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 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 caseby-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 4 th -order Theory of Figures (ToF) 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.

Interior and Evolution of the Giant Planets

“…In both cases, it is believed that the interaction of the material in the semiconducting region with the magnetic field leads to a decay of the flows [34]. While using less accurate measurements, some estimations were made for the depth of the zonal flows and extent of differential rotation for Uranus and Neptune, which was found to extend up to approximately 0.93-0.95 of the planets' radii using their gravity constraints [35] and through the analysis of the total induced Ohmic dissipation in their deep atmospheres [36,37].…”