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.     

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.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

The effects of vigorous mixing in a convective model of zonal flow on the ice giants

Previous studies have used models of three-dimensional (3D) Boussinesq convection in a rotating spherical shell to explain the zonal flows on the gas giants, Jupiter and Saturn. In this paper we demonstrate that this approach can also generate flow patterns similar to those observed on the ice giants, Uranus and Neptune. The equatorial jets of Uranus and Neptune are often assumed to result from baroclinic cloud layer processes and have been simulated with shallow layer models. Here we show that vigorous, 3D convection in a spherical shell can produce the retrograde (westward) equatorial flows that occur on the ice giants as well as the prograde (eastward) equatorial flows of the gas giants. In our models, the direction of the equatorial jet depends on the ratio of buoyancy to Coriolis forces in the system. In cases where Coriolis forces dominate buoyancy, cylindrical Reynolds stresses drive prograde equatorial jets. However, as buoyancy forces approach and exceed Coriolis forces, the cylindrical nature of the flow is lost and 3D mixing homogenizes the fluid's angular momentum; the equatorial jet reverses direction, while strong prograde jets form in the polar regions. Although the results suggest that conditions involving strong atmospheric mixing are responsible for generating the zonal flows on the ice giants, our present models require roughly 100 and 10 times the internal heat fluxes observed on Uranus and Neptune, respectively.     

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.     

Models of Jupiter and Saturn after Galileo mission

New models of Jupiter are based on observational data provided by the Galileo spaceprobe, which considerably improved previously existing estimates of the helium abundance in the atmosphere of Jupiter. These data yield for Jupiter’s atmosphere 20% of the solar oxygen abundance and do not agree with the results of the analysis of the collision of comet Shoemaker-Levy 9 with Jupiter (10 times the solar value). Therefore, both the models of Jupiter with water-depleted and water-enriched atmosphere are considered. By analogy with Jupiter, trial models of Saturn with a water-depleted external envelope are also developed. The molecular-metallic phase transition pressure of hydrogen P_m was taken to be 1.5, 2 and 3 Mbar. Since Saturn’s internal molecular envelope is noticeably enriched in the IR-component (its weight concentration, 0.25–0.30, being by a factor of 3–4 higher than in Jupiter), the phase transition pressure in Saturn can be lower than in Jupiter. In the constructed models, the IR-core masses are 3–3.5 M_⊕ for Jupiter and 3–5.5 M_⊕ for Saturn. Jupiter’s and Saturn’s IR-cores can be considered embryos onto which the accretion of the gas occurred during the formation of the planets. The mass of the hydrogen–helium component dispersed in the zone of planetary formation constitutes ≈2–5 planetary masses for Jupiter and ≈11–14 planetary masses for Saturn.     

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.     

Eddy mixing coefficient on Saturn

Data on the composition and thermal structure, and the Lyman-alpha dayglow of Saturn when analyzed in conjunction with photochemical models of the hydrocarbons and the atomic hydrogen production yield the homopause value of the eddy diffusion coefficient to be approximately 10⁸ cm² s^?1. The equatorial value of the eddy diffusion coefficient at the homopause of Saturn is thus found to be approximately 100 times greater than on Jupiter. The mesosphere (and presumably, troposphere) of Saturn appears to be considerably more turbulent than the upper atmosphere of Jupiter.     

Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009

Every three years the IAU Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets. This report takes into account the IAU Working Group for Planetary System Nomenclature (WGPSN) and the IAU Committee on Small Body Nomenclature (CSBN) definition of dwarf planets, introduces improved values for the pole and rotation rate of Mercury, returns the rotation rate of Jupiter to a previous value, introduces improved values for the rotation of five satellites of Saturn, and adds the equatorial radius of the Sun for comparison. It also adds or updates size and shape information for the Earth, Mars?? satellites Deimos and Phobos, the four Galilean satellites of Jupiter, and 22 satellites of Saturn. Pole, rotation, and size information has been added for the asteroids (21) Lutetia, (511) Davida, and (2867) ?teins. Pole and rotation information has been added for (2) Pallas and (21) Lutetia. Pole and rotation and mean radius information has been added for (1) Ceres. Pole information has been updated for (4) Vesta. The high precision realization for the pole and rotation rate of the Moon is updated. Alternative orientation models for Mars, Jupiter, and Saturn are noted. The Working Group also reaffirms that once an observable feature at a defined longitude is chosen, a longitude definition origin should not change except under unusual circumstances. It is also noted that alternative coordinate systems may exist for various (e.g. dynamical) purposes, but specific cartographic coordinate system information continues to be recommended for each body. The Working Group elaborates on its purpose, and also announces its plans to occasionally provide limited updates to its recommendations via its website, in order to address community needs for some updates more often than every 3 years. Brief recommendations are also made to the general planetary community regarding the need for controlled products, and improved or consensus rotation models for Mars, Jupiter, and Saturn.     

Comparative evolution of Jupiter and Saturn

We present evolutionary sequences for Jupiter and Saturn, based on new non-gray model atmospheres, which take into account the evolution of the solar luminosity and partitioning of dense components to deeper layers. The results are used to set limits on the extent to which possible interior phase separation of hydrogen and helium may have progressed in the two planets. When combined with static models constrained by the gravity field, our evolutionary calculations constrain the helium mass fraction in Jupiter to be between 0.20 and 0.27, relative to total hydrogen and helium. This is consistent with the Galileo determination. The helium mass fraction in Saturn’s atmosphere lies between 0.11 and 0.21, higher than the Voyager determination. Based on the discrepancy between the Galileo and Voyager results for Jupiter, and our models, we predict that revised observational results for Saturn will yield a higher atmospheric helium mass fraction relative to the Voyager value.     

Pressure-induced absorption by H2 in the atmosphere of Jupiter and Saturn

The S(1) line of the pressure-induced fundamental band of H₂ was identified and measured in the spectra of Saturn and Jupiter. This broad line at 4750 cm^?1 lies in a region free from telluric and planetary absorptions. It is about 99% absorbing in the core; the high-frequency wing extends to at least 5100 cm^?1. We compare the obseved line shape to the predictions of both a reflecting-layer model (RLM) and a homogeneous scattering model (HSM). The RLM provides a good fit to the Saturn line profile for temperatures near 150K; the derived base-level density is 0.52 (+0.26, ?0.17) amagat and the H₂ abundance is 25 (+10, ?9) km-amagat, assuming a scale height of 48 km. The Jupiter line profile is fit by both the RLM and HSM, but for widely differing temperatures, neither of which seems probable. The precise fitting of the observed S(1) line profile to computed models depends critically on the determination of the true continuum level; difficulties encountered in finding the continuum, especially for Jupiter, are discussed. Derived RLM densities and abundances for both planets are substantially lower than those derived from RLM analyses of the H₂ quadrupole lines, the 3ν₃ band of CH₄, and from other sources.     

The structure of the planets Jupiter and Saturn

Planetary models for Jupiter and Saturn are computed using a fourth-order theory and a new molecular equation of state. The equation of state for the molecular hydrogen and helium planetary envelopes is taken from the Monte Carlo calculations of Slattery and Hubbard [Icarus 29, 187–192 (1976)]. Models for Jupiter are found that have a small amount of heavy elements either mixed with hydrogen and helium throughout the interior of the planet or concentrated in a small dense core. Saturn is modeled with a solar-composition hydrogen and helium envelope and a small derse core. We conclude that the molecular equation of state linked with suitable interior equations of state can produce Jovian models which satisfy the observational data. The planetary models show that the enrichment of heavy elements (relative to solar composition) is approximately 3 times for Jupiter and 10 times for Saturn.     

Solar Cycle Effects on the Dynamics of Jupiter’s and Saturn’s Magnetospheres

The giant planetary magnetospheres surrounding Jupiter and Saturn respond in quite different ways, compared to Earth, to changes in upstream solar wind conditions. Spacecraft have visited Jupiter and Saturn during both solar cycle minima and maxima. In this paper we explore the large-scale structure of the interplanetary magnetic field (IMF) upstream of Saturn and Jupiter as a function of solar cycle, deduced from solar wind observations by spacecraft and from models. We show the distributions of solar wind dynamic pressure and IMF azimuthal and meridional angles over the changing solar cycle conditions, detailing how they compare to Parker predictions and to our general understanding of expected heliospheric structure at 5 and 9 AU. We explore how Jupiter’s and Saturn’s magnetospheric dynamics respond to varying solar wind driving over a solar cycle under varying Mach number regimes, and consider how changing dayside coupling can have a direct effect on the nightside magnetospheric response. We also address how solar UV flux variability over a solar cycle influences the plasma and neutral tori in the inner magnetospheres of Jupiter and Saturn, and estimate the solar cycle effects on internally driven magnetospheric dynamics. We conclude by commenting on the effects of the solar cycle in the release of heavy ion plasma into the heliosphere, ultimately derived from the moons of Jupiter and Saturn.     

Building the terrestrial planets: Constrained accretion in the inner Solar System

To date, no accretion model has succeeded in reproducing all observed constraints in the inner Solar System. These constraints include: (1) the orbits, in particular the small eccentricities, and (2) the masses of the terrestrial planets - Mars’ relatively small mass in particular has not been adequately reproduced in previous simulations; (3) the formation timescales of Earth and Mars, as interpreted from Hf/W isotopes; (4) the bulk structure of the asteroid belt, in particular the lack of an imprint of planetary embryo-sized objects; and (5) Earth’s relatively large water content, assuming that it was delivered in the form of water-rich primitive asteroidal material. Here we present results of 40 high-resolution (N = 1000-2000) dynamical simulations of late-stage planetary accretion with the goal of reproducing these constraints, although neglecting the planet Mercury. We assume that Jupiter and Saturn are fully-formed at the start of each simulation, and test orbital configurations that are both consistent with and contrary to the “Nice model”. We find that a configuration with Jupiter and Saturn on circular orbits forms low-eccentricity terrestrial planets and a water-rich Earth on the correct timescale, but Mars’ mass is too large by a factor of 5-10 and embryos are often stranded in the asteroid belt. A configuration with Jupiter and Saturn in their current locations but with slightly higher initial eccentricities (e = 0.07-0.1) produces a small Mars, an embryo-free asteroid belt, and a reasonable Earth analog but rarely allows water delivery to Earth. None of the configurations we tested reproduced all the observed constraints. Our simulations leave us with a problem: we can reasonably satisfy the observed constraints (except for Earth’s water) with a configuration of Jupiter and Saturn that is at best marginally consistent with models of the outer Solar System, as it does not allow for any outer planet migration after a few Myr. Alternately, giant planet configurations which are consistent with the Nice model fail to reproduce Mars’ small size.     

Typical Velocities and Magnetic Field Strengths in Planetary Interiors

Recent studies of convection-driven dynamos in the outer core of the Earth have improved our understanding of the dynamical regime in fluid planetary cores. We consider the possible dynamical regimes in the cores of the Earth, Jupiter, and Saturn, and hence we estimate the typical velocities and magnetic fields expected in their interiors. These estimates are in reasonable agreement with observations of the large-scale internal fields of those planets. We use the fully self-consistent anelastic MHD (magnetohydrodynamics) equations which have been developed for the Earth, while the details of similar systems for Jupiter and Saturn are specified here. The known heat and composition fluxes together with magnetic, Archimedean, and Coriolis force balance give us typical velocity, entropy, and composition strengths independent of the rather poorly known transport coefficients. Those turbulent diffusion and magnetic diffusion coefficients are also estimated from mixing length theory and compared with available numerical models and standard kinematic approaches.     

Addition of water and ammonia cloud microphysics to the EPIC model

An active hydrological cycle has been added to the EPIC general circulation model (GCM) for planetary applications, with a special emphasis on Jupiter. Scientists have suspected for decades that clouds, and in particular latent heating, strongly influence Jupiter's atmospheric dynamics and this research provides a tool to investigate this phenomenon. Components of the model have been adapted for the planetary setting from recently published Earth microphysics schemes. The behavior of the cloud model is investigated in two steps. First, we explore in detail the runtime properties of a nominal model, and second, through sensitivity tests we determine how the full microphysics and selected components of the scheme affect the formation and evolution of clouds and precipitation. Results from our one-dimensional (vertical) simulations match expectations based on thermochemical models about the vertical positioning of ammonia and water clouds, and the nature of precipitation. Using (two-dimensional) meridional plane simulations, we investigate the latitudinal variation of clouds. We conclude that the zonal-wind structure under the visible cloud deck strongly affects the position of the cloud bases, also that the atmospheric dynamics modifies the resulting cloud structure that we can determine in 1D models. We describe in detail an equatorial storm system observed in our 2D simulations. We also show that simplification of our microphysics scheme would improperly simulate large-scale weather phenomena on Jupiter. We support future laboratory tests and in situ measurements that would improve the cloud parameterization scheme and would also add more constraints on the global distribution of condensibles and on the zonal wind-structure. The complete computer program resulting from this research can be downloaded as open-source software from NASA's Planetary Data System (PDS) Atmospheres node.     

Radiative-convective equilibrium models of Jupiter and Saturn

Radiative-convective equilibrium models for Jupiter and Saturn have been produced in a study centered primarily on the stratospheric energy balance and the possible role of aerosol heating. These models are compared directly to the thermal structure profiles obtained from Voyager radio occultation measurements. The method is based on a straightforward flux divergence formulation derived from earlier work (J. S. Hogan, S. I. Rasool, and T. Encrenaz 1969, J. Atmos. Sci.26, 898–905). The balance between absorbed and emitted energies is computed iteratively at each level in the atmosphere, assuming local thermodynamic equilibrium and employing a standard treatment of opacities. Results for Jupiter indicate that a dust-free model (no aerosol heating) furnishes a good mean thermal profile for the stratosphere when compared with the Voyager 1 radio occultation (RSS) measurements. These observations of the equatorial region (0° and 12°S, respectively) exhibit periodic vertical structure. Of course, among many possible complications, the Voyager profiles may not represent typical excursions from the mean. The aerosol heat depositions required to match these profiles exactly, relative to the nominal dust-free model, are reasonably consistent with independent estimates for “continuum” absorbers. Other interpretations are discussed, along with a survey of problems encountered in intercomparing the lower portions (P ? 300 mb) of the models, the RSS profiles, and a recent IRIS equatorial profile. Although aerosol heating cannot be ruled out at low latitudes on Jupiter, our results indicate that it may not be required to reproduce the Voyager 1 RSS profiles. On the other hand, heating by aerosols or some other absorber seems necessary in order to match the high-latitude Voyager 2 RSS temperature profile. The Saturn models are relatively simple and in good-to-excellent agreement with the Voyager 2 RSS profiles at all levels. Our comparisons indicate that aerosol heating played a minor role in Saturn's midlatitude stratospheric energy balance at the time of the Voyager 2 encounter. These models, however, may need to be reassessed once the hydrocarbon concentrations have been more precisely determined.     

Dynamical objectives of observation of mutual events

Recently the motion of the main satellites of Jupiter, Saturn and Uranus have been modelled in order to get accurate ephemerides. These models have been fitted over a large amount of observations. Among these ones, the positions issued from the observations of mutual events are the most accurate. We can then expect to obtain a new kind of dynamical informations directly linked to planetological questions. We have to determine what information is used in these observations to get the still unknown dynamical parameters. We look after these questions especially in the Jovian and Saturnian systems.     

The atmospheric composition and structure of Jupiter and Saturn from ISO observations: a preliminary review

Infrared spectra of Jupiter and Saturn have been recorded with the two spectrometers of the Infrared Space Observatory (ISO) in 1995–1998, in the 2.3–180 μm range. Both the grating modes (R=150–2000) and the Fabry-Pérot modes (R=8000–30,000) of the two instruments were used. The main results of these observations are (1) the detection of water vapour in the deep troposphere of Saturn; (2) the detection of new hydrocarbons (CH₃C₂H, C₄H₂, C₆H₆, CH₃) in Saturn’s stratosphere; (3) the detection of water vapour and carbon dioxide in the stratospheres of Jupiter and Saturn; (4) a new determination of the D/H ratio from the detection of HD rotational lines. The origin of the external oxygen source on Jupiter and Saturn (also found in the other giant planets and Titan in comparable amounts) may be either interplanetary (micrometeoritic flux) or local (rings and/or satellites). The D/H determination in Jupiter, comparable to Saturn’s result, is in agreement with the recent measurement by the Galileo probe (Mahaffy, P.R., Donahue, T.M., Atreya, S.K., Owen, T.C., Niemann, H.B., 1998. Galileo probe measurements of D/H and ³He/⁴He in Jupiters atmosphere. Space Science Rev. 84 251–263); the D/H values on Uranus and Neptune are significantly higher, as expected from current models of planetary formation.