Turbulent convection in rapidly rotating spherical shells: A model for equatorial and high latitude jets on Jupiter and Saturn

The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths—a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors.     

Stability of jets on Jupiter and Saturn

The linear stability of a zonal jet that decays with depth is investigated under the assumption that the thermal stratification is very small. A westerly cosine jet is found to be more stable than it is in a thin fluid shell with two-dimensional flow. This is in agreement with observations of Jupiter and Saturn, where jet curvature exceeds the barotropic stability criterion. This result constitutes an alternative hypothesis to that of Ingersoll and Pollard [Icarus 52 (1982) 62], who showed that deep jets extending through the interior are also more stable than thin shell jets. The flow regime assumed in the present work requires that a small stratification can exist and persist even in the presence of horizontal temperature gradients. Further work will be needed to test whether this is realistic.     

Phosphine on Jupiter and Saturn from Cassini/CIRS

The global distribution of phosphine (PH₃) on Jupiter and Saturn is derived using 2.5 cm⁻¹ spectral resolution Cassini/CIRS observations. We extend the preliminary PH₃ analyses on the gas giants [Irwin, P.G.J., and 6 colleagues, 2004. Icarus 172, 37-49; Fletcher, L.N., and 9 colleagues, 2007a. Icarus 188, 72-88] by (a) incorporating a wider range of Cassini/CIRS datasets and by considering a broader spectral range; (b) direct incorporation of thermal infrared opacities due to tropospheric aerosols and (c) using a common retrieval algorithm and spectroscopic line database to allow direct comparison between these two gas giants.The results suggest striking similarities between the tropospheric dynamics in the 100-1000 mbar regions of the giant planets: both demonstrate enhanced PH₃ at the equator, depletion over neighbouring equatorial belts and mid-latitude belt/zone structures. Saturn's polar PH₃ shows depletion within the hot cyclonic polar vortices. Jovian aerosol distributions are consistent with previous independent studies, and on Saturn we demonstrate that CIRS spectra are most consistent with a haze in the 100-400 mbar range with a mean optical depth of 0.1 at 10 μm. Unlike Jupiter, Saturn's tropospheric haze shows a hemispherical asymmetry, being more opaque in the southern summer hemisphere than in the north. Thermal-IR haze opacity is not enhanced at Saturn's equator as it is on Jupiter.Small-scale perturbations to the mean PH₃ abundance are discussed both in terms of a model of meridional overturning and parameterisation as eddy mixing. The large-scale structure of the PH₃ distributions is likely to be related to changes in the photochemical lifetimes and the shielding due to aerosol opacities. On Saturn, the enhanced summer opacity results in shielding and extended photochemical lifetimes for PH₃, permitting elevated PH₃ levels over Saturn's summer hemisphere.     

Renewed acceleration of the 24° N jet on Jupiter

Jupiter's eastward jet at 24° N, which formerly had the fastest winds on the planet, has maintained a less extreme speed of ∼135 m/s since 1991, carrying a series of long-lived vortices at 125 m/s. In 2002-2003, as the albedo of the adjacent North Temperate Belt increased, the tracks of the vortices accelerated slightly, and they had disappeared by 2005. In 2005, small tracers had a mean speed of 146.4 (±0.9) m/s, significantly faster than the previous mean speed of the jet, suggesting that the jet peak itself has accelerated at cloud-top level, and that the jet is beginning to return to the super-fast state. These changes may resemble the even greater transformations occurring in the equatorial jet of Saturn.     

Jupiter and Saturn rotation periods

Anderson and Schubert [2007. Saturn's Gravitational field, internal rotation, and interior structure. Science 317, 1384-1387 (paper I)] proposed that Saturn's rotation period can be ascertained by minimizing the dynamic heights of the 100 mbar isosurface with respect to the geoid; they derived a rotation period of 10 h 32 m 35 s. We investigate the same approach for Jupiter to see if the Jovian rotation period is predicted by minimizing the dynamical heights of its isobaric (1 bar pressure level) surface using zonal wind data. A rotation period of 9 h 54 m 29.7 s is found. Further, we investigate the minimization method by fitting Pioneer and Voyager occultation radii for both Jupiter and Saturn. Rotation periods of 9 h 55 m 30 s and 10 h 32 m 35 s are found to minimize the dynamical heights for Jupiter and Saturn, respectively. Though there is no dynamical principle requiring the minimization of the dynamical heights of an isobaric surface, the successful application of the method to Jupiter lends support to its relevance for Saturn.We derive Jupiter and Saturn rotation periods using equilibrium theory to explain the difference between equatorial and polar radii. Rotation periods of 9 h 55 m 20 s and 10 h 31 m 49 s are found for Jupiter and Saturn, respectively. We show that both Jupiter's and Saturn's shapes can be derived using solid-body rotation, suggesting that zonal winds have a minor effect on the planetary shape for both planets.The agreement in the values of Saturn's rotation period predicted by the different approaches supports the conclusion that the planet's period of rotation is about 10 h 32 m.     

A three-dimensional model of moist convection for the giant planets II: Saturn's water and ammonia moist convective storms

Moist convective storms constitute a key aspect in the global energy budget of the atmospheres of the giant planets. Among them, Saturn is known to develop the largest scale convective storms in the Solar System, the Great White Spots (GWS) which occur rarely and have been detected once every 30 years approximately. On the average, Saturn seems to show much less convective storms than Jupiter with smaller size and reduced frequency and intensity. Here we present detailed simulations of the onset and development of storms at the Equator and mid-latitudes of Saturn. These are the regions where most of the recent convective activity of the planet has been observed. We use a 3D anelastic model with parameterized microphysics (Hueso and Sánchez-Lavega, 2001, Icarus 151, 257) studying the onset and evolution of water and ammonia moist convective storms up to sizes of a few hundred km. Water storms, while more difficult to initiate than in Jupiter, can be very energetic, arriving to the 150 mbar level and developing vertical velocities on the order of 150 m s⁻¹. Ammonia storms develop easier but with a much smaller intensity unless very large abundances of ammonia (10 times solar) are present in Saturn's atmosphere. The Coriolis forces play a major role in the morphology and properties of water based storms.     

Constraints on deep-seated zonal winds inside Jupiter and Saturn

The atmospheres of Jupiter and Saturn exhibit strong and stable zonal winds. How deep the winds penetrate unabated into each planet is unknown. Our investigation favors shallow winds. It consists of two parts. The first part makes use of an Ohmic constraint; Ohmic dissipation associated with the planet's magnetic field cannot exceed the planet's net luminosity. Application to Jupiter (J) and Saturn (S) shows that the observed zonal winds cannot penetrate below a depth at which the electrical conductivity is about six orders of magnitude smaller than its value at the molecular-metallic transition. Measured values of the electrical conductivity of molecular hydrogen yield radii of maximum penetration of 0.96RJ and 0.86RS, with uncertainties of a few percent of R. At these radii, the magnetic Reynolds number based on the zonal wind velocity and the scale height of the magnetic diffusivity is of order unity. These limits are insensitive to difficulties in modeling turbulent convection. They permit complete penetration along cylinders of the equatorial jets observed in the atmospheres of Jupiter and Saturn. The second part investigates how deep the observed zonal winds actually do penetrate. As it applies heuristic models of turbulent convection, its conclusions must be regarded as tentative. Truncation of the winds in the planet's convective envelope would involve breaking the Taylor-Proudman constraint on cylindrical flow. This would require a suitable nonpotential acceleration which none of the obvious candidates appears able to provide. Accelerations arising from entropy gradients, magnetic stresses, and Reynolds stresses appear to be much too weak. These considerations suggest that strong zonal winds are confined to shallow, stably stratified layers, with equatorial jets being the possible exception.     

Deep jets on gas-giant planets

Three-dimensional numerical simulations of the atmospheric flow on giant planets using the primitive equations show that shallow thermal forcing confined to pressures near the cloud tops can produce deep zonal winds from the tropopause all the way down to the bottom of the atmosphere. These deep winds can attain speeds comparable to the zonal jet speeds within the shallow, forced layer; they are pumped by Coriolis acceleration acting on a deep meridional circulation driven by the shallow-layer eddies. In the forced layer, the flow reaches an approximate steady state where east-west eddy accelerations balance Coriolis accelerations acting on the meridional flow. Under Jupiter-like conditions, our simulations produce 25 to 30 zonal jets, similar to the number of jets observed on Jupiter and Saturn. The simulated jet widths correspond to the Rhines scale; this suggests that, despite the three-dimensional nature of the dynamics, the baroclinic eddies energize a quasi-two-dimensional inverse cascade modified by the β effect (where β is the gradient of the Coriolis parameter). In agreement with Jupiter, the jets can violate the barotropic and Charney-Stern stability criteria, achieving curvatures ^∂2u/∂y² of the zonal wind u with northward distance y up to 2β. The simulations exhibit a tendency toward neutral stability with respect to Arnol'd's second stability theorem in the upper troposphere, as has been suggested for Jupiter, although deviations from neutrality exist. When the temperature varies strongly with latitude near the equator, our simulations can also reproduce the stable equatorial superrotation with wind speeds greater than . Diagnostics show that barotropic eddies at low latitudes drive the equatorial superrotation. The simulations also broadly explain the distribution of jet-pumping eddies observed on Jupiter and Saturn. While idealized, these simulations therefore capture many aspects of the cloud-level flows on Jupiter and Saturn.     

Merging circulations on Jupiter: Observed differences between cyclonic and anticyclonic mergers

The dynamics of mergers of large circulations in Jupiter's atmosphere may permit different models of the atmosphere to be tested. We report well-resolved observations of such events at visible wavelengths: three anticyclonic and three cyclonic events. A merger of anticyclonic white ovals in the South South Temperate domain (2002 March) is compared with the previously reported merger of ovals BE and FA in the South Temperate domain (2000 March). In each case, the two similar-sized ovals converged rapidly once they were separated by less than the sum of their diameters; they orbited around each other anticyclonically during the merger; the merged oval initially had the same rapid drift as the western parent; and, in an unexpected similarity, a cyclonic oval emerged westward from the point of merger. Evidence suggests that a merger of smaller ovals in the North North Temperate domain (2002 February) had similar dynamics. In contrast, mergers of cyclonic ovals in the North Equatorial Belt (‘barges’: 2001 November, 2005 May) proceeded in a different manner. The two parent barges showed no consistent acceleration towards each other as they converged; on contact there was no obvious sign of mutual circulation, and the low-albedo regions had almost passed each other before they finally merged; and the resulting barge had a drift rate intermediate between the two parents, and a length that was greater than either parent. Again, a third such event involving a smaller barge (2002 December) showed many of the same characteristics. These observations define different dynamical behaviour during anticyclonic and cyclonic mergers.     

Saturn eddy momentum fluxes and convection: First estimates from Cassini images

We apply an automated cloud feature tracking algorithm to estimate eddy momentum fluxes in Saturn's southern hemisphere from Cassini Imaging Science Subsystem near-infrared continuum image sequences. Voyager Saturn manually tracked images had suggested no conversion of eddy to mean flow kinetic energy, but this was based on a small sample of <1000 wind vectors. The automated procedure we use for the Cassini data produces an order of magnitude more usable wind vectors with relatively unbiased sampling. Automated tracking is successful in and around the westward jet latitudes on Saturn but not in the vicinity of most eastward jets, where the linearity and non-discrete nature of cloud features produces ambiguous results. For the regions we are able to track, we find peak eddy fluxes and a clear positive correlation between eddy momentum fluxes and meridional shear of the mean zonal wind, implying that eddies supply momentum to eastward jets and remove momentum from westward jets at a rate . The behavior we observe is similar to that seen on Jupiter, though with smaller eddy-mean kinetic energy conversion rates per unit mass of atmosphere (). We also use the appearance and rapid evolution of small bright features at continuum wavelengths, in combination with evidence from weak methane band images where possible, to diagnose the occurrence of moist convective storms on Saturn. Areal expansion rates imply updraft speeds of over the convective anvil cloud area. As on Jupiter, convection preferentially occurs in cyclonic shear regions on Saturn, but unlike Jupiter, convection is also observed in eastward jet regions. With one possible exception, the large eddy fluxes seen in the cyclonic shear latitudes do not seem to be associated with convective events.     

Zonal jets in rotating convection with mixed mechanical boundary conditions

Large-scale zonal flows, as observed on the giant planets, can be driven by thermal convection in a rapidly rotating spherical shell. Most previous models of convectively-driven zonal flow generation have utilized stress-free mechanical boundary conditions (FBC) for both the inner and the outer surfaces of the convecting layer. Here, using 3D numerical models, we compare the FBC case to the case with a stress free outer boundary and a non-slip inner boundary, which we call the mixed case (MBC). We find significant differences in surface zonal flow profiles produced by the two cases. In low to moderate Rayleigh number FBC cases, the main equatorial jet is flanked by a strong, high-latitude retrograde jets in the northern and southern hemispheres. For the highest Rayleigh number FBC case, the equatorial jet is flanked by strong reversed jets as well as two additional large-scale alternating jets at higher latitudes. The MBC cases feature stronger equatorial jets but, much weaker, small-scale alternating zonal flows are found at higher latitudes. Our high Rayleigh number FBC results best compare with the zonal flow pattern observed on Jupiter, where the equatorial jet is flanked by strong retrograde jets as well as small-scale alternating jets at high latitude. In contrast, the MBC results compare better with the observed flow pattern on Saturn, which is characterized by a dominant prograde equatorial jet and a lack of strong high latitude retrograde flow. This may suggest that the mechanical coupling at the base of the jovian convection zone differs from that on Saturn.     

Life cycles of spots on Jupiter from Cassini images

Using the sequence of 70-day continuum-band (751 nm) images from the Cassini Imaging Science System (ISS), we record over 500 compact oval spots and study their relation to the large-scale motions. The ∼100 spots whose vorticity could be measured—the large spots in most cases—were all anticyclonic. We exclude cyclonic features (chaotic regions) because they do not have a compact oval shape, but we do record their interactions with spots. We distinguish probable convective storms from other spots because they appear suddenly, grow rapidly, and are much brighter than their surroundings. The distribution of lifetimes for spots that appeared and disappeared during the 70-day period follows a decaying exponential with time constant (mean lifetime) of 3.5 days for probable convective storms and 16.8 days for all other spots. Extrapolating the exponential beyond 70 days seriously underestimates the number of spots that existed for the entire 70-day period. This and other evidences (size, shape, distribution in latitude) suggest that these long-lived spots with lifetime larger than 70 days are from a separate population. The zonal wind profile obtained manually by tracking individual features (this study) agrees with that obtained automatically by correlating brightness variations in narrow latitude bands (Porco et al., 2003). Some westward jets have developed more curvature and some have developed less curvature since Voyager times, but the number of westward jets that violate the barotropic stability criterion is about the same. In the northern hemisphere the number of spots is greatest at the latitudes of the westward jets, which are the most unstable regions according to the barotropic stability criterion. During the 70-day observation period the Great Red Spot (GRS) absorbed nine westward-moving spots that originated in the South Equatorial Belt (SEB), where most of the probable convective storms originate. Although the probable convective storms do not directly transform themselves into westward-moving spots, their common origin in the SEB suggests that moist convection and the westward jet compose a system that has maintained the GRS over its long lifetime.     

Deep zonal winds can result from shallow driving in a giant-planet atmosphere

A simple model shows that acceleration of Jupiter and Saturn's multiple jets at altitudes confined near the top of the adiabatic region (e.g., at a few bars pressure) can produce jets that penetrate deeply into the molecular envelope. This result disproves the common assertion that jet acceleration near the outer margin can only produce zonal winds that are confined to these outer layers.     

Interaction between eddies and mean flow in Jupiter's atmosphere: Analysis of Cassini imaging data

Beebe et al. [Beebe, R.F., et al., 1980. Geophys. Res. Lett. 17, 1-4] and Ingersoll et al. [Ingersoll, A.P., et al., 1981. J. Geophys. Res. 86, 8733-8743] used images from Voyagers 1 and 2 to analyze the interaction between zonal winds and eddies in Jupiter's atmosphere. They reported a high positive correlation between Jupiter's eddy momentum flux, , and the variation of zonal velocity with latitude, . This correlation implied a surprisingly high rate of conversion of energy from eddies to zonal flow: , a value more than 10% of Jupiter's thermal flux emission. However, Sromovsky et al. [Sromovsky, L.A., et al., 1982. J. Atmos. Sci. 39, 1413-1432] argued that possible biases in the analysis could have caused an artificially high correlation. In addition, significant differences in the derived eddy flux between datasets put into question the robustness of any one result. We return to this long-standing puzzle using images of Jupiter from the Cassini flyby of December 2000. Our method is similar to previous analyses, but utilizes an automatic feature tracker instead of the human eye. The number of velocity vectors used in this analysis is over 200,000, compared to the 14,000 vectors used by Ingersoll et al. We also find a positive correlation between and and derive a global average power per unit mass, , ranging from . Utilizing Ingersoll et al.'s estimate of the mass per unit area involved in the transport, this would imply a rate of energy conversion of . We discuss the implications of this result and employ several tests to demonstrate its robustness.     

Gravitational signature of rotationally distorted Jupiter caused by deep zonal winds

Both deep zonal winds, if they exist, and the basic rotational distortion of Jupiter contribute to its zonal gravity coefficients J_n for n ? 2. In order to capture the gravitational signature of Jupiter that is caused solely by its deep zonal winds, one must take into account the full effect of rotational distortion by computing the coefficients J_n in non-spherical geometry. This represents a difficult and challenging problem because the widely-used spherical-harmonic-expansion method becomes no longer suitable. Based on the model of a polytropic Jupiter with index unity, we compute Jupiter’s gravity coefficients J₂, J₄, J₆, … , J₁₂ taking into account the full effect of rotational distortion of the gaseous planet using a finite element method. For the model of deep zonal winds on cylinders parallel to the rotation axis, we also compute the variation of the gravity coefficients ΔJ₂, ΔJ₄, ΔJ₆, … , ΔJ₁₂ caused solely by the effect of the winds in non-spherical geometry. It is found that the effect of the zonal winds on lower-order coefficients is weak, ∣ΔJ_n/J_n∣ < 1%, for n = 2, 4, 6, but it is substantial for the high-degree coefficients with n ? 8.     

Long slit spectropolarimetry of Jupiter and Saturn

We present ground-based limb polarization measurements of Jupiter and Saturn consisting of full disk imaging polarimetry for the wavelength 7300 Å and spatially resolved (long-slit) spectropolarimetry covering the wavelength range 5200-9350 Å.For the polar region of Jupiter we find for λ = 6000 Å a very strong radial (perpendicular to the limb) fractional polarization with a seeing corrected maximum of about +11.5% in the South and +10.0% in the North. This indicates that the polarizing haze layer is thicker at the South pole. The polar haze layers extend down to 58° in latitude. The derived polarization values are much higher than reported in previous studies because of the better spatial resolution of our data and an appropriate consideration of the atmospheric seeing. Model calculations demonstrate that the high limb polarization can be explained by strongly polarizing (p ≈ 1.0), high albedo (ω ≈ 0.98) haze particles with a scattering asymmetry parameter of g ≈ 0.6 as expected for aggregate particles of the type described by West and Smith (West, R.A., Smith, P.H. [1991]. Icarus 90, 330-333). The deduced particle parameters are distinctively different when compared to lower latitude regions.The spectropolarimetry of Jupiter shows a decrease in the polar limb polarization towards longer wavelengths and a significantly enhanced polarization in strong methane bands when compared to the adjacent continuum. This is a natural outcome for a highly polarizing haze layer above an atmosphere where multiple scatterings are suppressed in absorption bands. For lower latitudes the fractional polarization is small, negative, and it depends only little on wavelength except for the strong CH₄-band at 8870 Å.The South pole of Saturn shows a lower polarization (p ≈ 1.0-1.5%) than the poles of Jupiter. The spectropolarimetric signal for Saturn decrease rapidly with wavelength and shows no significant enhancements in the fractional polarization in the absorption bands. These properties can be explained by a vertically extended stratospheric haze region composed of small particles <100 nm as suggested previously by Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2005]. Icarus 179, 195-221).In addition we find in the V- and R-band a previously not observed strong polarization feature (p = 1.5-2.0%) near the equator of Saturn. The origin of this polarization signal is unclear but it could be related to a seasonal effect.Finally we discuss the potential of ground-based limb polarization measurements for the investigation of the scattering particles in the atmospheres of Jupiter and Saturn.     

Phase separation in giant planets: inhomogeneous evolution of Saturn

We present the first models of Jupiter and Saturn to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium and other admixtures. We find that prior calculated phase diagrams in which Saturn's interior reaches a region of predicted helium immiscibility do not allow enough energy release to prolong Saturn's cooling to its known age and effective temperature. We explore modifications to published phase diagrams that would lead to greater energy release, and propose a modified H-He phase diagram that is physically reasonable, leads to the correct extension of Saturn's cooling, and predicts an atmospheric helium mass fraction Y_atmos=0.185, in agreement with recent estimates. We also explore the possibility of internal separation of elements heavier than helium, and find that, alternatively, such separation could prolong Saturn's cooling to its known age and effective temperature under a realistic phase diagram and heavy element abundance (in which case Saturn's Y_atmos would be solar but heavier elements would be depleted). In none of these scenarios does Jupiter's interior evolve to any region of helium or heavy-element immiscibility: Jupiter evolves homogeneously to the present day. We discuss the implications of our calculations for Saturn's primordial core mass.     

Lightning storms on Saturn observed by Cassini ISS and RPWS during 2004-2006

We report on Cassini Imaging Science Subsystem (ISS) data correlated with Radio and Plasma Wave Science (RPWS) observations, which indicate lightning on Saturn. A rare bright cloud erupt at ∼35° South planetocentric latitude when radio emissions (Saturn Electrostatic Discharges, or SEDs) occur. The cloud consisting of few consecutive eruptions typically lasts for several weeks, and then both the cloud and the SEDs disappear. They may reappear again after several months or may stay inactive for a year. Possibly, all the clouds are produced by the same atmospheric disturbance which drifts West at 0.45 °/day. As of March 2007, four such correlated visible and radio storms have been observed since Cassini Saturn Orbit Insertion (July 2004). In all four cases the SEDs are periodic with roughly Saturn's rotation rate (h¹⁰m³⁹), and show correlated phase relative to the times when the clouds are seen on the spacecraft-facing side of the planet, as had been shown for the 2004 storms in [Porco, C.C., and 34 colleagues, 2005. Science 307, 1243-1247]. The 2000-km-scale storm clouds erupt to unusually high altitudes and then slowly fade at high altitudes and spread at low altitudes. The onset time of individual eruptions is less than a day during which time the SEDs reach their maximum rates. This suggests vigorous atmospheric updrafts accompanied by strong precipitation and lightning. Unlike lightning on Earth and Jupiter, where considerable lightning activity is known to exist, only one latitude on Saturn has produced lightning strong enough to be detected during the two and a half years of Cassini observations. This may partly be a detection issue.     

Time-dependent flexure of the lithospheres on the icy satellites of Jupiter and Saturn

Previous analyses into flexural deformation on the icy satellites of Jupiter and Saturn have assumed static, elastic lithospheres. Viscous creep within the lithosphere, however, can cause evolution over time. Here, we apply a finite-element model that employs a time-dependent elastic–viscous-plastic rheology in order to investigate flexure on icy satellites. Factors that affect this time-dependent response are those that control creep rates; surface temperature, heat flow, and grain size. Our results show that surface temperature is by far the dominant factor. At higher surface temperatures (100–130 K), the evolution of the deformation is such that the thickness of a modeled elastic lithosphere could vary by up to an order of magnitude, depending on the time scale over which the deformation occurred. Because the flexure observed on icy satellites generally indicates transient high heat flow events, our results indicate that the duration of the heat pulse is an important factor. For the icy worlds of Jupiter and Saturn, static models of lithospheric flexure should be used with caution.     

Hadley circulations and Kelvin wave-driven equatorial jets in the atmospheres of Jupiter and Saturn

We propose a dynamical mechanism that can plausibly explain the origin of the broad prograde equatorial winds observed on Jupiter and Saturn, and examine the feasibility of this mechanism using two- (2D) and three-dimensional (3D) numerical simulation models. The idea is based on combining a narrow Gaussian jet peaking at the equator, which is induced by the momentum transfer from an upward propagating equatorial Kelvin-wave, and a pair of off-equatorial jets due to a meridional-vertical circulation similar to the tropical Hadley circulation on Earth. We employ for this feasibility study a 2D mechanistic mean-flow model which incorporates the influence of prescribed waves, and a 3D general circulation model, based on the generalised primitive equations of atmospheric motion. We then confirm that the dynamical models of both kinds can successfully reproduce theoretically expected flows of a reasonable magnitude, and that when two mechanisms are combined, a broad super-rotating jet is produced with off-equatorial maxima in zonal velocity for both Jupiter and Saturn, approximately in accordance with observations.