 18°S), wind speeds were found to pick up again, especially at the equator, where a jet of 140 ms-1 was deduced at a pressure of 3mbar to 4mbar. It is thought that this stratospheric jet is related to the QQO.

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