Moist thermal wind balance between zonal jets and the latitudinal methane gradient on Uranus and Neptune

The atmospheric circulation of Uranus and Neptune is particularly intense and shows strong similarities between the two planets. It is characterised by a retrograde jet (westerly winds) at the equator, reaching speeds of up to 400 m/s on Neptune, as well as prograde jets (easterly winds) located at the mid-latitudes of each hemisphere, with speeds of up to 250 m/s on both planets [1,2]. The origin of these jets remains poorly understood.

 

More recently, observations have revealed a latitudinal gradient in methane within the tropospheres of both planets [3,4]. The molar fraction of methane varies approximately between 1% and 5% on Uranus and between 2% and 6% on Neptune, from the poles to the equator. Due to its high molecular weight relative to that of hydrogen and helium, its variation in mass fraction reaches up to 15–20% between the poles and the equator for both planets. This gradient therefore induces significant variations in the average molecular weight. The wet thermal wind equation therefore predicts significant shear associated with this latitudinal gradient, suggesting that the prograde jets could be in dynamic equilibrium with this methane distribution.

 

To investigate the effect of the latitudinal methane gradient on the general circulation of ice giants, numerical simulations at a resolution of 2° were carried out between 15 bar and 0.01 mbar using the DYNAMICO dynamical core [5], coupled with a seasonal radiative-convective model previously applied to these planets [6]. To maintain this latitudinal gradient, the methane concentration is relaxed towards the values imposed at pressures above 2.5 bar. Variations in average molecular weight were taken into account in the dynamic solver. Thus, the potential temperature used in the thermodynamic equation was replaced by the potential enthalpy. The effects of molecular mass were also incorporated into the dry and moist convective adjustments. For dry convection, the potential temperature was replaced by a local adiabatic temperature consistent with variations in molecular mass as a criterion for convective instability. In the case of moist convection, the critical mixing ratio controls the inhibition of convection. In both adjustment schemes, the enthalpy conservation equation has been reformulated and condensates have been explicitly accounted for. Finally, the condensation scheme, comprising condensation, re-evaporation and mass redistribution, has also been modified to include effects related to variations in molecular weight.

 

According to our GCM, an intense prograde jet is simulated in each hemisphere at mid-latitudes for both planets. Their intensity varies between 200 m/s and 300 m/s and the eastward winds extend from the poles to low latitudes, similar to what was observed during the Voyager 2 flyby. These two jets also extend to high altitudes, which is consistent with recent observations. As for the retrograde jet observed at the equator, our simulations produce a jet twice as intense as the one observed on Uranus, and half as intense as the observed one on Neptune. When the methane gradient is excluded, the prograde jets reach only 30 m/s; and when the relaxation towards this gradient is halted during the simulation, the methane gradient does not persist and becomes homogeneous from the poles to the equator. Thus, an unknown mechanism is required to maintain this latitudinal gradient. There is also a discrepancy between the latitudinal position of the maximum of the prograde jet and the region where the latitudinal methane gradient is most pronounced, indicating a a momentum convergence linked to wave dissipation at these latitudes.

 

The tropospheric thermal structure is also affected by the presence of this gradient, where local maxima and minima develop on either side of the jets. At lower pressures, seasonal thermal variations are greatly attenuated by atmospheric dynamics. With regard to the meridional circulation, the Transformed eulerian formalism has been modified to take into account the variation in molar mass in the calculation of the mass stream function. We will present the main features of the resulting meridional circulation and how it differs from the one suggested from observations

 

References

[1] Allison et al. (1991), Uranus atmospheric dynamics and circulation. 253–295.

[2] Limaye et al. (1991), Journal of Geophysics Research, 96:18941–18960.

[3] Karkoschka and Tomasko (2009), Icarus, 202(1):287– 309.

[4] Karkoschka and Tomasko (2011), Icarus, 211(1):780– 797.

[5] Dubos et al. (2015), Geoscientific Model Development, 8(10):3131– 3150.

[6] Milcareck et al (2024), Astronomy & Astrophysics, 686:A303.