Modeling of Atmospheric Convection with Phase Changes

Turbulent convection in the atmosphere is characterized by phase changes of water and latent heat release, and may organize itself on multiple length and time scales. Under the simplifying assumptions of a Boussinesq dynamical core and asymptotically fast cloud microphysics, the possibility for intermediate-scale convective organization is explored numerically using the test case of a tropical squall line. Adding the constraint of strong rotation, a large-scale, precipitating quasi-geostrophic (PQG) model is derived, analogous to the dry quasi-geostrophic equations, which have been foundational for turbulence theory in the mid-latitude atmosphere. Theoretical and numerical results from the PQG model are discussed, e.g., (i) the existence of exact solutions that are propagating fronts with discontinuous temperature, winds and total water, and (ii) dependence on rainfall speed of the spectral scaling for the variance of rainwater.