The interior structure of Saturn, the depth of its winds, and the mass and age of its rings constrain its formation and evolution. In the final phase of the Cassini mission, the spacecraft dived ...between the planet and its innermost ring, at altitudes of 2600 to 3900 kilometers above the cloud tops. During six of these crossings, a radio link with Earth was monitored to determine the gravitational field of the planet and the mass of its rings. We find that Saturn's gravity deviates from theoretical expectations and requires differential rotation of the atmosphere extending to a depth of at least 9000 kilometers. The total mass of the rings is (1.54 ± 0.49) × 10
kilograms (0.41 ± 0.13 times that of the moon Mimas), indicating that the rings may have formed 10
to 10
years ago.
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 optimization for the flow field using thermal wind balance, we calculate the 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.
Plain Language Summary
Observations show strong east‐west flows at the cloud level of Saturn. These winds are strongest at the equatorial regions, reaching up to 400 m/s, about 4 times stronger than tornado strength winds on Earth. Yet until now we had no knowledge on how deep these winds penetrate into the interior of the gas giant. The gravity experiment executed during the Grand Finale stage (May–August 2017) of the NASA Cassini mission helps answering this question. It is well established that any large‐scale motion of the fluid would have a signature in the density distribution and therefore in the planet gravity field. If we can estimate the internal structure and shape of the planet, we might be able to decipher the depth of the winds from its signal in the gravity measurements. Moreover, the rigid‐body and flow contribution to gravity field are entangled together, therefore it is necessary to use a wide range of rigid‐body models in order to define the wind‐induced gravity signal. In this work we propose a solution to the problem. We find that the gravity measurements can be explained with a flow pattern, similar to that observed at the cloud level, penetrating to depths of more than 8,000 km into the planet interior. This has important implications not only for the atmospheric dynamics but also for the interior density structure, composition, magnetic field, and core mass.
Key Points
Cassini gravity measurements point to deep differential flows within Saturn
Using a wide range of rigid body internal structure models, the required wind‐induced gravity signal is defined
With a conservatively modified cloud‐level wind and an optimized vertical profile, extended to a depth of 8,800km, all gravity measurements are explained
The Juno spacecraft reached the mid‐point of its nominal mission in December 2018, after completing 17 perijove passes. Ten of these were dedicated to the determination of the gravity field of the ...planet, with the aim of constraining its interior structure. We provide an update on Jupiter's gravity field, its tidal response and spin axis motion over time. The analysis of the Doppler data collected during the perijove passes hints to a non‐static and/or non‐axially symmetric field, possibly related to several different physical mechanisms, such as normal modes or localized atmospheric or deeply‐rooted dynamics.
Plain Language Summary
Jupiter's gravity field has been updated with the use of Juno's data collected up to the mid‐point of its mission. The field is largely symmetric about the rotation axis, and shows conspicuous north‐south asymmetry. Possible non‐static and/or non‐axially symmetric field is compatible with the data.
Key Points
Juno updates Jupiter's gravity field halfway through its mission, revealing a largely axially symmetric, north‐south asymmetric field
Hints to a non‐static and/or non‐axially symmetric field, possibly related to several different physical mechanisms, appear in the data
The tidal response is evaluated and compared to interior model predictions
The combination of the Doppler data from the first two Juno science orbits provides an improved estimate of the gravity field of Jupiter, crucial for interior modeling of giant planets. The ...low‐degree spherical harmonic coefficients, especially J4 and J6, are determined with accuracies better than previously published by a factor of 5 or more. In addition, the independent estimates of the Jovian gravity field, obtained by the orbits separately, agree within uncertainties, pointing to a good stability of the solution. The degree 2 sectoral and tesseral coefficients, C2,1, S2,1, C2,2, and S2,2, were determined to be statistically zero as expected for a fluid planet in equilibrium.
Key Points
The Jupiter gravity field has been evaluated for the first two Juno orbits
The zonal harmonics J4 and J6 improve over previous results by factors of 5 and 22, respectively, providing strong constraints on Jupiter interior models
The gravity harmonics of a fluid, rotating planet can be decomposed into static components arising from solid-body rotation and dynamic components arising from flows. In the absence of internal ...dynamics, the gravity field is axially and hemispherically symmetric and is dominated by even zonal gravity harmonics J
that are approximately proportional to q
, where q is the ratio between centrifugal acceleration and gravity at the planet's equator. Any asymmetry in the gravity field is attributed to differential rotation and deep atmospheric flows. The odd harmonics, J
, J
, J
, J
and higher, are a measure of the depth of the winds in the different zones of the atmosphere. Here we report measurements of Jupiter's gravity harmonics (both even and odd) through precise Doppler tracking of the Juno spacecraft in its polar orbit around Jupiter. We find a north-south asymmetry, which is a signature of atmospheric and interior flows. Analysis of the harmonics, described in two accompanying papers, provides the vertical profile of the winds and precise constraints for the depth of Jupiter's dynamical atmosphere.
Jupiter's atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant's interior has been ...unknown, limiting our ability to probe the structure and composition of the planet. The discovery by the Juno spacecraft that Jupiter's gravity field is north-south asymmetric and the determination of its non-zero odd gravitational harmonics J
, J
, J
and J
demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops. Here we report an analysis of Jupiter's even gravitational harmonics J
, J
, J
and J
as observed by Juno and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.
The depth to which Jupiter's observed east-west jet streams extend has been a long-standing question. Resolving this puzzle has been a primary goal for the Juno spacecraft, which has been in orbit ...around the gas giant since July 2016. Juno's gravitational measurements have revealed that Jupiter's gravitational field is north-south asymmetric, which is a signature of the planet's atmospheric and interior flows. Here we report that the measured odd gravitational harmonics J
, J
, J
and J
indicate that the observed jet streams, as they appear at the cloud level, extend down to depths of thousands of kilometres beneath the cloud level, probably to the region of magnetic dissipation at a depth of about 3,000 kilometres. By inverting the measured gravity values into a wind field, we calculate the most likely vertical profile of the deep atmospheric and interior flow, and the latitudinal dependence of its depth. Furthermore, the even gravity harmonics J
and J
resulting from this flow profile also match the measurements, when taking into account the contribution of the interior structure. These results indicate that the mass of the dynamical atmosphere is about one per cent of Jupiter's total mass.
On 27 August 2016, the Juno spacecraft acquired science observations of Jupiter, passing less than 5000 kilometers above the equatorial cloud tops. Images of Jupiter's poles show a chaotic scene, ...unlike Saturn's poles. Microwave sounding reveals weather features at pressures deeper than 100 bars, dominated by an ammonia-rich, narrow low-latitude plume resembling a deeper, wider version of Earth's Hadley cell. Near-infrared mapping reveals the relative humidity within prominent downwelling regions. Juno's measured gravity field differs substantially from the last available estimate and is one order of magnitude more precise. This has implications for the distribution of heavy elements in the interior, including the existence and mass of Jupiter's core. The observed magnetic field exhibits smaller spatial variations than expected, indicative of a rich harmonic content.
The Diffused Vortex Hydrodynamics (DVH) is a Vortex Particle Method widely validated in the last decade. This numerical approach allows cost-effective simulations of viscous flows past bodies at ...moderate and high Reynolds numbers, by taking into account only the rotational part of the flow field. In the present work a novel multi-resolution technique is presented in order to limit the number of particles in the computational domain, further improving the solver efficiency. The proposed technique preserves the total circulation and uses the (Benson et al., 1989) deterministic algorithm to regularize the particle spatial distribution during the diffusion step. Simulations of the planar flow past five cylindrical sections at Re=10,000 are discussed: flat plate, triangle, square, circular cylinder and a symmetrical airfoil. Although the simulations are carried out in a two-dimensional framework, complex vorticity patterns develop because of the flow separation and the Reynolds number considered. Comparisons with a Finite Volume solver are carried out and discussed, such highlighting the advantages of the present numerical approach.
•A multi-resolution algorithm for the DVH method has been developed.•Long wakes can be accurately simulated limiting the computational resources.•Comparisons with a Finite Volume approach are offered.•Viscous flows past five geometries at Reynolds number 10,000 are discussed.•The capabilities of the present approach are highlighted.
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