Heat-Flux Limited Cloud Activity and Vertical Mixing in Giant Planet Atmospheres with an Application to Uranus and Neptune

Storms operated by moist convection and the condensation of $\rm CH_{4}$ or $\rm H_{2}S$ have been observed on Uranus and Neptune. However, the mechanism of cloud formation, thermal structure, and mixing efficiency of ice giant weather layers remains unclear. In this paper, we show that moist convection is limited by heat transport on giant planets, especially on ice giants where planetary heat flux is weak. Latent heat associated with condensation and evaporation can efficiently bring heat across the weather layer through precipitations. This effect was usually neglected in previous studies without a complete hydrological cycle. We first derive analytical theories and show the upper limit of cloud density is determined by the planetary heat flux and microphysics of clouds but independent of the atmospheric composition. The eddy diffusivity of moisture depends on the heat fluxes, atmospheric composition, and gravity of the planet but is not directly related to cloud microphysics. We then conduct convection- and cloud-resolving simulations with SNAP to validate our analytical theory. The simulated cloud density and eddy diffusivity are smaller than the results acquired from the equilibrium cloud condensation model and mixing length theory by several orders of magnitude but consistent with our analytical solutions. Meanwhile, the mass-loading effect of $\rm CH_{4}$ and $\rm H_{2}S$ leads to superadiabatic and stable weather layers. Our simulations produced three cloud layers that are qualitatively similar to recent observations. This study has important implications for cloud formation and eddy mixing in giant planet atmospheres in general and observations for future space missions and ground-based telescopes.