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Jupiter's equatorial eastward zonal flows reach wind velocities of ~100 m/s, while on Saturn they are three times as strong and extend about twice as wide in latitude, despite the two planets being overall dynamically similar. Recent gravity measurements obtained by the Juno and Cassini spacecraft uncovered that the depth of zonal flows on Saturn is about three times greater than on Jupiter. Here we show, using 3D deep convection simulations, that the atmospheric depth is the determining factor controlling both the strength and latitudinal extent of the equatorial zonal flows, consistent with the measurements for both planets. We show that the atmospheric depth is proportional to the convectively driven eddy momentum flux, which controls the strength of the zonal flows. These results provide a mechanistic explanation for the observed differences in the equatorial regions of Jupiter and Saturn, and offer new understandings about the dynamics of gas giants beyond the Solar System., Comment: 16 pages, 4 figures

NASA's Juno mission provided exquisite measurements of Jupiter's gravity field that together with the Galileo entry probe atmospheric measurements constrains the interior structure of the giant planet. Inferring its interior structure range remains a challenging inverse problem requiring a computationally intensive search of combinations of various planetary properties, such as the cloud-level temperature, composition, and core features, requiring the computation of ~10^9 interior models. We propose an efficient deep neural network (DNN) model to generate high-precision wide-ranged interior models based on the very accurate but computationally demanding concentric MacLaurin spheroid (CMS) method. We trained a sharing-based DNN with a large set of CMS results for a four-layer interior model of Jupiter, including a dilute core, to accurately predict the gravity moments and mass, given a combination of interior features. We evaluated the performance of the trained DNN (NeuralCMS) to inspect its predictive limitations. NeuralCMS shows very good performance in predicting the gravity moments, with errors comparable with the uncertainty due to differential rotation, and a very accurate mass prediction. This allowed us to perform a broad parameter space search by computing only ~10^4 actual CMS interior models, resulting in a large sample of plausible interior structures, and reducing the computation time by a factor of 10^5. Moreover, we used a DNN explainability algorithm to analyze the impact of the parameters setting the interior model on the predicted observables, providing information on their nonlinear relation., Comment: 8 pages, 6 figures, 4 tables, accepted for publication in A&A

Jupiter's atmosphere comprises several dynamical regimes: the equatorial eastward flows and surrounding retrograde jets; the midlatitudes, with the eddy-driven, alternating jet-streams and meridional circulation cells; and the jet-free turbulent polar region. Despite intensive research conducted on each of these dynamical regimes over the past decades, they remain only partially understood. Saturn's atmosphere also encompasses similar distinguishable regimes, but observational evidence for midlatitude deep meridional cells is lacking. Models offer a variety of explanations for each of these regions, but only a few are capable of simulating more than one of the regimes at once. This study presents new numerical simulations using a 3D deep anelastic model that can reproduce the equatorial flows as well as the midlatitudinal pattern of the mostly barotropic, alternating eddy-driven jets and the meridional circulation cells accompanying them. These simulations are consistent with recent Juno mission gravity and microwave data. We find that the vertical eddy momentum fluxes are as important as the meridional eddy momentum fluxes, which drive the midlatitudinal circulation on Earth. In addition, we discuss the parameters controlling the number of midlatitudinal jets/cells, their extent, strength, and location. We identify the strong relationship between meridional circulation and the zonal jets in a deep convection setup, and analyze the mechanism responsible for their generation and maintenance. The analysis presented here provides another step in the ongoing pursuit of understanding the deep atmospheres of gas giants., Comment: 14 pages, 7 figures

The shape of the two gas giants, Jupiter and Saturn, is determined primarily by their rotation rate, and interior density distribution. It is also affected by their zonal winds, causing an anomaly of O(10 km) at low latitudes. However, uncertainties in the observed cloud-level wind and the polar radius, translate to an uncertainty in the shape with the same order of magnitude. The Juno (Jupiter) and Cassini (Saturn) missions gave unprecedented accurate gravity measurements, constraining better the uncertainty in the wind structure. Using an accurate shape calculation, and a joint optimization, given both gravity and radio-occultation measurements, we calculate the possible range of dynamical height for both planets. We find that for Saturn there is an excellent match to the radio-occultation measurements, while at Jupiter such a match is not achieved. This may point to deviations from a barotropic flow above the cloud level, which might be tested with the forthcoming radio-occultation measurements by Juno.

ESA's Jupiter Icy Moons Explorer (JUICE) will provide a detailed investigation of the Jovian system in the 2030s, combining a suite of state-of-the-art instruments with an orbital tour tailored to maximise observing opportunities. We review the Jupiter science enabled by the JUICE mission, building on the legacy of discoveries from the Galileo, Cassini, and Juno missions, alongside ground- and space-based observatories. We focus on remote sensing of the climate, meteorology, and chemistry of the atmosphere and auroras from the cloud-forming weather layer, through the upper troposphere, into the stratosphere and ionosphere. The Jupiter orbital tour provides a wealth of opportunities for atmospheric and auroral science: global perspectives with its near-equatorial and inclined phases, sampling all phase angles from dayside to nightside, and investigating phenomena evolving on timescales from minutes to months. The remote sensing payload spans far-UV spectroscopy (50-210 nm), visible imaging (340-1080 nm), visible/near-infrared spectroscopy (0.49-5.56 $\mu$m), and sub-millimetre sounding (near 530-625\,GHz and 1067-1275\,GHz). This is coupled to radio, stellar, and solar occultation opportunities to explore the atmosphere at high vertical resolution; and radio and plasma wave measurements of electric discharges in the Jovian atmosphere and auroras. Cross-disciplinary scientific investigations enable JUICE to explore coupling processes in giant planet atmospheres, to show how the atmosphere is connected to (i) the deep circulation and composition of the hydrogen-dominated interior; and (ii) to the currents and charged particle environments of the external magnetosphere. JUICE will provide a comprehensive characterisation of the atmosphere and auroras of this archetypal giant planet., Comment: 83 pages, 24 figures, accepted to Space Science Reviews special issue on ESA's JUICE mission

Jupiter's atmosphere is dominated by multiple jet streams which are strongly tied to its 3D atmospheric circulation. Lacking a rigid bottom boundary, several models exist for how the meridional circulation extends into the planetary interior. Here we show, collecting evidence from multiple instruments of the Juno mission, the existence of mid-latitudinal meridional circulation cells which are driven by turbulence, similar to the Ferrel cells on Earth. Different than Earth, which contains only one such cell in each hemisphere, the larger, faster rotating Jupiter can incorporate multiple cells. The cells form regions of upwelling and downwelling, which we show are clearly evident in Juno's microwave data between latitude 60S and 60N. The existence of these cells is confirmed by reproducing the ammonia observations using a simplistic model. This study solves a long-standing puzzle regarding the nature of Jupiter's sub-cloud dynamics and provides evidence for 8 cells in each Jovian hemisphere., Comment: 13 pages, 5 figures, Supporting information. Accepted to Geophysical Research Letters

During the past few years, both the Cassini mission at Saturn and the Juno mission at Jupiter, provided measurements with unprecedented accuracy of the gravity and magnetic fields of the two gas giants. Using the gravity measurements, it was found that the strong zonal flows observed at the cloud-level of the gas giants are likely to extend thousands of kilometers deep into the planetary interior. However, the gravity measurements alone, which are by definition an integrative measure of mass, cannot constrain with high certainty the exact vertical structure of the flow. Taking into account the recent Cassini magnetic field measurements of Saturn, and past secular variations of Jupiter's magnetic field, we obtain an additional physical constraint on the vertical decay profile of the observed zonal flows on these planets. Our combined gravity-magnetic analysis reveals that the cloud-level winds on Saturn (Jupiter) extend with very little decay, i.e., barotropically, down to a depth of around 7,000~km (2,000~km) and then decay rapidly in the semiconducting region, so that within the next 1,000 km (600~km) their value reduces to about 1\% of that at the cloud-level. These results indicate that there is no significant mechanism acting to decay the flow in the outer neutral region, and that the interaction with the magnetic field in the semiconducting region might play a central role in the decay of the flows.

The asymmetric gravity field measured by the Juno spacecraft allowed estimation of the depth of Jupiter's zonal jets, showing that the winds extend approximately $3000$ km beneath the cloud-level. This estimate was based on an analysis using a combination of all measured odd gravity harmonics $J_{3}$, $J_{5}$, $J_{7}$, and $J_{9}$, but the wind profile dependence on each of them separately has not been investigated. Furthermore, these calculations assumed the meridional profile of the cloud-level wind extends to depth. However, it is possible that the interior jet profile varies from that of the cloud-level as hinted by the Juno microwave measurement that find a smoother nadir brightness temperature profile at depth compared to the cloud-level. Here we analyze in detail the possible meridional and vertical structure of Jupiter's deep jet-streams. We find that each odd gravity harmonic constrains the flow at a different depth, with $J_{3}$ being the most dominant at depths below $3000$ km, $J_{5}$ being the most restrictive overall, and $J_{9}$ not constraining the flow at all if the other odd harmonics are within the measurement range. Interior flow profiles constructed from perturbations to the cloud-level winds allow a more extensive range of vertical wind profiles, yet when the profiles differ substantially from the cloud-level, the ability to match the gravity data reduces significantly. Overall, we find that while interior wind profiles that do not resemble the cloud-level are possible, they are statistically unlikely. However, slightly smoother profiles, which resemble the Juno's microwave radiometer temperature profile at depth, are still compatible with the gravity measurements., Comment: 17 pages, 8 figures, In review (JGR planets)

The nature and structure of the observed east-west flows on Jupiter and Saturn has been one of the longest-lasting mysteries in planetary science. This mystery has been recently unraveled due to the accurate gravity measurements provided by the Juno mission to Jupiter and the Grand Finale of the Cassini mission to Saturn. These two experiments, which coincidentally happened around the same time, allowed determination of the vertical and meridional profiles of the zonal flows on both planets. This paper reviews the topic of zonal jets on the gas giants in light of the new data from these two experiments. The gravity measurements not only allow the depth of the jets to be constrained, yielding the inference that the jets extend roughly 3000 and 9000 km below the observed clouds on Jupiter and Saturn, respectively, but also provide insights into the mechanisms controlling these zonal flows. Specifically, for both planets this depth corresponds to the depth where electrical conductivity is within an order of magnitude of 1 S/m, implying that the magnetic field likely plays a key role in damping the zonal flows., Comment: Submitted to Space Science Reviews. Part of ISSI special collection on Diversity of Atmospheres

Jupiter's internal flow structure is still not fully known, but can be now better constrained due to Juno's high-precision measurements. The recently published gravity and magnetic field measurements have led to new information regarding the planet and its internal flows, and future magnetic measurements will allow taking another step in resolving this puzzle. In this study, we propose a new method to better constrain Jupiter's internal flow field using the Juno gravity measurements combined with the expected measurements of magnetic secular variation. Based on a combination of hydrodynamical and magnetic field considerations we show that an optimized vertical profile of the zonal flows that fits both measurements can be obtained. Incorporating the magnetic field effects on the flow better constraints the flow decay profile. This will allow getting closer to answering the long-lived question regarding the depth and nature of the flows on Jupiter., Comment: 11 pages, 5 figures, accepted to Astrophysical Journal Letters

One of Jupiter's most prominent atmospheric features, the Great Red Spot (GRS), has been observed for more than two centuries, yet little is known about its structure and dynamics below its observed cloud-level. While its anticyclonic vortex appearance suggests it might be a shallow weather-layer feature, the very long time span for which it was observed implies it is likely deeply rooted, otherwise it would have been sheared apart by Jupiter's turbulent atmosphere. Determining the GRS depth will shed light not only on the processes governing the GRS, but on the dynamics of Jupiter's atmosphere as a whole. The Juno mission single flyby over the GRS (PJ7) discovered using microwave radiometer measurements that the GRS is at least a couple hundred kilometers deep (Li et al. 2017). The next flybys over the GRS (PJ18 and PJ21), will allow high-precision gravity measurements that can be used to estimate how deep the GRS winds penetrate below the cloud-level. Here we propose a novel method to determine the depth of the GRS based on the new gravity measurements and a Slepian function approach that enables an effective representation of the wind-induced spatially-confined gravity signal, and an efficient determination of the GRS depth given the limited measurements. We show that with this method the gravity signal of the GRS should be detectable for wind depths deeper than 300 kilometers, with reasonable uncertainties that depend on depth (e.g., $\pm$100km for a GRS depth of 1000km).

Deciphering the flow below the cloud-level of Jupiter remains a critical milestone in understanding Jupiter's internal structure and dynamics. The expected high-precision Juno measurements of both the gravity field and the magnetic field might help to reach this goal. Here we propose a method that combines both fields to constrain the depth dependent flow field inside Jupiter. This method is based on a mean-field electrodynamic balance that relates the flow field to the anomalous magnetic field, and geostrophic balance that relates the flow field to the anomalous gravity field. We find that the flow field has two distinct regions of influence - an upper region in which the flow affects mostly the gravity field, and a lower region in which the flow affects mostly the magnetic field. An optimization procedure allows to reach a unified flow structure that is consistent with both the gravity and the magnetic fields.

How deep do Saturn's zonal winds penetrate below the cloud-level has been a decades-long question, with important implications not only for the atmospheric dynamics, but also for the interior density structure, composition, magnetic field and core mass. The Cassini Grand Finale gravity experiment enables answering this question for the first time, with the premise that the planet's gravity harmonics are affected not only by the rigid body density structure but also by its flow field. Using a wide range of rigid body interior models and an adjoint based thermal wind balance, we calculate the optimal flow structure below the cloud-level and its depth. We find that with a wind profile, largely consistent with the observed winds, when extended to a depth of around 8,800 km, all the gravity harmonics measured by Cassini are explained. This solution is in agreement with considerations of angular momentum conservation, and is consistent with magnetohydrodynamics constraints.

Observations of the flow on Jupiter exists essentially only for the cloud-level, which is dominated by strong east-west jet-streams. These have been suggested to result from dynamics in a superficial thin weather-layer, or alternatively be a manifestation of deep interior cylindrical flows. However, it is possible that the observed winds are indeed superficial, yet there exists deep flow that is completely decoupled from it. To date, all models linking the wind, via the induced density anomalies, to the gravity field, to be measured by Juno, consider only flow that is a projection of the observed could-level wind. Here we explore the possibility of complex wind dynamics that include both the shallow weather-layer wind, and a deep flow that is decoupled from the flow above it. The upper flow is based on the observed cloud-level flow and is set to decay with depth. The deep flow is constructed to produce cylindrical structures with variable width and magnitude, thus allowing for a wide range of possible scenarios for the unknown deep flow. The combined flow is then related to the density anomalies and gravitational moments via a dynamical model. An adjoint inverse model is used for optimizing the parameters controlling the setup of the deep and surface-bound flows, so that these flows can be reconstructed given a gravity field. We show that the model can be used for examination of various scenarios, including cases in which the deep flow is dominating over the surface wind. We discuss extensively the uncertainties associated with the model solution. The flexibility of the adjoint method allows for a wide range of dynamical setups, so that when new observations and physical understanding will arise, these constraints could be easily implemented and used to better decipher Jupiter flow dynamics., Comment: Submitted to Icarus

The nature of the flow below the cloud level on Jupiter and Saturn is still unknown. Relating the flow on these planets to perturbations in their density field is key to the analysis of the gravity measurements expected from both the Juno (Jupiter) and Cassini (Saturn) spacecrafts during 2016-17. Both missions will provide latitude-dependent gravity fields, which in principle could be inverted to calculate the vertical structure of the observed cloud-level zonal flow on these planets. Theories to date connecting the gravity field and the flow structure have been limited to potential theories under a barotropic assumption, or estimates based on thermal wind balance that allow analyzing baroclinic wind structures, but have made simplifying assumptions. Those include the effects of the deviations from spherical symmetry, the centrifugal force due to density perturbations, and self-gravitational effects of the density perturbations. Recent studies attempted to include some effects but not in a self-consistent manner. The present study introduces such a self-consistent perturbation approach to the thermal wind balance that incorporates all physical effects, and applies it to several example wind structures, both barotropic and baroclinic. The contribution of each term is analyzed, and the results are compared in the barotropic limit to those of potential theory. It is found that the dominant balance involves the original simplified thermal wind approach. This balance produces a good order-of-magnitude estimate of the gravitational moments, and is able, therefore, to address the order one question of how deep the flows are given measurements of gravitational moments. The additional terms are significantly smaller and none of these terms is dominant, so any approximation attempting to improve over the simplified thermal wind approach needs to include all other terms., Comment: Journal of Fluid Mechanics - in revision - August 2016

During 2016-17 the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. This data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus allowing only calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model, is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, taking into account also measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-midlatitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths, therefore we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini.

The alignment of Saturn's magnetic pole with its rotation axis precludes the use of magnetic field measurements to determine its rotation period. The period was previously determined from radio measurements by the Voyager spacecraft to be 10h 39m 22.4s. When the Cassini spacecraft measured a period of 10h 47m 6s, which was additionally found to change between sequential measurements, it became clear that the radio period could not be used to determine the bulk planetary rotation period. Estimates based upon Saturn's measured wind fields have increased the uncertainty even more, giving numbers smaller than the Voyager rotation period, and at present Saturn's rotation period is thought to be between 10h 32m and 10h 47m, which is unsatisfactory for such a fundamental property. Here we report a period of 10h 32m 45s +- 46s, based upon an optimization approach using Saturn's measured gravitational field and limits on the observed shape and possible internal density profiles. Moreover, even when solely using the constraints from its gravitational field, the rotation period can be inferred with a precision of several minutes. To validate our method, we applied the same procedure to Jupiter and correctly recovered its well-known rotation period., Comment: Accepted for publication in Nature, published online on March 25, 2015 Includes methods and supplementary figures

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