Three-dimensional dynamical evolution of cloud particle microphysics in sub-stellar atmospheres

Context. Understanding cloud microphysics and the evolution of cloud structures in sub-stellar atmospheres remains a key challenge in the JWST era. The abundance of new JWST data necessitates models that are suitable for coupling with large-scale simulations, such as general circulation models (GCMs), in order to fully understand and assess the complex feedback effects of clouds on the atmosphere, and their influence on observed spectral and variability characteristics. Aims. We aim to develop a two-moment, time-dependent bulk microphysical cloud model that is suitable for GCMs of sub-stellar atmospheres. Methods. We derived a set of moment equations for the particle mass distribution and developed a microphysical cloud model employing a two-moment approach. We included homogeneous nucleation, condensation, and collisional microphysical processes that evolve the moments of a particle size distribution in time. We coupled our new two-moment scheme with the Exo-FMS GCM to simulate the evolution of KCl clouds for a WISE 0359-54 Y-dwarf parameter regime, and examined the effect of cloud opacity on the atmospheric characteristics. Results. Our results show a global KCl cloud structure, with a patchy coverage at higher latitudes, as well as an equatorial belt region that shows increased particle sizes and variations in longitude. Patchy regions are long lived, being present over many rotations of the brown dwarf. Our synthetic spectra conform well with JWST observations of WISE 0359-54, but more cloud opacity is required to dampen the spectral features at wavelengths below ∼7 µm. Our GCM shows periodic and sub-rotational variability of the order of 0.5–1% in the Spitzer [3.6] and [4.5] micron bands, lower than that observed on other Y-dwarf objects. Conclusions. Our study demonstrates that the two-moment bulk cloud microphysical scheme is a highly suitable method for investigating cloud characteristics and feedback in GCMs and other large scale simulations of sub-stellar atmospheres. Split moment schemes and mixed material grains will be explored in a follow-up study.