Numerical simulations help revealing the dynamics underneath the clouds of Jupiter

Since its arrival at Jupiter in 2016, NASA’s Juno spacecraft has been performing high-precision measurement of the gravity and magnetic fields. When combined with numerical simulations, they provide a unique window to the dynamics in the planet’s deep atmosphere.

0.94 r J 5 . Which physical effect could put on the brakes at this specific depth? Perhaps the magnetic forces, which were neglected in these simulations?
Like Earth, Jupiter has a global magnetic field that is produced by a dynamo process. Earth's dynamo operates in the liquid iron core, but what about Jupiter? Below about 0.9 r J , the extreme pressures squeeze the atoms so close together that hydrogen becomes metallic 7 . Above 0.9 r J , the electrical conductivity decreases rapidly in the so-called transition region and eventually becomes negligible. Since dynamo action and the magnetic Lorentz forces scale with conductivity, they are most efficiently in the inner metallic region but can be significant in the transition region. Where the Lorentz forces remain negligible in the veryouter atmosphere, the jets should retain their cylindrical geometry. Somewhere in the transition region, however, the Lorentz forces would kick in abruptly and quench the jets over a depth range of about 1000 km 8 .
To test these ideas, scientists ran a number of ambitious numerical simulations that not only model the jets but also the deeper dynamo processes. The results reveal interesting but also puzzling new aspects [9][10][11][12] . The magnetic field of Jupiter, like the field of Earth, is dominated by an axial dipole. However, the jets tend to promote magnetic field configurations with rather weak axial dipole contributions. The key to reproducing Jupiter's magnetic field therefore lies in limiting the role of the jets in the dynamo process. Rather than simply quenching the jets in the transition region, however, the simulation choses another option (Fig. 1d): the Lorentz forces push the eastward equatorial jet to the outer envelope but slow down rather than truncate the remaining jets 10,11 .
These simulations cannot exactly reproduce Jupiter's complex jet structure (Fig. 1d). They also use unrealistically high viscosities to suppress the smallest turbulent features that cannot be resolved with current computer resources. One consequence is that the zonal winds are not as dominant as on Jupiter. However, the models seem to capture the essence of the dynamo process and reproduce the very inhomogeneous field distribution that sets the magnetic fields of Jupiter and Earth apart 13 . Particularly obvious is the concentration of outward directed field (Fig. 2a,   red) in a latitudinal band between 30 and 60°north. In the southern hemisphere, a prominent patch of inward (blue) field sits just south of the equator, but overall the field seems more homogeneous than in the north. The simulation snapshot (Fig. 2b) shows very similar banded structures in the northern hemisphere 10 . The southern blue patch is missing, but similar features appear later in the simulation. The numerical models generate the Jupiter-like magnetic field in a two-stage process. A deeper primary dynamo produces the main dipole-dominated magnetic field in the metallic region. A shallower secondary dynamo operates where the equatorial jet reaches sizeable conductivities in the transition region 10,11 and generates the banded or patchy features observed at low to mid latitude. This suggests that the jets contribute to shaping the magnetic field of Jupiter. They also give rise to density difference and thus to tiny modifications of Jupiter's gravity field. Both magnetic and gravity measurements can thus potentially constrain the deeper jet structure.
Exploiting gravity and magnetic data For the first time, Juno gravity measurements are precise enough to detect the tiny signature of the deeper zonal jets. However, the interpretation is difficult. The first attempts in principle adopt the cylindrical jet geometry but report that an additional gradual decay with depth is required 14,15 : While the jets blow with up to 150 m/s at cloud level, they slow down to about 10 m/s at 0.96 r J and to 2 m/s at 0.94 r J . This is at odds with the abrupt decay expected from Lorentz forces. A comparison of the magnetic fields measured by Juno and by previous spacecrafts gives rise to further doubts: The modest variations over the 45-year time span covered by the missions indicate that the jet velocity cannot exceed 0.01 m/s at 0.94 r J 16 . Further analysis of gravity and magnetic data seem in order to resolve the contradictions.
A stable layer in the outer atmosphere of Jupiter? A recent numerical study 17 of jets in a simplified Cartesian box puts a promising new idea on the table: An additional stable layer where the density stratification tend to suppresses radial motions. Lorentz forces drive radial flows in the transition region, which are much slower than the jets and therefore normally have little effect. However, once the radial flows penetrate a stable layer and encounter the density stratification, they can promote a very effectively quenching of the jets.
The upper boundary of the stable layer should lie between 0.94 r J and 0.96 r J . Interestingly, some newer interior structure models suggest a somewhat deeper stable layer below 0.93 r J 18 . However, it remains unclear which physical mechanism could support such a layer. Helium rain, a process deemed responsible for a thick stable layer in Saturn, only happens in metallic hydrogen and thus not above 0.9 r J in Jupiter.

Conclusion
The combination of observations and numerical simulations provides a powerful tool for peering underneath the cloud deck of Jupiter. The results suggest that the fast jets are limited to the outer 4-6% in radius, assume a cylindrical geometry, and are abruptly quenched at the lower boundary, perhaps by a combination Lorentz forces and a stable layer. While first evaluations of Juno gravity data propose a more gradual quenching, the analysis is complex and ambiguous and leaves room for alternative models.
State-of-the-art numerical dynamo simulations reproduce many features of Jupiter's magnetic field and highlight the important role of the dominant equatorial jet. However, they fail in reproducing the multiple jet system. Two options for improvement are the adoption of lower viscosities and the implementation of a stable layer. Juno gravity data also indicate a higher concentration of heavy elements below perhaps 0.6 r J 18 . Future numerical studies could clarify whether such a scenario is consistent with Jupiter's magnetic field.
The simulations also suggest that Jupiter's magnetic field bears signs of zonal jet action. However, deducing the jet properties from the magnetic field structure is very challenging. Observations of magnetic field variations, on the other hand, are an established tool for accessing the dynamic in Earth's core and have already proven useful at Jupiter 16 . There is a chance that Juno will observe minor variations during its mission time. More promising data will become available when ESA's Juice spacecraft arrives at Jupiter in 2029.

Code availability
Most of the simulations discussed here were performed with the code MagIC, which is freely available at GitHub: https://github.com/magic-sph.  Fig. 2 The magnetic field of Jupiter. a Jupiter's radial surface field model JRM09 based on Juno measurements 3 . b Snapshot of the radial surface field in a Jupiter-like dynamo simulations 10 . Outgoing field is shown in yellow and red and ingoing field in blue.