Zonal Winds of Uranus and Neptune: Gravitational Harmonics, Dynamic Self-gravity, Shape, and Rotation

Abstract

Uranus and Neptune exhibit fast surface zonal winds that can reach up to a few hundred meters per second. Previous studies on zonal gravitational harmonics and ohmic dissipation constraints suggest that the wind speeds diminish rapidly in relatively shallow depths within the planets. Through a case-by-case comparison between the missing dynamical gravitational harmonic J 4 ′ from structure models, and with that expected from fluid perturbations, we put constraints on zonal wind decay in Uranus and Neptune. To this end, we generate polytropic empirical structure models of Uranus and Neptune using fourth-order theory of figures that leave hydrostatic J 4 as an open parameter. Allotting the missing dynamical contribution to density perturbations caused by zonal winds (and their dynamic self-gravity), we find that the maximum scale height of zonal winds are ∼2%–3% of the planetary radii for both planets. Allowing the models to have J 2 solutions in the ±5 × 10−6 range around the observed value has similar implications. The effect of self-gravity on J 4 ′ is roughly a factor of ten lower than that of zonal winds, as expected. The decay scale heights are virtually insensitive to the proposed modifications to the bulk rotation periods of Uranus and Neptune in the literature. Additionally, we find that the dynamical density perturbations due to zonal winds have a measurable impact on the shape of the planet, and could potentially be used to infer wind decay and bulk rotation period via future observations.

Uranus Orbiter and Probe: A Radio Science Investigation to Determine the Planet’s Gravity Field, Depth of the Winds, and Tidal Deformations

“…Employing a diverse set of interior models to eliminate the influence of the deep interior structure, their analysis provided evidence that the atmospheric circulation of Uranus is constrained to the initial 1000 km of the upper atmosphere. In more recent studies, Soyuer et al (2020Soyuer et al ( , 2022 obtained findings aligned with the earlier research, reinforcing the understanding that the scale height of Uranus's zonal winds does not exceed approximately 3% of the planet's mean radius. These critical insights into the zonal wind dynamics of Uranus provide valuable data for refining models and deepening our comprehension of the intricate atmospheric behavior on the ice giant.…”

The Uranus System from Occultation Observations (1977-2006): Rings, Pole Direction, Gravity Field, and Masses of Cressida, Cordelia, and Ophelia

“…Significantly, they also demonstrated that more accurate values of J 2 and J 4 can further constrain the density distribution and narrow the range of predicted solutions in J 6 , J 8 , and MoI of Uranus and Neptune. Finally, Soyuer et al (2023) conclude from model studies that the scale height of the zonal winds on Uranus is below ∼ 0.03R U (770 km), somewhat shallower than found by Kaspi et al (2013).…”