The Interplay between Zonal Winds and Magnetic Fields in Uranus and Neptune

Uranus and Neptune exhibit strong zonal winds reaching up to 200 m/s and 400 m/s relative to their assumed bulk rotation, respectively. Furthermore, recent studies show that planetary ices such as water and ammonia become ionically conducting under conditions present in the ice giants. With rapidly increasing electrical conductivity, zonal flows inevitably couple to the background magnetic field, inducing electrical currents and magnetic field perturbations spatially correlated with zonal flows. Induced currents generate Ohmic dissipation, which can be used to constrain the depth of the zonal winds via the energy/entropy flux throughout the planetary interior. Constraining the zonal wind decay can be used to estimate the strength of magnetic field perturbations. Flows coupled to the background magnetic field induce poloidal and toroidal field perturbations through the ω-effect. Toroidal perturbations are expected to diffuse downwards and produce poloidal fields through turbulent convection, which are comparable to those induced by the ω-effect.We present a method for calculating electrical conductivity profiles of ionically conducting H-He-H₂O mixtures using results from ab-initio simulations. We then apply this prescription on several published interior structure models of Uranus and Neptune, assuming the heavy elements are represented by water. Structure models with higher water abundances (hot models) also have larger electrical conductivity values and their zonal winds need to decay faster compared to colder models. Using our solutions for the zonal wind decay, we estimate the strength of magnetic field perturbations induced by the zonal flows. We find that colder models could potentially have poloidal field perturbations that reach up to O(0.1) of the background magnetic field in the most extreme case. The possible existence of poloidal field perturbations spatially correlated with zonal flows could be used to constrain the interior structure of Uranus and Neptune.