Initial investigations of precipitating quasi-geostrophic turbulence with phase changes

Asymptotic models have provided valuable insight into the atmosphere and its dynamics. Nevertheless, one shortcoming of the classic asymptotic models, such as the quasi-geostrophic (QG) equations, is that they describe a “dry” atmosphere and do not account for water vapor, clouds, and rainfall. Recently, precipitating QG (PQG) equations were derived in an asymptotic limit, starting from atmospheric equations that include changes of water between different phases (vapor, liquid, etc.). The PQG equations include Heaviside nonlinearities due to phase changes, which can potentially have a significant influence on QG turbulence. Here, simple numerical methods are presented for the PQG equations, accounting for the Heaviside nonlinearities, and an initial set of numerical experiments is conducted to probe the behavior of PQG turbulence. A two-vertical-level setup is used for an idealized vertical structure, as in the classic Phillips model. Due to phase changes and rainfall, the mid-latitude jet variability displays a variety of behaviors, including poleward propagation of the latitude of the jet. The simulations suggest a new set of phenomena that arise in QG turbulence due to phase changes, in a simplified model that is potentially amenable to mathematical analysis.